LtrJir^, 


GANOT'S     PHYSICS. 


PRINTED    BY 

SPOTTISVVOODE    AND    CO.,    NEW-STREET    SQUARE. 
LONDON 


ADVERTISEMENT 

TO 

THE      TWELFTH      EDITION. 


IN  the  present  edition  the  additions  made  have  increased  by  about 
twenty-six  pages  the  size  of  the  work  as  it  stood  in  the  last  edition. 
The  new  matter  contains  also  twenty  five  additional  illustrations. 

Some  alterations  have  been  made  in  Book  I. :  in  making  these 
I  have  availed  myself  of  an  introductory  chapter  which  Prof.  Nipher,  of 
the  University  of  Missouri,  prepared  for  the  use  of  his  classes,  and 
which  he  kindly  placed  at  my  disposal. 

The  continued  favour  with  which  the  work  has  been  received, 
as  a  Text-book  for  Colleges  and  Schools,  and  also  as  a  book  of 
reference  for  the  general  reader,  renders  any  apology  for  omissions 
perhaps  unnecessary  ;  it  may,  however,  be  as  well  once  more  to 
point  out  that  the  book  is  intended  to  be  a  general  Elementary 
Treatise  on  Physics,  and  that,  while  it  accordingly  aims  at  giving  an 
account  of  the  most  important  facts  and  general  laws  of  all  branches 
of  Physics,  an  attempt  to  treat  completely  and  exhaustively  of  any  one 
branch  would  both  be  inconsistent  with  the  general  plan  of  the  book 

and  impossible  within  the  available  space. 

E.  ATKINSON. 

STAFF  COLLEGE  :  May  1886. 

219787 


EXTRACT  FROM  ADVERTISEMENT  TO    THE 
SEVENTH  EDITION. 

I  HAVE  added  an  Appendix  containing  a  series  of  numerical  problems 
and  examples  in  Physics.  This  Appendix  is  based  upon  a  similar 
one  contained  in  the  French  edition  of  the  work.  But  I  have  been 
able  to  use  only  a  small  proportion  of  the  problems  contained  in  that 
Appendix,  as  the  interest  of  the  solution  was  in  most  cases  geome- 
trical of  algebraical.  Hence  I  have  substituted  or  added  others,  which 
have  been  so  selected  as  to  involve  in  the  solution  a  knowledge  of  some 
definite  physical  principle. 

Such  an  Appendix  has  from  time  to  time  been  urged  upon  me  by 
teachers  and  others  who  use  the  work.  It  will,  I  conceive,  be  most 
useful  to  those  students  who  have  not  the  advantage  of  regular  instruc- 
tion ;  affording  to  them  a  means  of  personally  testing  their  knowledge. 
Such  a  student  should  not  aim  solely  at  getting  a  result  which  numeri- 
cally agrees  with  the  answer.  He  should  habituate  himself  to  write  out 
at  length  the  several  steps  by  which  the  result  is  obtained,  so  that  he 
may  bring  clearly  before  himself  the  physical  principles  involved  in  each 
stage.  Some  of  the  solutions  of  the  problems  are  therefore  worked  out 
at  length. 

E.  A. 


TRANSLATOR'S  PREFACE   TO  FIRST  EDITION. 


THE  Elements  de  Physique  of  Professor  GANOT,  of  which  the  present 
work  is  a  translation,  has  acquired  a  high  reputation  as  an  Introduction 
to  Physical  Science.  In  France  it  has  passed  through  Nine  large 
editions  in  little  more  than  as  many  years,  and  it  has  been  translated 
into  German  and  Spanish. 

This  reputation  it  doubtless  owes  to  the  clearness  and  conciseness 
with  which  the  principal  physical  laws  and  phenomena  are  explained, 
to  its  methodical  arrangement,  and  to  the  excellence  of  its  illustrations. 
In  undertaking  a  translation,  I  was  influenced  by  the  favourable  opinion 
which  a  previous  use  of  it  in  teaching  had  enabled  me  to  form. 

I  found  that  its  principal  defect  consisted  in  its  too  close  adaptation 
to  the  French  systems  of  instruction ;  and  accordingly,  my  chief  labour, 
beyond  that  of  mere  translation,  has  been  expended  in  making  such 
alterations  and  additions  as  might  render  it  more  useful  to  the  English 
student. 

I  have  retained  throughout  the  use  of  the  Centigrade  thermometer, 
and  in  some  cases  have  expressed  the  smaller  linear  measures  on  the 
metrical  system.  These  systems  are  now  everywhere  gaining  ground, 
and  an  apology  is  scarcely  needed  for  an  innovation  which  may  help  to 
familiarise  the  English  student  with  their  use  in  the  perusal  of  the  larger 
and  more  complete  works  on  Physical  Science  to  which  this  work  may 
serve  as  an  introduction. 


E.    A. 


ROYAL  MILITARY  COLLEGE,  SANDHURST 
1863. 


CONTENTS. 


BOOK   I. 

ON    MATTER,   FORCE,   AND   MOTION. 

CHAPTER  PAGE 

I.     GENERAL  PRINCIPLES  .          ff--\    \    .v;    '  ..        '    .  .  .          i 

II.  GENERAL  PROPERTIES  OF  BODIES      ...  .  .  .          4 

III.     ON  FORCE,  EQUILIBRIUM,  AND  MOTION       .          V         ;V'  •        .        u 

BOOK   II. 
ON   GRAVITATION   AND   MOLECULAR  ATTRACTION. 

I.  GRAVITY,  CENTRE  OF  GRAVITY,  THE  BALANCE       .  .  .        54 

II.  LAWS  OF  FALLING  BODIES.    INTENSITY  OF  TERRESTRIAL  GRAVITY. 

THE  PENDULUM    .  .'  .'  . v/    ?    .  .  .         63 

III.  MOLECULAR  FORCES    .  .  .•          ,•          .  .*         .        73 

IV.  PROPERTIES  PECULIAR  TO  SOLIDS       .  .*  .  l.!''        .         77 

BOOK   III. 
ON    LIQUIDS. 

I.     HYDROSTATICS.  .  .  ,  .  .  *  f        85 

II.  CAPILLARITY,  ENDOSMOSE,  EFFUSION,  AND  ABSORPTION    .  .113 

III.  HYDRODYNAMICS         „          •.          „  .  .  .  .       124 

BOOK   IV. 

ON     GASES. 

I.  PROPERTIES  OF  GASES.     ATMOSPHERE.     BAROMETERS         .            .132 

II.  MEASUREMENT  OF  THE  ELASTIC  FORCE  OF  GASES  .            .            .       153 

III.  PRESSURE  ON  BODIES  IN  AIR.     BALLOONS   ....       168 

IV.  APPARATUS  WHICH  DEPEND  ON  THE  PROPERTIES  OF  AIR  .  .       173 


xii  Contents. 


BOOK   V. 
ON     SOUND. 

CHAPTER  PAGE 

I.     PRODUCTION,  PROPAGATION,  AND  REFLECTION  OF  SOUND  .  192 

II.     MEASUREMENT  OF  THE  NUMBER  OF  VIBRATIONS  .            .  .  210 

III.  THE  PHYSICAL  THEORY  OF  Music              .            .            .  .  215 

IV.  VIBRATIONS  OF  STRETCHED  STRINGS,  AND  OF  COLUMNS  OF  AIR  231 
V.     VIBRATIONS  OF  RODS,  PLATES,  AND  MEMBRANES.            .  .  244 

VI.     GRAPHICAL  METHOD  OF  STUDYING  VIBRATORY  MOTIONS  .  248 


BOOK  VI. 
ON      HEAT. 

I.     PRELIMINARY  IDEAS.     THERMOMETERS     ;^iif        .  ,  r-    •.  >k  260 

II.     EXPANSION  OF  SOLIDS          .                        ,            .  .  .  275 

III.  EXPANSION  OF  LIQUIDS     j{           .            ,        -    .  •  .  .  283 

IV.  EXPANSION  AND  DENSITY  OF  GASES           .            .  .  .  289 
V.     CHANGES  OF  CONDITION.     VAPOURS       k    '/"      'V  "  '    .'  P%  298 

VI.     HYGROMETRY          ..  r.  ,        .           ,, .. .{.     .,;»r    .     ,r>t.r,  ^  ^  .  ,(  348 

VII.     CONDUCTIVITY  OF  SOLIDS,  LIQUIDS,  AND  GASES  .  7  •    ,  *••»  35^ 

VIII.     RADIATION  OF  HEAT            .            .            .            ju  ?  /••  Y  •  3^ 

IX.     CALORIMETRY            .            .            .            .        ;,  ,^    :  „  ,•  ,,..M  4°5 

X.     STEAM  ENGINES        *            .            .         ...    ;     ,  f,,  ,,  .,  .  425 

XL     SOURCES  OF  HEAT  AND  COLD         . .          .        -    .  .  -  .  440 

XII.     MECHANICAL  EQUIVALENT  OF  HEAT          *            .  .  .  455 

BOOK  VII. 
ON     LIGHT. 

I.     TRANSMISSION,  VELOCITY,  AND  INTENSITY  OF  LIGHT  .  .  462 

II.     REFLECTION  OF  LIGHT.     MIRRORS  .            .            .  ' .  474 

III.  SINGLE  REFRACTION.     LENSES         ...  .  492 

IV.  DISPERSION  AND  ACHROMATISM       .            .            .  .  .  514 

V.  OPTICAL  INSTRUMENTS         .....  ,.  538 
VI.     THE  EYE  CONSIDERED  AS  AN  OPTICAL  INSTRUMENT  .  ,   v  565 

VII.     SOURCES  OF  LIGHT.     PHOSPHORESCENCE    .            .  .,,,  *,  582 

VIII.     DOUBLE  REFRACTION.     INTERFERENCE.     POLARISATION  .  ,  586 


Contents.  xiii 


BOOK   VIII. 
ON   MAGNETISM. 

CHAPTER  PAGE 

I.  PROPERTIES  OF  MAGNETS     ......  623 

II.  TERRESTRIAL  MAGNETISM.     COMPASSES      ....  629 

III.  LAWS  OF  MAGNETIC  ATTRACTIONS  AND  REPULSIONS        .            .  642 

IV.  PROCESSES  OF  MAGNETISATION         .....  650 

BOOK   IX.     . 
ON   FRICTIONAL   ELECTRICITY. 

I.     FUNDAMENTAL  PRINCIPLES  ......  660 

II.     QUANTITATIVE  LAWS  OF  ELECTRICAL  ACTION      .            .            .  668 

III.  ACTION  OF  ELECTRIFIED  BODIES  ON  BODIES  IN  THE  NATURAL 

STATE.     INDUCED  ELECTRICITY.     ELECTRICAL  MACHINES    .  68 1 

IV.  CONDENSATION  OR  ACCUMULATION  OF  ELECTRICITY        .            .  707 

BOOK   X. 
ON   DYNAMICAL  ELECTRICITY. 

I.    VOLTAIC  PILE.     ITS  MODIFICATIONS           ....  739 

II.  DETECTION  AND  MEASUREMENT  OF  VOLTAIC  CURRENTS  .            .  759 

III.  EFFECTS  OF  THE  CURRENT  ......  772 

IV.  ELECTRODYNAMICS.     ATTRACTION  AND  REPULSION  OF  CURRENTS 

BY  CURRENTS     .            .            ...            .            .            .  808 

V.    MAGNETISATION   BY  CURRENTS.     ELECTROMAGNETS.     ELECTRIC 

TELEGRAPHS       .......  826 

VI.     VOLTAIC  INDUCTION             ......  849 

VII.     OPTICAL  EFFECTS  OF  POWERFUL  MAGNETS.     DIAMAGNETISM      .  903 
VIII.     THERMO-ELECTRIC  CURRENTS          .            .            .            .            .910 

IX.     DETERMINATION  OF  ELECTRICAL  CONSTANTS        .            .            .  922 

X.     ANIMAL  ELECTRICITY           ......  942 

ELEMENTARY  OUTLINES  OF  METEOROLOGY  AND  CLIMATOLOGY    .            .  947 

PROBLEMS  AND  EXAMPLES  IN  PHYSICS       .....  987 

INDEX  ion 


LIST  OF  TABLES. 


161 


ABSORBING  powers 
Absorption  of  gases 

heat  by  gases  . 

liquids 

-  vapours 

various 

Atmosphere,  composition  of . 

BAROMETRIC  variations 

Boiling  points 

Breaking  weight  of  substances 


CAPILLARITY  in  barometers  . 
Capillary,  constant 
Combustion,  heat  of 
Conducting   powers   of    solids   for 

heat 

liquids  for  heat 

Conductors  of  electricity        .    t  .••••• 

DENSITIES  of  gases 

vapours  .         » -'.      . 

Density  of  water  .... 
Diamagnetism       ...» 
Diathermanous  power  .         . 
Diffusion  of  solutions     .         .         . 

,,        of  heat. 
Dulong  and  Petit's  law        .         . 


PAGE 

377 
,  166 

393 

387 
389 

394 
135 

146 
317 

83 

144 
119 
448 

360 
662 

297 

347 
288 
909 
387 

122 
391 
415 


ELASTICITY 78 

Electrical  conductivity  .         .         .  932 

Electricity,  positive  and  negative  .  665 
Electromotive    force    of    different 

elements  .  .       .         .        '.         .  756 

series     .         .         .         .  744 

Endosmotic  equivalents          .          .  121 
Expansion,  coefficients  of  solids  278,  279 

liquids  .  286 

gases      .  293 

Eye,  dimensions  of        ...  567 
refractive  indices  of  media  of .  567 


FREEZING  mixtures 
Fusing  points  of  bodies 


PAGE 

GLAISHER'S  factors       .        .        .     354 
Gravity,  force  of,  at  various  places        69 


HARDNESS,  scale  of     . 

LATENT  heat,  of  evaporation 
fusion 

MAGNETIC  declination . 

. — inclination . 

Molecular  velocity  of  gases    . 


RADIATING  powers 
Radiation  of  powders    . 
Reflecting  powers 
Refraction,  angle  of  double    . 
Refractive  indices 
of  media  of  eye 


84 


.     420 

.  631 
.  637 
.  263 

378,  385 

•  397 

•  376 

•  591 
502 


SOUND,  transmission  of,  in  tubes  .  198 
Specific  gravity  of  liquids  .  .  109 
solids  .  .  107 


heat  of  solids  and  liquids 
gases 


inductive  capacities  . 


417 
687 


TANGENT  galvanometer  and  volta- 
meter, comparison  between         .     799 
Temperatures,  various  remarkable  .     274 

at  different  latitudes  . 

thermal  springs 


Tension 


measurement  of 
of  aqueous  vapo 
—  vapours  of  lie 


Thermo-electric  series 


984 
.  986 
.  294 

ur     .     309,  313 
quids          .      314 
9II 


UNDULATIONS,  length  of      .  .     586 

VELOCITY  of  sound  in  gases .  .201 

liquids  .     203 

rocks .  .     204 

solids  .     204 

Vibrations  of  musical  scale     .  .216 


LIST  OF  PLATES. 
TABLE  OF  SPECTRA     .........          Frontispiece 

COLOURED  RINGS  PRODUCED  BY  POLARISED  LIGHT  IN  DOUBLE  REFRACT- 
ING CRYSTALS To  face  p.  611 

LINES  OF  EQUAL  MAGNETIC  VARIATION  FOR  THE  YEAR  1882  .  .  .  632 
LINES  OF  EQUAL  MAGNETIC  DIP  FOR  THE  YEAR  1882  ....  637 
LINES  OF  EQUAL  HORIZONTAL  FORCE  FOR  THE  YEAR  1882  .  .  .  640 


Inch 


|2          |3          [4          15          !6          17          |8          19      10 

Millimetres  Centimetres 


The  area  of  the  figure  within  the  heavy  lines  is 
that  of  a  square  decimetre.  A  cube,  one  of  whose 
sides  is  this  area,  is  a  cubic  decimetre  or  litre.  A 
litre  of  water  at  the  temperature  of  4°  C.  weighs  a 
kilogramme.  A  litre  of  air  at  o°  C.  and  76omm 
pressure  weighs  1*293  gramme. 

A  litre  is  1-^6  pint ;  a  pint  is  0-568  of  a  litre. 

The  smaller  figures  in  dotted  lines  represent  the 
areas  of  a  square  centimetre  and  of  a  square  inch. 

A  cubic  centimetre  of  water  at  4°  C.  weighs  a 
gramme. 


Square  Inch 


Square  : 
Centi-  ; 
metre  '• 


Inches  Feet 

Millimetre             ....          0*03937  0*003281 

Centimetre 0-39371  0-032819 

Decimetre 3'937o8  0*328090 

Metre 39'37<=>79  3-280899 

Kilometre 3937070000  3280-899167 

A  Hectare  or  10,000  square  metres  is  equal  to  2-47114  acres,  each  of  which  is  43,560 
square  feet.  A  kilometre  is  0*6214  of  a  statute  mile.  A  statute  mile  is  1*609  kilometres. 
A  knot  (in  telegraphy)  is  2,029  yards  or  1*1528  statute  mile. 

Measures  of  Capacity. 

-      Cubic  Feet 

Cubic  Inches  1,728  c.  in.  =  i  c.  ft. 

Cubic  centimetre  or  millimetre     .  0-06103  0*000035 

Litre  or  cubic  decimetre  .         .     .         61*02705  0*035317 

Kilolitre  or  cubic  metre         .         .61,027*05152  35'3l^>5^1 

Measures  of  Weight. 

Avoirdupois  Pounds 
English  Grains  of  7,000  grains 

Milligramme 0*01543  0*0000022 

Gramme        .  .  *5'43235  0*0022046 

Kilogramme 15,432*34880  2*2046213 

I  grain  =  0*064799  gramme  ;  i  pound  avoirdupois  is  0*453593  kilogramme. 


ELEMENTARY     TREATISE 

ON 

PHYSICS. 


BOOK   I. 

ON    MATTER,   FORCE,   AND   MOTION. 


CHAPTER    I. 

GENERAL   PRINCIPLES. 

1.  Object  of  Physics. — The  object  of  Physics  is  the  study  of  the  phe- 
nomena presented  to  us  by  bodies.     It  should,  however,  be   added,  that 
changes  in  the  nature  of  the  body  itself,  such  as  the  decomposition  of  one 
body  into  others,  are  phenomena  whose  study  forms  the  more  immediate 
object  of  chemistry. 

2.  Matter.— That  which   possesses  the  properties   whose   existence   is 
revealed  to  us  by  our  senses,  we  call  matter  or  substance. 

All  substances  at  present  known  to  us  may  be  considered  as  chemical 
combinations  of  sixty-seven  elementary  or  simple  substances.  This  number, 
however,  may  hereafter  be  diminished  or  increased  by  the  discovery  of  some 
more  powerful  means  of  chemical  analysis  than  we  at  present  possess. 

3.  Atoms,  molecules. — From  various  properties  of  bodies,  we  conclude 
that  the  matter  of  which  they  are  formed  is  not  perfectly  continuous,  but 
consists  of  an  aggregate  of  an  immense  number  of  exceedingly  small  por- 
tions or  atoms  of  matter.     These  atoms  cannot  be  divided  physically  ;  they 
are  retained  side  by  side,  without  touching  each  other,  being  separated  by 
distances  which  are  great  in  comparison  with  their  supposed  dimensions. 

A  group  of  two  or  more  atoms  forms  a  molecule,  so  that  a  body  may  be 
considered  as  an  aggregate  of  very  small  molecules,  and  these  again  as 
aggregates  of  still  smaller  atoms.  The  smallest  masses  of  matter  we  ever 
obtain  artificially  are  particles,  and  not  molecules  or  atoms.  Molecules 
retain  their  position  in  virtue  of  the  action  of  certain  forces  called  molecular 
forces. 

From  considerations  based  upon  various  physical  phenomena  Sir  W. 
Thomson  has  calculated  that  in  ordinary  solids  and  liquids  the  average 

B 


2  On  Matter,  Force,  and  Motion.  [3- 

distance  between  contiguous  molecules  is  less  than  the  one  hundred-millionth 
but  greater  than  the  one  two  thousand-millionth  of  a  centimetre. 

To  form  an  idea  of  the  degree  of  the  size  of  the  molecules  Sir  W. 
Thomson  gives  this  illustration  : — '  Imagine  a  drop  of  rain,  or  a  glass  sphere 
the  size  of  a  pea,  magnified  to  the  size  of  the  earth,  the  molecules  in  it  being 
increased  in  the  same  proportion.  The  structure  of  the  mass  would  then  be 
coarser  than  that  of  a  heap  of  fine  shot,  but  probably  not  so  coarse  as  that 
of  a  heap  of  cricket-balls.' 

The  number  of  molecules  of  gas  in  a  cubic  centimetre  of  air  is  calculated 
at  twenty-one  trillions. 

By  dissolving  in  alcohol  a  known  weight  of  fuchsine,  and  diluting  the 
liquid,  it  was  observed  that  a  solution  containing  not  more  than  0-00000002 
of  a  gramme  in  one  cubic  centimetre  had  still  a  distinct  colour  ;  that  is,  that 
a  weight  of  not  more  than  the  ^-millionth  of  a  gramme  can  be  perceived  by 
the  naked  eye.  As  the  molecular  weight  of  this  substance  is  337  times  that 
of  hydrogen  it  follows  that  the  weight  of  an  atom  of  hydrogen  cannot  be 
greater  than  the  one  2O,ooo-millionth  of  a  gramme. 

Loschmidt  gives  the  diameter  of  the  molecules  of  hydrogen  at  0-00000004 
of  a  centimetre  ;  and  according  to  Mousson  and  Quincke  the  diameter  of 
the  sphere  within  which  one  molecule  can  act  upon  an  adjacent  one  is  be- 
tween the  O'OOOo6  and  0-00008  of  a  millimetre,  and  is  therefore  from  5  to  10 
times  less  than  the  wave-length  of  light. 

4.  Molecular  state  of  bodies. — With  respect  to  the  molecules  of  bodies 
three  different  stages  of  aggregation  present  themselves. 

First )  the  solid  state,  as  observed  in  wood,  stone,  metals,  &c.,  at  the 
ordinary  temperature.  The  distinctive  character  of  this  state  is,  that  the 
relative  positions  of  the  molecules  of  the  bodies  is  fixed  and  cannot  be 
.changed  without  the  expenditure  of  more  or  less  force.  Solid  bodies  tend, 
therefore,  to  retain  whatever  form  may  have  been  given  to  them  by  nature  or 
by  art. 

Secondly,  the  liquid  state,  as  observed  in  water,  alcohol,  oil,  &c.  Here 
the  relative  position  of  the  molecules  is  no  longer  fixed,  the  molecules  glide 
past  each  other  with  the  greatest  ease,  and  the  body  assumes  with  readiness 
the  form  of  any  vessel  in  which  it  may  be  placed. 

Thirdly,  the  gaseous  state,  as  in  air    and  in  hydrogen.     In  gases  the 
mobility  of  the  molecules  is  still  greater  than  in  liquids  ;  but  the  distinctive 
character  of  a  gas  is  its  incessant  struggle  to  occupy  a  greater  space,  in  con- 
sequence of  which  a  gas  has  neither  an  independent  form  nor  an  independent 
volume,  for  this  depends  upon  the  pressure  to  which  it  is  subject. 
The  general  term  fluid  is  applied  to  both  liquids  and  gases. 
Most  simple  bodies,  and  many  compound  ones,  may  be  made  to  pass 
successively  through  all  the  three  states.     Water  presents  the  most  familiar 
example  of  this.     Sulphur,  iodine,  mercury,  phosphorus,  and  zinc  are  other 
instances. 

5.  Physical  phenomena,  laws,  and  theories. — Every  change  which 
can  happen  to  a  body,  mere  alteration  of  its  chemical  constitution  being  ex- 
cepted,  may  be  regarded  as  a.  physical  phenomenon.  The  fall  of  a  stone,  the 
vibration  of  a  string,  and  the  sound  which  accompanies  it,  the  attraction  of 
light  particles  by  a  rod  of  sealing-wax  which  has  been  rubbed  by  flannel, 


-6]  Physical  Agents.  3 

the  rippling  of  the  surface  of  a  lake,  and  the  freezing  of  water,  are  examples 
of  such  phenomena. 

A  physical  law  is  the  constant  relation  which  exists  between  any  pheno- 
menon and  its  cause.  As  an  example,  we  have  the  phenomenon  of  the 
diminution  of  the  volume  of  a  gas  by  the  application  of  pressure  ;  the  cor- 
responding law  has  been  discovered,  and  is  expressed  by  saying  that  the 
'volume  of  a  gas  is  inversely  proportional  to  the  pressure. 

In  order  to  explain  the  cause  of  whole  classes  of  phenomena,  suppositions, 
or  hypotheses,  are  made  use  of.  The  utility  and  probability  of  a  hypothesis 
or  theory  are  the  greater  the  simpler  it  is,  and  the  more  varied  and  numerous 
are  the  phenomena  which  are  explained  by  it  ;  that  is  to  say,  are  brought 
into  regular  causal  connection  among  themselves  and  with  other  natural 
phenomena.  Thus  the  adoption  of  the  undulatory  theory  of  light  is  justified 
by  the  simple  and  unconstrained  explanation  it  gives  of  all  luminous  pheno- 
mena, and  by  the  connection  it  reveals  with  the  phenomena  of  heat. 

6.  Physical  agents. — In  our  attempts  to  ascend  from  a  phenomenon  to 
its  cause,  we  assume  the  existence  Oti'physical  agents,  or  natural  forces  acting 
upon  matter  ;  as  examples  of  such  we  have  gravitation,  heat,  light,  magnet- 
ism, and  electricity. 

Since  these  physical  agents  are  disclosed  to  us  only  by  their  effects,  their 
intimate  nature  is  completely  unknown.  In  the  present  state  of  science,  we 
cannot  say  whether  they  are  properties  inherent  in  matter,  or  whether  they 
result  from  movements  impressed  on  the  mass  of  subtile  and  imponderable 
forms  of  matter  diffused  through  the  universe.  The  latter  hypothesis  is,  how- 
ever, generally  admitted.  This  being  so,  it  may  be  further  asked,  are  there 
several  distinct  forms  of  imponderable  matter,  or  are  they  in  reality  but  one 
and  the  same  ?  As  the  physical  sciences  extend  their  limits,  the  opinion 
tends  to  prevail  that  there  is  a  subtile,  imponderable,  and  eminently  elastic 
fluid  called  the  ether  distributed  through  the  entire  universe  ;  it  pervades 
the  mass  of  all  bodies,  the  densest  and  most  opaque,  as  well  as  the  lightest 
or  the  most  transparent.  It  is  also  considered  that  the  ultimate  particles  of 
which  matter  is  made  up  are  capable  of  definite  motions  varying  in  character 
and  velocity,  and  which  can  be  communicated  to  the  ether.  A  motion  of  a 
particular  kind  communicated  to  the  ether  can  give  rise  to  the  phenomenon 
of  heat ;  a  motion  of  the  same  kind,  but  of  greater  velocity,  produces  light  ; 
and  it  may  be  that  a  motion  different  in  form  or  in  character  is  the  cause  of 
electricity.  Not  merely  do  the  atoms  of  bodies  communicate  motion  to  the 
atoms  of  the  ether,  but  this  latter  can  impart  it  to  the  former.  Thus  the 
atoms  of  bodies  are  at  once  the  sources  and  the  recipients  of  the  motion. 
All  physical  phenomena,  referred  thus  to  a  single  cause,  are  but  transforma- 
tions of  motion. 


On  Matter,  Force,  and  Motion.  [7- 


CHAPTER    II. 

GENERAL   PROPERTIES   OF   BODIES. 

7.  Different  kinds  of  properties. — By  the  term  properties,  as  applied 
to  bodies,  we  understand  the  different  ways  in  which  bodies  present  them- 
selves to  our  senses.     We  distinguish  general  from  specific  properties.     The 
former  are  shared  by  all  bodies,  and  amongst  them  the  most  important  are 
impenetrability,    extension,   divisibility,  porosity,   compressibility,  elasticity, 
mobility,  and  inertia. 

Specific  properties  are  such  as  are  observed  in  certain  bodies  only,  or  in 
certain  states  of  these  bodies  ;  such  are  solidity,  fluidity,  tenacity,  dtictility, 
malleability,  hardness,  transparency,  colour,  &c. 

With  respect  to  the  above  general  properties,  impenetrability  and  exten- 
sion might,  perhaps,  be  more  aptly  termed  essential  attributes  of  matter, 
since  they  suffice  to  define  it  ;  while  divisibility,  porosity,  compressibility, 
and  elasticity  do  not  apply  to  atoms,  but  only  to  bodies  or  aggregates  of 
atoms  (3). 

8.  Impenetrability. — Impenetrability  is  the  property  in  virtue  of  which 
two  portions  of  matter  cannot  at  the  same  time  occupy  the  same  portion  of 
space.     Thus  when  a  stone  is  placed  in  a  vessel  of  water  the  volume  of  the 
water  rises  by  an  amount  depending  on  the  volume  of  the  stone  ;  this  method, 
indeed,  is  used  to  determine  the  bulk  of  irregularly  shaped  bodies  by  means 
of  graduated  measures. 

Strictly  speaking,  this  property  applies  only  to  the  atoms  of  a  body.  In 
many  phenomena  bodies  appear  to  penetrate  each  other ;  thus,  the  volume 
of  a  compound  body  is  always  less  than  the  sum  of  the  volumes  of  its  con- 
stituents ;  for  instance,  the  volume  of  a  mixture  of  water  and  sulphuric  acid, 
o,r  of  water  and  alcohol,  is  less  than  the  sum  of  the  volumes  before  mixture. 
In  all  these  cases,  however,  the  penetration  is  merely  apparent,  and  arises 
from  the  fact  that  in  every  body  there  are  interstices,  or  spaces  unoccupied 
by  matter  (13). 

9.  Extension. — Extension  or  magnitude  is  the  property  in  virtue  of  which 
every  body  occupies  a  limited  portion  of  space. 

Many  instruments  have  been  invented  for  measuring  linear  extension  or 
lengths  with  great  precision.  Two  of  these,  the  vernier  and  micrometer 
screw,  on  account  of  their  great  utility  deserve  to  be  here  mentioned. 

10.  Vernier. — The  vernier  forms  a  necessary  part  of  all  instruments 
where  lengths  or  angles  have  to  be  estimated  with  precision  ;  it  derives  its 
name  from  its  inventor,  a  French  mathematician,  who  died  in   1637,  and 
consists  essentially  of  a  short  graduated  scale,  ab  (fig.  i),  which  is  made  to 


-11]  Micrometer  Screw.  5 

slide  along  a  fixed  scale,  AB,  so  that  the  graduations  of  both  may  be  com- 
pared with  each  other.  The  fixed  scale  AB,  being  divided  into  equal  parts, 
the  whole  length  of  the  vernier,  ab,  may  be  taken  equal  to  nine  of  those  parts, 
and  is  itself  divided  into  ten  equal  parts.  Each  of  the  parts  of  the  vernier, 
ab,  will  then  be  less  than  a  part  of  the  scale  by  one  tenth  of  the  latter. 

This  granted,  in  order  to  measure  the  length  of  any  object,  ;;z;z,  let  us 
suppose  that  the  latter,  when  placed  as  in  the  figure,  has  a  length  greater 
than  four  but  less  than  five  parts  of  the  fixed  scale.  In  order  to  determine 
by  what  fraction  of  a  part  mn  exceeds  four,  one  of  the  ends,  rt,  of  the  vernier, 
ab,  is  placed  in  contact  with  one  extremity  of  the  object,  mn,  and  the 
division  on  the  vernier  is  sought  which  coincides  with  a  division  on  the 
scale,  AB.  In  the  figure  this  coincidence  'occurs  at  the  eighth  division  ot 
the  vernier,  counting  from  the  end,  ;/,  and  indicates  that  the  fraction  to  be 
measured  is  equal  to  j^ths  of  a  part  of  the  scale,  AB.  In  fact,  each  of  the 
parts  of  the  vernier  being  less  than  a  part  of  the  scale  by  ~th  of  the  latter,  it 
is  clear  that  on  proceeding  towards  the  left  from  the  point  of  coincidence 
the  divisions  of  the  vernier  are  respectively  one,  two,  three,  etc.  tenths, 


A 

B 

s 

51                                             10                                             151 

I 

1  rj  —  r—  r 

1      ,     '    ,  —  U  U  !,  1  

1  L  >  !  1           1      ( 

8-  '    '    L 

!  1         1         1         1          1 
15                                         10 

JL°L 


Fig.   i. 

behind  the  divisions  of  the  scale  ;  so  that  the  end,  n,  of  the  object  (that  is  to 
say,  the  eighth  division  of  the  vernier)  is  —ths  behind  the  division  4  on  the 
scale  ;  in  other  words,  the  length  of  mn  is  equal  to  4T8oths  of  the  parts  into 
which  the  scale  AB  is  divided.  Consequently  if  the  scale  AB  were  divided 
into  inches  the  length  of  mn  would  be  4—  =  4!  inches.  The  divisions  on 
the  scale  remaining  the  same,  it  would  be  necessary  to  increase  the  length 
of  the  vernier  in  order  to.  measure  the  length  mn  more  accurately.  For 
instance,  if  the  length  of  the  vernier  were  equal  to  nineteen  of  the  parts  on 
the  scale,  and  this  length  were  divided  into  twenty  equal  parts,  the  length  mn 
could  be  determined  to  the  twentieth  of  a  part  on  the  scale,  and  so  on.  In 
instruments  like  the  theodolite,  intended  for  measuring  angles,  the  scale  and 
vernier  have  a  circular  form,  and  the  latter  usually  carries  a  magnifier  in 
order  to  determine  with  greater  precision  the  coincident  divisions  of  vernier 
and  scale. 

ii.  Micrometer  screw. — Another  useful  little  instrument  for  measuring 
small  lengths  with  precision  is  the  micrometer  screw.  It  is  used  under 
various  forms,  but  the  principle  is  the  same  in  all,  and  may  be  illustrated  by 
reference  to  the  splierometer.  This  consists  of  an  accurately  turned  screw 
with  a  blunt  point  which  works  in  a  companion  supported  on  three  steel 
points  (fig.  2).  To  one  of  these  is  fixed  a  vertical  graduated  scale,  each 
division  of  which  is  equal  to  the  distance  between  two  threads  of  the  screw. 


On  Matter •,  Force,  and  Motion. 


EH- 


Fig.  2. 


This  distance  may  be  accurately  determined  by  measuring  a  given  length  of 
the  screw  by  compasses,  and  counting  the  number  of  the  threads  in  this 
length.  A  milled  head  attached  to  the  screw  is  graduated  at  the  periphery 

into  any  given  number  of  parts,  say  500. 
Suppose  now  the  distance  between  the 
threads  is  I  millimetre,  when  the  head  has 
made  a  complete  turn  it  will  have  risen  or 
sunk  through  one  millimetre,  and  so  on  in 
proportion  for  any  multiple  or  fraction  of  a 
turn. 

In  order  to  determine  the  thickness  of  a 
piece  of  glass  for  instance,  the  apparatus  is 
placed  on  a  perfectly  plane  polished  surface, 
and  the  point  of  the  screw  is  brought  in 
contact  with  the  glass.  The  division  on  the 
vertical  scale  immediately  above  the  limb, 
and  that  on  the  limb  are  read  off.  After 
removing  the  glass  plate  the  point  is  brought  in  contact  with  the  plane 
surface,  and  corresponding  readings  are  again  made,  from  which  the  thick- 
ness can  be  at  once  deduced. 

The  same  process  is  obviously  applicable  to  determining  the  diameter  of 
a  wire. 

To  ascertain  whether  a  surface  is  spherical,  three  points  are  applied  to 
the  surface,  and  the  screw  is  also  made  to  touch  as  described  above.  It  is 
then  moved  along  the  surface,  and  if  all  four  points  are  everywhere  in  con- 
tact the  surface  is  truly  spherical.  This  application  is  of  great  value  in 
ascertaining  the  exact  curvature  of  lenses. 

The  diameter  of  a  sphere  may  also  be  measured  by  its  means ;  for  it 
can  be  shown  by  a  simple  geometrical  construction  that  the  distance  of  the 
movable  point  from  the  plane  of  the  fixed  points,  multiplied  by  the  diameter 
of  the  sphere,  is  equal  to  the  square  of  the  distance  of  the  movable  point 
from  one  of  the  fixed  points. 

12.  Divisibility — is  the  property  in  virtue  of  which  a  body  may  be 
separated  into  distinct  parts. 

Numerous  examples  may  be  cited  of  the  extreme  divisibility  of  matter  (3). 
The  tenth  part  of  a  grain  of  musk  will  continue  for  years  to  fill  a  room 
with  its  odoriferous  particles,  and  at  the  end  of  that  time  will  scarcely  be 
diminished  in  weight.  Blood  is  composed  of  red,  flattened  globules,  floating 
in  a  colourless  liquid  called  serum.  In  man  the  diameter  of  one  of  these 
globules  is  less  than  the  3,5ooth  part  of  an  inch,  and  the  drop  of  blood  which 
might  be  suspended  from  the  point  of  a  needle  would  contain  about  a  million 
of  globules. 

Again,  the  microscope  has  disclosed  to  us  the  existence  of  insects  smaller 
even  than  these  particles  of  blood  ;  the  struggle  for  existence  reaches  even 
to  these  little  creatures,  for  they  devour  still  smaller  ones.  If  blood  runs  in 
the  veins  of  these  devoured  ones,  how  infinitesimal  must  be  the  magnitude 
of  its  component  globules  ! 

Although  experiment  fails  to  determine  whether  there  be  a  limit  to  the 
divisibility  of  matter,  many  facts  in  chemistry,  such  as  the  invariability  in 


-13] 


Porosity. 


the  relative  weights  of  the  elements  which  combine  with  each  other,  would 
lead  us  to  believe  that  such  a  limit  does  exist.  It  is  on  this  account  that 
bodies  are  conceived  to  be  composed  of  extremely  minute  and  indivisible 
parts  called  atoms  (3). 

13.  Porosity. — Porosityis  the  quality  in  virtue  of  which  interstices  or 
pores  exist  between  the  molecules  of  a  body. 

Two  kinds  of  pores  may  be  distinguished  :  physical  pores,  where  the 
interstices  are  so  small  that  the  surrounding  molecules  remain  within  the 
sphere  of  each  other's  attracting  or  repelling  forces  ;  and  sensible  pores,  or 
actual  cavities  across  which  these  molecular  forces  cannot  act.  The  con- 
tractions and  expansions  resulting  from  variations  of  temperature  are  due  to 
the  existence  of  physical  pores,  whilst  in  the  organic  world  the  sensible  pores 
are  the  seat  of  the  phenomena  of  exhalation  and  absorption. 

In  wood,  sponge,  and  a  great  number  of  stones — for  instance,  pumice 
stone — the  sensible  pores  are  apparent  ;  physical  pores  never  are.     Yet, 
since  the  volume  of  every  body  may  be  dimin- 
ished,   we   conclude  that  all   possess  physical 
pores. 

The  existence  of  sensible  pores  may  be 
shown  by  the  following  experiment  :— A  long 
glass  tube,  A  (fig.  3),  is  provided  with  a  brass 
cup  at  the  top,  and  a  brass  foot  made  to  screw 
on  to  the  plate  of  an  air-pump.  The  bottom  of 
the  cup  consists  of  a  thick  piece  of  leather. 
After  pouring  mercury  into  the  cup  so  as 
entirely  to  cover  the  leather,  the  air-pump  is  put 
in  action,  and  a  partial  vacuum  produced  within 
the  tube.  By  so  doing  a  shower  of  mercury  is 
at  once  produced  within  the  tube,  for  the  atmo- 
spheric pressure  on  the  mercury  forces  that 
liquid  through  the  pores  of  the  leather.  In  the 
same  manner  water  or  mercury  may  be  forced 
through  the  pores  of  wood,  by  replacing  the 
leather  in  the  above  experiment  by  a  disc  of 
wood  cut  perpendicular  to  the  fibres. 

When  a  piece  of  chalk  is  thrown  into  water, 
air-bubbles  at  once  rise  to  the  surface,  in  con- 
sequence of  the  air  in  the  pores  of  the  chalk 
being  expelled  by  the  water.  The  chalk  will  be 
found  to  be  heavier  after  immersion,  than  it  was 
before,  and  knowing  its  volume,  the  volume  of 
its  pores  may  be  easily  determined  from  the 
increase  of  its  weight. 

The  porosity  of  gold  was  demonstrated  by 

the  celebrated  Florentine  experiment  made  in  1661.  Some  academicians  at 
Florence,  wishing  to  try  whether  water  was  compressible,  filled  a  thin  globe 
of  gold  with  that  liquid,  and,  after  closing  the  orifice  hermetically,  they  ex- 
posed the  globe  to  pressure  with  a  view  of  altering  its  form,  knowing  that 
any  alteration  in  form  must  be  accompanied  by  a  diminution  in  volume. 


Fig.  3. 


8  On  Matter^  Force,  and  Motion.  [13- 

The  consequence  was,  that  the  water  forced  its  way  through  the  pores  of  the 
gold,  and  stood  on  the  outside  of  the  globe  like  dew.  More  than  twenty 
years  previously  the  same  fact  was  demonstrated  by  Francis  Bacon  by  means 
of  a  leaden  sphere  ;  the  experiment  has  since  been  repeated  with  globes  of 
other  metals,  and  similar  results  obtained. 

A  glass  tube  about  a  metre  long,  closed  at  one  end,  is  half  filled  with 
water,  and  then  pure  alcohol  poured  upon  it  to  a  mark  near  the  top  ;  on  then 
closing  the  open  end  with  the  thumb  and  inverting  the  tube  several  times 
the  mixture  shrinks  so  that  its  level  is  now  nearly  an  inch  below  the 
mark  ;  at  the  same  time  very  minute  bubbles  are  seen  to  rise,  owing  to  the 
water  having  penetrated  into  the  pores  of  the  alcohol  and  expelled  the  air 
present. 

14.  Apparent  and  real  volumes. — In   consequence  of  the  porosity   of 
bodies,  it  becomes  necessary  to  distinguish  between  their  real  and  apparent 
volumes.     The  real  volume  of  a  body  is  the  portion  of  space  actually  occu- 
pied by  the  matter  of  which  the  body  is  composed  ;  its  apparent  volume  is 
the  sum  of  its  real  volume  and  the  total  volume  of  its  pores.     The  real 
volume  of  a  body  is  invariable,  but  its  apparent  volume  can  be  altered  in 
various  ways. 

15.  Applications. — The  property  of  porosity  is  utilised  in  filters  of  paper, 
felt,  stone,  charcoal,  &c.     The  pores  of  these  substances  are  sufficiently  large 
to  allow  liquids  to  pass,  but  small  enough  to  arrest  the  passage  of  any  sub- 
stances which  these  liquids  may  hold  in  suspension.     Again,  large  blocks  of 
stone  are  often  detached  in  quarries  by  introducing  wedges  of  dry  wood  into 
grooves  cut  in  the  rock.     These  wedges  being  moistened,  water  penetrates 
their  pores,  and  causes  them  to  swell  with  considerable  force.     Dry  cords, 
when  moistened,  increase  in  diameter  and  diminish  in  length — a  property  of 
which  advantage  has  been  taken  in  order  to  raise  great  weights. 

1 6.  Compressibility.— Compressibility  is  the  property  in  virtue  of  which 
the  volume  of  a  body  may  be  diminished  by  pressure.     This  property  is  at 
once  a  consequence  and  a  proof  of  porosity. 

Bodies  differ  greatly  with  respect  to  compressibility.     The  most  com- 
pressible bodies  are  gases  ;  by  sufficient  pressure  they  may  be  made    to 
occupy  ten,  twenty,  or  even  some  hundred  times  less  space  than  they  do  under 
ordinary  circumstances.     In  most  cases,  however,  there  is  a  limit  beyond/ 
which,  when  the  pressure  is  increased,  they  become  liquids. 

The  compressibility  of  solids  is  much  less  than  that  of  gases,  and  is  found 
in  all  degrees.  Cloths,  paper,  cork,  woods,  are  amongst  the  most  com- 
pressible. Metals  are  so  also  to  a  great  extent,  as  is  proved  by  the  process 
of  coining,  in  which  the  metal  receives  the  impression  from  the  die.  There 
is,  in  most  cases,  a  limit  beyond  which,  when  the  pressure  is  increased,  bodies 
are  fractured  or  reduced  to  powder. 

The  compressibility  of  liquids  is  so  small  as  to  have  remained  for  a  long 
time  undetected  :  it  may,  however,  be  proved  by  experiment,  as  will  be  seen 
in  the  chapter  on  Hydrostatics. 

17.  Elasticity.— Elasticity  is  the  property  owing  to  which  bodies  resume 
their  original  form  or  volume,  when  the  force  which  altered  that  form  or 
volume  ceases  to  act.     Elasticity  may  be  developed  in  bodies  by  pressure 
by  traction  or  pulling,  flexion  or  bending^  and  by  torsion  or  twisting.     In 


-19]  Inertia.  g 

treating  of  the  general  properties  of  bodies,  the  elasticity  developed  by 
pressure  alone  requires  consideration  ;  the  other  kinds  of  elasticity,  being 
peculiar  to  solid  bodies,  will  be  considered  amongst  their  specific  properties 
(arts.  89,  90,  91). 

Gases  and  liquids  are  perfectly  elastic  ;  in  other  words,  after  undergoing 
a  change  in  volume  they  regain  exactly  their  original  volume  when  the 
pressure  becomes  what  it  originally  was.  Solid  bodies  present  different  de- 
grees of  elasticity,  though  none  present  the  property  in  the  same  perfec- 
tion as  liquids  and  gases,  and  in  all  it  varies  according  to  the  time  during 
which  the  body  has  been  exposed  to  pressure.  Caoutchouc,  ivory,  glass, 
and  marble  possess  considerable  elasticity  ;  lead,  clay,  and  fats,  scarcely 
any. 

There  is  a  limit  to  the  elasticity  of  solids,  beyond  which  they  either  break 
or  are  incapable  of  regaining  their  original  form  and  volume.  This  is  called 
the  limit  of  elasticity  ;  within  this  limit  all  substances  are  perfectly  elastic. 
In  sprains,  for  instance,  the  elasticity  of  the  tendons  has  been  exceeded. 
In  gases  and  liquids,  on  the  contrary,  no  such  limit  can  be  reached  ;  they 
always  regain  their  original  volume  when  the  original  pressure  is  restored. 

If  a  ball  of  ivory,  glass,  or  marble  be  allowed  to  fall  upon  a  slab  of  polished 
marble,  which  has  been  previously  slightly  smeared  with  oil,  it  will  rebound 
and  rise  to  a  height  nearly  equal  to  that  from  which  it  fell.  On  afterwards 
examining  the  ball  a  circular  blot  of  oil  will  be  found  upon  it,  more  or  less 
extensive  according  to  the  height  of  the  fall.  From  this  we  conclude  that  at 
the  moment  of  the  shock  the  ball  was  flattened,  and  that  its  rebound  was 
caused  by  the  effort  to  regain  its  original  form. 

18.  Mobility,  motion,  rest. — Mobility  is  the  property  in  virtue  of  which 
the  position  of  a  body  in  space  may  be  changed. 

Motion  and  rest  may  be  either  relative  or  absolute.  By  the  relative 
motion  or  rest  of  a  body  we  mean  its  change  or  permanence  of  position  with 
respect  to  surrounding  bodies ;  by  its  absolute  motion  or  rest  we  mean  the 
change  of  permanence  of  its  position  with  respect  to  ideal  fixed  points  in 
space. 

Thus  a  passenger  in  a  railway  carriage  may  be  in  a  state  of  relative  rest 
with  respect  to  the  train  in  which  he  travels,  but  he  is  in  a  state  of  relative 
motion  with  respect  to  the  objects,  such  as  trees,  houses,  &c.,  past  which  the 
train  rushes.  These  houses  again  enjoy  merely  a  state  of  relative  rest,  for 
the  earth  itself  which  bears  them  is  in  a  state  of  incessant  relative  motion 
with  respect  to  the  celestial  bodies  of  our  solar  system,  inasmuch  as  it  moves 
at  the  rate  of  more  than  eighteen  miles  in  a  second.  In  short,  absolute 
motion  and  rest  are  unknown  to  us  ;  in  nature,  relative  motion  and  rest  are 
alone  presented  to  our  observation. 

19.  Inertia. — Inertia  is  a  purely  negative  though  universal  property  of 
matter  (2  6) ;  it  is  the  property  that  matter  cannot  of  itself  change  its  own 
state  of  motion  or  of  rest.     If  a  body  is  at  rest  it  remains  so  until  some 
force  acts  upon  it ;  if  it  is  in  motion  this  motion  can  only  be  changed  by  the 
application  of  some  force. 

This  property  of  inertia  is  what  is  expressed  by  Newton's  first  law  of 
motion. 

A  body,  when  unsupported  in  mid-air,  does  not  fall  to  the  earth  in  virtue 


io  On  Matter,  Force,  and  Motion.  [19- 

of  any  inherent  property,  but  because  it  is  acted  upon  by  the  force  of  gravity. 
A  billiard  ball  gently  pushed  does  not  move  more  and  more  slowly,  and 
finally  stop,  because  it  has  any  preference  for  a  state  of  rest,  but  because  its 
motion  is  impeded  by  the  friction  on  the  cloth  on  which  it  rolls,  and  by  the 
resistance  of  the  air.  If  all  impeding  causes  were  withdrawn,  a  body  once 
in  motion  would  continue  to  move  for  ever  in  a  straight  line  with  unchanging 
velocity. 

20.  Illustrations. — Numerous  phenomena  may  be  explained  by  the 
inertia  of  matter.  For  instance,  before  leaping  a  ditch  we  run  towards  it,  in 
order  that  the  motion  of  our  bodies  at  the  moment  of  leaping  may  add  itself 
to  the  muscular  effort  then  made. 

On  descending  carelessly  from  a  carriage  in  motion,  the  upper  part  of  the 
body  retains  its  motion,  whilst  the  feet  are  prevented  from  doing  so  by  friction 
against  the  ground  ;  the  consequence  is  we  fall  towards  the  moving  carriage. 
A  rider  falls  over  the  head  of  a  horse  if  it  suddenly  stops.  In  striking  the 
handle  of  a  hammer  against  the  ground  the  handle  suddenly  stops,  but  the 
head,  striving  to  continue  its  motion,  fixes  itself  more  firmly  on  the  handle. 

By  the  property  of  inertia  may  also  be  explained  the  following  experi- 
ments : — Let  a  card  be  placed  upon  a  tumbler,  and  a  shilling  on  the  card  ; 
if  the  edge  of  the  card  be  smartly  flicked  with  the  finger  the  card  is  driven 
away  and  the  coin  falls  into  the  tumbler.  A  gentle  push  with  the  finger  will 
move  a  door  on  its  hinges  ;  but  if  a  pistol  bullet  be  fired  against  the  door  it 
perforates  the  door  without  moving  it.  A  clay  tobacco  pipe,  which  is  sus- 
pended by  two  vertical  hairs,  may  be  cut  in  two  by  a  powerful  stroke  with  a 
sharp  sword  without  breaking  the  hairs. 

A  string  which  gently  applied  will  raise  a  weight,  snaps  at  once  when  a 
sudden  pull  is  exerted.  Substances  which  explode  with  great  rapidity,  such 
as  fulminating  mercury,  chloride  of  nitrogen,  cannot  be  used  with  fire-arms, 
because  there  is  not  sufficient  time  to  transfer  the  motion  to  the  projectiles, 
and  hence  the  weapons  are  burst. 

The  terrible  accidents  on  our  railways  are  chiefly  due  to  inertia.  When 
the  motion  of  the  engine  is  suddenly  arrested  the  carriages  strive  to  continue 
the  motion  they  had  acquired,  and  in  doing  so  are  shattered'  against  each 
other.  Hammers,  pestles,  stampers  are  applications  of  inertia.  So  are  also 
the  enormous  iron  fly-wheels,  by  which  the  motion  of  steam-engines  is 
regulated. 


-22  Measure  of  Space.  \  \ 


CHAPTER   III. 

ON    FORCE,    EQUILIBRIUM,   AND   MOTION. 

21.  Measure  of  time. — To    obtain    a   proper   measure    of  force   it    is 
necessary,    as    a   preliminary,    to    define    certain    conceptions    which    are 
presupposed  in   that  measure  ;    and   in  the  first  place,  it  is  necessary  to 
define  the  unit  of  time.     Whenever  a  second  is  spoken  of  without  qualifi- 
cation it  is  understood  to  be  a  second  of  mean  solar  time.   The  exact  length  of 
this  unit  is  fixed  by  the  following  considerations.    The  instant  when  the  sun's 
centre  is  on  an  observer's  meridian — in  other  words,  the  instant  of  the  transit 
of  the  sun's  centre — can  be  determined  with  exactitude,  and  thus  the  interval 
which  elapses  between  two  successive  transits  also  admits  of  exact  determina- 
tion, and  is  called  an  apparent  day.     The  length  of  this    interval    differs 
slightly  from  day  to  day,  and  therefore  does  not  serve  as  a  convenient  measure 
of  time.      Its  average  length  is  not  open  to  this  objection,  and  therefore 
serves  as  the  required  measure,  and  is  called  a  mean  sola*  day.     The  short 
hand  of  a  common  clock  would  go  exactly  twice  round  the  face  in  a  mean 
solar  day  if  it  went  perfectly.    The  mean  solar  day  consists  of  24  equal  parts 
called  hours,  these  of  60  equal  parts  called  minutes,  and  these  again  of  60 
equal  parts  called  seconds.     Consequently,  the  second  is  the  86,4ooth  part 
of  a  mean  solar  day,  and  is  the  generally  received  unit  of  time. 

22.  Measure  of  space. — Space  may  be  either  length  or  distance,  which 
is  space  of  one  dimension  ;  area,  which  is  space  of  two  dimensions  ;  or 
volume,  which  is  space  of  three  dimensions.     In  England  the  standard  of 
length  is  the  British  Imperial  Yard,  which  is  the  distance  between  two  fixed 
points  on  a  certain  metal  rod,  kept  in  the  Tower  of  London,  when  the  tempera- 
ture of  the  whole  rod  is  60°  F.  =  i5°'5  C.     It  is,  however,  usual  to  employ  as 
a  unit,  &foot,  which  is  the  third  part  of  a  yard.     In  France  the  standard  of 
length  is  the  metre ;  this  is  approximately  equal  to  the  ten-millionth  part  of 
a  quadrant  of  the  earth's  meridian,  that  is  of  the  arc  from  the  Equator  to  the 
North  Pole  ;  it  is  practically  fixed  by  the  distance  between  two  marks  on  a 
certain  standard  rod.     The  relation  between  these  standards  is  as  follows  : 

I  yard   =0-914401  metre. 
I  metre  =  1-093612  yard. 

The  unit  of  length  having  been  fixed,  the  units  of  area  and  volume  are 
connected  with  it  thus  :  the  unit  of  area  is  the  area  of  a  square,  one  side  of 
which  is  the  unit  of  length.  The  unit  of  volume  is  the  volume  of  a  cube,  one 
edge  of  whfch  is  the  unit  of  length.  These  units  in  the  case  of  English  mea- 
sures are  the  square  yard  (or  foot)  and  the  cubic  yard  (or  foot)  respectively ; 
in  the  case  of  French  measures,  the  square  metre  and  cubic  metre  respec- 


1 2  On  Matter,  Force,  and  Motion.  [22- 

tively.  The  length  of  the  seconds  pendulum,  in  lat.  45°,  which  is  about  that 
of  Milan,  is  0-9935111.,  and  thus  only  differs  from  a  metre  by  6-5  millimetres. 

23.  Measure  of  mass. — Two  bodies  are  said  to  have  equal  masses  when, 
if  placed  in  a  perfect  balance  in  vacuo,  they  counterpoise  each  other.    Suppose 
we  take  lumps  of  any  substance,  lead,  butter,  wood,  stone,  etc.,  and  suppose 
that  any  one  of  them  when  placed  on  the  one  pan  of  a  balance  will  exactly 
counterpoise  any  other  of  them  when  placed  on  the  opposite  pan — the  balance 
being  perfect  and  the  weighing  performed  in  vacuo;  this  being  the  case, 
these  lumps  are  said  to  have  equal  masses. 

The  British  unit  of  mass  is  the  standard  pound  (avoirdupois),  which  is  a 
certain  piece  of  platinum  kept  in  the  Exchequer  Office  in  London.  This  unit 
having  been  fixed,  the  mass  of  a  given  substance  is  expressed  as  a  multiple 
or  submultiple  of  the  unit. 

It  need  scarcely  be  mentioned  that  many  distances  are  ascertained  and 
expressed  in  yards  which  it  would  be  physically  impossible  to  measure 
directly  by  a  yard  measure.  In  like  manner  the  masses  of  bodies  are  fre- 
quently ascertained  and  expressed  numerically  which  could  not  be  placed  in 
a  balance  and  subjected  to  direct  weighing. 

24.  Density  and  relative  density. — -If  we  consider  any  body  or  portion 
of  matter,  and  if  we  conceive  it  to  be  divided  into  any  number  of  parts  having 
equal  volumes,  then,  if  the  masses  of  these  parts  are  equal,  in  whatever 
way  the  division  be  conceived  as  taking  place  that  body  is  one  of  uniform 
density.    The  density  of  such  a  body  is  the  mass  of  the  unit  of 'volume.    Con- 
sequently, if  M  denote  the  mass,  V  the  volume,  and  D  the  density  of  the 
body,  we  have 

M=VD. 

If  now  we  have  an  equal  volume  V  of  any  second  substance  whose  mass  is 
M'  and  density  D',  we  shall  have 

M'  =  VD'. 

Consequently,  D  :  D'::M  :  M' ;  that  is,  the  densities  of  substances  are 
in  the  same  ratio  as  the  masses  of  equal  volumes  of  those  substances. 
If  now  we  take  the  density  of  distilled  water  at  4°  C.  to  be  unity,  the  relative 
density  of  any  other  substance  is  the  ratio  which  the  mass  of  any  given 
volume  of  that  substance  at  that  temperature  bears  to  the  mass  of  an  equal 
volume  of  water.  Thus  it  is  found  that  the  mass  of  any  volume  of  platinum 
is  22-069  times  that  of  an  equal  volume  of  water,  consequently  the  relative 
density  of  platinum  is  22-069. 

The  relative  density  of  a  substance  is  generally  called  its  specific  gravity. 
Methods  of  determining  it  are  given  in  Book  III. 

In  the  table  below  the  densities  D  of  various  substances,  expressed  in 
pounds  to  the  cubic  foot,  are  given,  and  column  G  gives  the  relative  densities 
of  the  same  substances. 

It  is  evident  that  column  G  is  obtained  by  dividing  the  values  in  column 

D  by  62-42. 

D.  G. 

Water 62-42  rooo 

Anthracite 112-36  r8oo 

Cast  iron 449-86  7-207 


-26]  Force.  1 3 

-A        D.  c, 

Cast  copper •  .       548-55  8788 

„     lead         .         .  .       708-59  11-352 

„     platinum          ......    1,269-43  20-332 

Melting  ice 58*05  0-930 

In  the  metric  system,  since  the  mass  of  the  cubic  centimetre  of  water 
is  one  gramme,  it  is  evident  that  the  density  D,  in  grammes  to  the  cubic 
centimetre,  has  the  same  numerical  value  as  the  relative  density  referred  to 
water. 

25.  Velocity  and  its  measure. — When  a  material  point  moves,  it  de- 
scribes a  continuous  line  which   may  be  either  straight  or  curved,  and  is 
called  its  path  and   sometimes   its   trajectory.     Motion  which  takes  place 
along  a  straight  line  is  called  rectilinear  motion  ;  that  which  takes  place 
along  a  curved  line  is  called  curvilinear  motion.     The  rate  of  the  motion  of 
a  point  is  called  its  'velocity.     Velocity  may  be  either  uniform  or  variable  ;  it 
is  uniform  when  the  point  describes  equal  spaces  or  portions  of  its  path  in 
all  equal  times  ;  it  is  variable  when  the  point  describes  unequal  portions  of 
its  path  in  any  equal  times. 

Uniform  velocity  is  measured  by  the  number  of  units  of  space  described 
in  a  given  unit  of  time.  The  units  commonly  employed  in  this  country 
are  feet  and  seconds.  If,  for  example,  a  velocity  5  is  spoken  of  without 
qualification,  this  means  a  velocity  of  5  feet  per  second.  Consequently, 
if  a  body  moves  for  t  seconds  with  a  uniform  velocity  v,  it  will  describe 
v  t  feet. 

The  following  are  a  few  examples  of  different  degrees  of  velocity  expressed 
in  this  manner.  A  snail  0-005  feet  m  a  second ;  the  Rhine  between  Worms 
and  Mainz  3-3;  military  quick  step  4-6  ;  moderate  wind  10;  fast  sailing 
vessel  iS-o;  Channel  steamer  22-0;  railway  train  3610  75  feet;  racehorse 
and  storm  50  feet ;  eagle  no  feet ;  carrier  pigeon  120  feet  ;  a  hurricane  160 
feet;  sound  at  o°  1,090;  a  shot  from  an  Armstrong  gun  1,180;  a  Martini- 
Henry  rifle  bullet  1,330;  a  point  on  the  Equator  in  its  rotation  about  the 
earth's  axis  1,520;  velocity  of  the  vibratory  motion  of  particles  of  air,  1590; 
velocity  of  the  centre  of  the  earth  101,000  feet ;  light,  and  also  electricity  in 
a  medium  destitute  of  resistance  192,000  miles. 

Variable  velocity  is  measured  at  any  instant  by  the  number  of  units  of 
space  a  body  would  describe  if  it  continued  to  move  uniformly  from  that 
instant  for  a  unit  of  time.  Thus,  suppose  a  body  to  run  down  an  inclined 
plane,  it  is  a  matter  of  ordinary  observation  that  it  moves  more  and  more 
quickly  during  its  descent ;  suppose  that  at  any  point  it  has  a  velocity  15, 
this  means  that  at  that  point  it  is  moving  at  the  rate  of  15  ft.  per  second,  or, 
in  other  words,  if  from  that  point  all  increase  of  velocity  ceased,  it  would  de- 
scribe 1 5  ft.  in  the  next  second. 

26.  Force. — Forces  manifest  themselves  to  us  by  the  changes  which  they 
produce,  or  tend  to  produce,  in  the  motion  of  matter.     The  action  of  forces 
in  causing  motion  is  best  expressed  in  Newton's  laws  :  The  first  law  is, 
Every  body  continues  in  its  state  of  rest  or  of  uniform  motion  in  a  straight 
line,  except  as  it  is  compelled  by  forces  to  change  that  state. 

A  body  may  be  at  rest,  or  may  be  moving  uniformly  in  a  straight  line, 
while  acted  upon  by  a  system  of  forces.  In  this  case  the  forces  are  said  to 


14  On  Matter,  Force,  and  Motion.  [26- 

balance  each  other.  If  a  constant  unbalanced  force  act  upon  a  body,  it  will  no 
longer  move  uniformly.  The  velocity  will  increase  continually,  at  a  uniform 
rate.  A  familiar  case  of  this  kind  is  found  in  the  attraction  of  the  earth  for 
other  bodies.  According  to  Newton's  law  of  gravitation,  the  attraction 
between  two  masses,  one  of  which  contains  m  and  the  other  m'  units  of 

mass,  is  7^L  where  r  is  the  distance  between  the  centres  of  the  masses 
r* 

(62).  If  one  of  the  masses  be  the  unit  mass,  or  one  pound,  the  other 
being  the  earth,  the  above  expression  represents  the  pull  which  the  earth 
exerts  upon  a  pound  of  matter  :  this  pull  is  the  weight  of  a  pound. 

It  is  important  to  distinguish  very  carefully  between  a  pound — the  unit 
of  mass— and  the  weight  of  a  pound,  which  is  a.  force.  Weight  is  not  a 
necessary  property  of  matter.  If  physical  conditions  were  such  that  we 
could  visit  the  centre  of  the  earth,  we  should  find  matter  without  weight, 
although  its  other  properties  would  remain  unchanged.  A  bullet  fired  from 
a  gun,  although  weightless,  would  have  the  same  effect  as  at  the  surface  of 
the  earth,  this  effect  being  dependent,  as  will  be  shown,  upon  the  amount  of 
matter  (mass)  in  the  bullet  and  the  velocity  imparted,  and  having  no  relation 
whatever  to  the  weight  of  the  bullet.  A  pound  of  sugar  at  the  centre  of  the 
earth  would  have  precisely  the  same  sweetening  properties  as  at  the  surface. 
The  commercial  value  of  provisions,  drugs,  &c.,  is  therefore  strictly  propor- 
tional to  the  number  of  units  of  mass  purchased,  and  has  no  necessary  rela- 
tion to  the  weights  of  those  masses. 

It  is  also  to  be  observed  that,  if  masses  are  counterpoised  on  a  lever 
balance  at  any  one  locality,  they  would  remain  balanced  at  any  other  point, 
since  the  weights  of  the  masses  would  change  in  the  same  ratio.  Hence 
the  lever  balance  with  standard  '  weights '  really  measures  the  mass  of  a 
body,  and  not  its  weight,  and  the  standard  '  weights '  should  really  be  called 
masses.  A  spring  balance  determines  weight  and  not  mass,  since  its  indi- 
cations change  as  the  weight  of  the  mass  changes. 

At  the  centre  of  the  earth,  masses  could  not  be  determined  by  means  of 
a  balance,  since  they  weigh  nothing,  and  any  mass  would  counterpoise  any 
other  mass. 

27.  Measure  of  Force. —  In  devising  a  unit  in  wrhich  to  measure  force,  it  is 
most  convenient  to  make  use  of  the  attractive  force  of  the  earth.    Suppose  that 
two  equal  masses,  P,  are  balanced  on  a  pulley  with  fixed  axle,  that  the  string 
and  pulley  are  without  mass,  and  that  there  is  no  friction  or 
^   ^\          air-resistance.    The  masses  P  are  then  perfectly  inert.     The 
•  tension  on  the  string  is  the  pull  of  the  earth  on  one  of  the  masses 
P,  or,  in  other  words,  the  weight  of  P.     If  the  pulley  is  started 
by  a  force  which  then  ceases  to  act,  the  masses  will  thereafter 
move  uniformly  according  to  the  first  law  of  motion,  the  tension 
•     on  the  string  being,  as  before,  the  weight  of  P.    This  will  all  be 
true,  whatever  may  be  the  amount  of  matter  in  the  masses  P. 
P  If,  now,  the  masses  P  being   at  rest,  an  additional    mass  m 

Fig.  4.  be  placed  on  one  side,  the  system  will  begin  to  move.     The 

tension  on  the  string  is  now  greater  than  the  weight  of  P,  and 
less  than  the  weight  of  P  +  m.  The  force  which  causes  the  motion  is  the 
pull  of  the  earth  on  w,  or  the  weight  of  the  added  mass.  The  motion  is 


_27]  Measure  of  Force.  1 5 

now  uniformly  accelerated.  At  the  instant  of  starting,  the  velocity  is  zero. 
At  the  end  of  the  first  second,  the  velocity  will  be — say  a  \  at  the  end  of 
the  second  second,  2a  ;  and  at  the  end  of/  seconds,  the  velocity  will  be  at. 
The  increase  in  the  velocity  per  second  is  «,  which  is  called  the  accelera- 
tion. 

If  the  mass  m  be  entirely  disconnected  from  the  masses  P  and  allowed 
to  fall  freely,  it  also  falls  with  an  uniformly  accelerated  motion  ;  but  experi- 
ment shows  that  the  acceleration  is  greater  than  in  the  former  case.  This 
acceleration  of  a  freely  falling  body  is  usually  denoted  by  g.  The  force 
which  causes  the  motion  is,  however,  the  same  as  before,  being  the  weight 
of  m.  The  difference  in  the  two  cases  is,  that,  in  the'  latter  case,  the  pull  of 
the  earth  on  in  is  employed  in  setting  in  motion  the  mass  m  only ;  while,  in 
the  former  case,  the  two  inert  masses  P  are  attached  to  ;;z,  and  are  con- 
strained to  move  with  it,  the  mass  to  be  moved  being  thus  increased  without 
a  corresponding  increase  of  the  force  employed  in  moving. 

It  is  evident  that  if  the  masses  P  should  diminish  to  zero,  or  the  mass  m 
should  increase  until  it  became  very  large,  or  infinite,  the  weight  of  m  would 
impart  a  greater  and  greater  acceleration,  until  finally  the  acceleration 
would  become  g.  On  the  other  hand,  if  the  masses  P  should  become  very 
large,  or  infinite,  or  the  mass  ;;z  very  small,  or  zero,  the  acceleration  would 
become  zero.  It  is  shown  by  experiment  that  if  the  mass  m  is  made  n 
times  as  great  (so  that  the  moving  force  is  n  times  as  great),  and  the  masses 
P  are  equally  diminished — so  that  2P  +  m  is  unchanged — the  acceleration 
becomes  n  times  as  great,  so  that,  the  mass  to  be  moved  being  unchanged, 
the  acceleration  is  directly  proportional  to  the  force  applied.  If,  however, 
the  mass  m  be  made  n  times  as  great,  and  it  is  desired  to  have  the  accelera- 
tion remain  unchanged,  it  is  found  that  the  masses  P  must  be  equally 
increased  in  such  a  way  that  2P  +  m  has  also  become  n  times  as  great. 
This  shows  that,  the  acceleration  remaining  constant,  the  force  applied  must 
change  in  the  same  ratio  as  the  mass. 

From  these  experiments  it  follows  that  if  any  force  F  is  applied  in  giving 
uniformly  accelerated  motion  to  a  mass  M,  the  acceleration  being  a,  then 

F-KM*. 

Here  M  is  measured  in  pounds,  and  the  acceleration  a  measures  the 
change  in  velocity  of  M  in  feet  per  second*.  K  is  a  constant,  the  numerical 
value  of  which  will  depend  upon  the  unit  which  we  now  adopt  in  which  to 
measure  F.  If,  as  is  customary,  we  adopt  as  the  unit  force  that  force  which 
will  make  a  =  I  when  M  =  i,  then  we  at  the  same  time  necessarily  make  the 
remaining  quantity  K  in  the  last  equation  equal  to  I ;  and,  measured  in  these 

UnitS'  F-Ma. 

The  unit  force  is  then  that  force  which  can  impart  unit  acceleration  to 
unit  mass. 

If  V  represent  the  initial  velocity  of  a  body,  and  v  its  final  velocity,  the 
change  in  velocity  having  taken  place  in  t  seconds,  then  the  change  per 
second  is 

v—v 


]  6  On  Matter,  Force,  and  Motion.  [27- 

This  value  of  a  in  the  previous  equation  gives 


28.  Momentum.  —  It  thus  appears  that  the  number  of  units  of  force   in 
any  force  which,  acting  for  t  seconds  on  amass  M,  is  capable  of  changing  its 
velocity  from  V  to  •z/,  is  measured  by  the  change  per  second  in  the  product 
Mz'.     This  quantity  Mz/,  being  thus  an  important  one,  has  received  a  special 
name—  momenbun.     We  may  now  say  that  the  number  of  units  in  a  force  is 
measured  ^H  ^Kb°J^>e  in  momentum  which  it  can  produce  per   second, 
which  is  the  iMHan|Kf  Newton's  second  law  of  motion. 

29.  Acceleration  of  Gravity.  —  At   London,   the  force  with  which  the 
earth  attracts  a  pound  of  matter  is  capable  of  imparting  to  the  pound  an 
acceleration  of  32-1912.     At  other  places,  the  acceleration  is  different,  and 
may  be  denoted  by  g.     Hence,  at  London,  the  weight  of  a  pound,  expressed 
in  the  units  which  we  have  chosen  for  measuring  forces,  will  be  32'  191  2.     At 
any  othet  poinr  on  the  earth,  or  in  the  interior  of  the  earth,  or  at  any  point 
outside,  where  the  acceleration  of  a  falling  body  is  g,  the  number  of  units  of 
force  in  the  weight  of  a  pound  is  g.     The  number  w  of  units  of  force  in  the 
weight  of  in  pounds  is  given  by  the  equation 

<w  =  mg. 

If  at  some  point  where  the  acceleration  is  32  it  is  found  that  the  weight 
of  10  lb.,  or  320  units  of  force,  is  sufficient  to  serve  as  the  driving-weight  to 
a  certain  clock,  then  at  some  other  point,  where  the  acceleration  is  16,  it 
would  be  necessary  to  use  the  weight  of  20  lb.  in  order  to  secure  the  same 
effect. 

The  weight  of  -  -  —  lb.,  or  0-49  oz.  at  London,  is  a  unit  of  force.     At 
32-1912 

any  other  point,  where  the  acceleration  is  g,  the  weight  of  -  lb.  is  the  unit  of 

& 

force.  Where  great  accuracy  is  not  required,  it  is  customary  to  take  the 
weight  of  the  pound  as  the  unit  of  force,  and  then  the  intensity  of  the  force 
is  given  in  pounds  weight,  a  unit  which  varies  slightly  for  different  places  on 
the  earth,  as  g  varies.  In  like  manner,  for  ordinary  purposes,  a  land 
surveyor  does  not  find  it  necessary  to  make  corrections  for  the  varying 
length  of  his  chain  due  to  changes  in  temperature,  although  such  correc- 
tions are  highly  important  in  the  more  refined  operations  of  a  geodetic 
survey. 

Pendulum  observations  (79)  show  that  at  any  given  place  the  acceleration 
of  a  falling  body  is  constant,  but  it  is  found  to  have  different  values  at  dif- 
ferent places  ;  adopting  the  units  of  feet  and  seconds,  it  is  found  that  very 
approximately 

g=gf(\  —0-00256  cos  20), 

at  a  station  whose  latitude  is  (/>,  where  g'  denotes  the  number  32-1724,  or 
the  value  of^-at  lat.  45°. 

Experience  teaches  that  in  all  cases  where  a  force  is  exerted  there  must 
be  two  bodies,  between  which  the  force  acts.  Newton's  third  law  asserts 


-30]  Representation  of  Forces.  iy 

that  the  mutual  action  of  the  two  bodies  is  always  equal  and  oppositely 
directed. 

The  attraction  of  the  earth  for  m  pounds  of  matter  is  ing,  where  g  is  the 
acceleration  of  the  body.  The  attraction  of  the  m  pounds  for  the  earth  is 
M  <z,  where  M  is  the  mass  of  the  earth  in  pounds,  and  a  is  the  acceleration 
with  which  it  moves  towards  m.  According  to  the  third  law  of  motion 

Ma  =  mg. 

If  m  is  a  small  body,  like  a  few  thousand  pounds,  since  the  mass  of  the 
earth  is  very  large,  the  acceleration  of  the  earth  will  be  inappreciable.  If  m 
and  M  were  equal,  a  and  g  would  be  equal.  Renumbering  that  the  accele- 
ration is  the  change  per  second  in  the  velocity,  if  the  two  bodies  move 
towards  each  other  for  /  seconds,  the  initial  velocities  being  Vx  arid  Va,  and 
the  final  velocities  iul  and  z/0,  the  above  expression  becomes 

MrV—  M  VT  _  ;;z?/0  -  mV '„ 
t  t 

As  t  divides  out  of  this  equation,  it  will  follow  that  the  two  bodies  which 
mutually  attract  each  other  will  suffer  equal  changes  of  momenta  in  the 
same  time.  If  the  two  bodies  start  from  rest  at  the  same  instant,  so  that  V1 
and  V2  are  zero,  then 

Mz/!  =  mVn 

or  they  will  have  equal  momenta  at  the  same  instant.  The  momenta  of  a 
freely-suspended  rifle  and  a  bullet  fired  from  it  will  be  equal  so  long  as  the 
ball  is  in  the  barrel.  If  the  rifle  is  supported,  the  supporting  body  must  be 
included  with  the  rifle  in  the  value  M. 

30.  Representation  of  forces. — Draw  any  straight  line  AB  (fig.  5),  and 
fix  on  any  point  O  in  it.  We  may  suppose  a  force  to  act  on  the  point  O, 
along  the  line  AB,  either  towards  A  or  B  :  then  O  is 

called  \ht  point  of  application  of  the  force,  AB  its  line  B  5J  5  5  A 
of  action  ;  if  it  acts  towards  A,  its  direction  is  OA,  if  F;g  5> 

towards  B,  its  direction  is  OB.    It  is  rarely  necessary 

to  make  the  distinction  between  the  line  of  action  and  direction  of  a  force  ; 
it  being  very  convenient  to  make  the  convention  that  the  statement — a  force 
acts  on  a  point  O  along  the  line  OA — means  that  it  acts  from  O  to  A.  Let 
us  suppose  the  force  which  acts  on  O  along  OA  to  contain  P  units  of  force  ; 
from  O  towards  A  measure  ON,  containing  P  units  of  length,  the  line  ON  is 
said  to  represent  the  force.  The  analogy  between  the  line  and  the  force  is 
very  complete  ;  the  line  ON  is  drawn  from  O  in  a  given  direction  OA,  and 
contains  a  given  number  of  units  P,  just  as  the  force  acts  on  O  in  the  direc- 
tion OA,  and  contains  a  given  number  of  units  P.  It  is  scarcely  necessary 
to  add,  that  if  an  equal  force  were  to  act  on  O  in  the  opposite  direction,  it 
would  be  said  to  act  in  the  direction  OB,  and  would  be  represented  by  OM, 
equal  in  magnitude  to  ON. 

When  we  are  considering  several  forceps  acting  along  the  same  line  we 
may  indicate  their  directions  by  the  positive  and  negative  signs.  Thus  the 
forces  mentioned  above  would  be  denoted  by  the  symbols  +  P  and  —  P 
respectively. 

c 


1 8  On  Matter,  Force,  and  Motion.  [31- 

31.  Torces  acting-  along-  the  same  line. — If  forces  act  on  the  point  O 
in  the  direction  OA  equal  to  P  and  O  units  respectively,  they  are  equivalent 
to  a  single  force  R  containing  as  many  units  as  P  and  O  together — that  is, 

R  =  P  +  O. 

If  the  sign  +  in  the  above  equation  denote  algebraical  addition,  the  equation 
will  continue  true  whether  one  or  both  the  forces  act  along  OA  or  OB.  It 
is  plain  that  the  same  rule  can  be  extended  to  any  number  of  forces,  and  if 
several  forces  have  the  same  line  of  action,  they  are  equivalent  to  one  force 
containing  the  same  number  of  units  as  their  algebraical  sum.  Thus  if 
forces  of  3  and  4  units  act  on  O  in  the  direction  OA,  and  a  force  of  8  in  the 
direction  OB,  they  are  equivalent  to  a  single  force  containing  R  units  given 
by  the  equation 

R=3+4-8=   _i ; 

that  is,  R  is  a  force  containing  one  unit  acting  along  OB.  This  force  R  is 
called  their  resultant.  If  the  forces  are  in  equilibrium  R  is  equal  to  zero. 
In  this  case  the  forces  have  equal  tendencies  to  move  the  point  O  in  opposite 
directions. 

32.  Resultant  and  components. — In  the  last  article  we  saw  that  a  single 
force  R  could  be  found  equivalent  to  several  others  ;  this  is  by  no  means 
peculiar  to  the  case  in  which  all  the  forces  have  the  same  line  of  action  ;  in 

fact,  when  a  material  point,  A  (fig.  6),  remains  in  equili- 
brium under  the  action  of  several  forces,  S,  P,  O,  it  does 
so  because  any  one  of  the  forces,  as  S,  is  capable  of 
neutralising  the  combined  effects  of  all  the  others.  If  the 
force  S,  therefore,  had  its  direction  reversed,  so  as  to  act 
along  AR,  the  prolongation  of  AS,  it  would  produce  the 
same  effect  as  the  system  of  forces  P,  Q. 

Now,  a  force  whose  effect  is  equivalent  to  the  combined 
effects  of  several  other  forces  is  called  their  resultant,  and 
with  respect  to  this  resultant,  the  other  forces  are  termed 
components. 

p\        When  the  forces  P,  Q  act  on  a  point  they  can  only 
Fig.  6.  have  one  resultant  ;  but  any  single  force  can  be  resolved 

into  components  in  an  indefinite  number  of  ways/ 

If  a  point  move  from  rest,  under  the  action  of  any  number  of  forces,  it 
will  begin  to  move  in  the  direction  of  their  resultant. 

33.  Parallelogram  of  forces. — When  two  forces  act  on  a  point  their 
resultant  is  found  by  the  following  theorem,  known  as  the  principle  of  the 
parallelogram  of  forces  : — If  two  forces  act  on  a  point,  and  if  lines  be  drawn 
from  that  point  representing  the  forces  in  magnitude  and  direction,  and  a 
parallelogram  be  constructed  on  these  lines  as  sides,  their  resultant  will  be 
represented  inmagnitude  and  direction  by  that  diagonal  which  passes  through 
the  point.  Thus  let  P  and  O  (fig.  7)  be  two  forces  acting  on  the  point  A 
along  AP  and  AQ  respectively,  and  let  AB  and  AC  be  taken  containing  the 
same  number  of  units  of  length  that  P  and  Q  contain  units  of  force  ;  let  the 
parallelogram  ABDC  be  completed,  and  the  diagonal  AD  drawn  ;  then  the 
theorem  states  that  the  resultant,  R,  of  P  and  Q  is  represented  by  AD  ;  that 
is  to  say,  P  and  O  together  are  equal  to  a  single  force  R  acting  along  the 


-33] 


Parallelogram  of  Forces. 


line  AD,  and  containing  as  many  units  of  force  as  AD  contains  units  of 
length. 

Proofs  of  this  theorem  are  given  in  treatises  on  Mechanics  ;  we  will  here 
give  an  account  of  a  direct  experimental  verification  of  its  truth  ;  but  before 
doing  so  we  must  premise  an  account  of  a  very  simple  experiment. 

Let  A  (fig.  8)  be  a  small  pulley,  and  let  it  turn  on  a  smooth,  hard,  and 
thin  axle  with  little  or  no  friction  :  let  W  be  a  weight  tied  to  the  end  of  a 
fine  thread  which  passes  over  the  pulley  :  let  a  spring  CD  be  attached  by 
one  end  to  the  end  C  of  the  thread  and  by  the  end  D  to  another  piece  of 
thread,  the  other  end  of  which  is  fastened  to  a  fixed  point  B  ;  a  scale  CE 
can  be  fastened  by  one  end  to  the  point  C  and  pass  inside  the  spring  so  that 
the  elongation  of  the  spring  can  be  measured.  Now  it  will  be  found  on  trial 
that  with  a  given  weight  W  the  elongation  of  the  spring  will  be  the  same 
whatever  the  angle  contained  between  the  parts  of  the  string  WA  and  BA. 


W 


Fig.  7. 


Fig.  8. 


Also  it  would  be  found  that  if  the  whole  were  suspended  from  a  fixed  point, 
instead  of  passing  over  the  pulley,  the  weight  would  in  this  case  stretch  the 
spring  to  the  same  extent  as  before.  This  experiment  shows  that  when  care 
is  taken  to  diminish  to  the  utmost  the  friction  of  the  axle  of  the  pulley,  and 
the  imperfect  flexibility  of  the  thread,  the  weight  of  W  is  transmitted  with- 
out sensible  diminution  to  B,  and  exerts  on  that  point  a  pull  or  force  along 
the  line  BA  virtually  equal  to  W. 

This  being  premised,  an  experimental  proof,  or  illustration  of  the  paral- 
lelogram of  forces,  may  be  made  as  follows  : — 

Suppose  H  and  K  (fig.  9)  to  be  two  pulleys  with  axles  made  as  smooth 
and  fine  as  possible ;  let  P  and  Q  be  two  -weights  suspended  from  fine  and 
flexible  threads  which,  after  passing  over  H  and 
K,  are  fastened  at  A  to  a  third  thread  AL,  from 
which  hangs  a  weight  R  ;  let  the  three  weights 
come  to  rest  in  the  positions  shown  in  the  figure- 
Now  the  point  A  is  acted  on  by  three  forces  in 
equilibrium — viz.  P  from  A  to  H,  Q  from  A  to 
K,  and  R  from  A  to  L,  consequently  any  orie  of 
them  must  be  equal  and  opposite  to  the  resul- 
tant of  the  other  two.  Now  if  we  suppose  the 
apparatus  to  be  arranged  immediately  in  front 
of  a  large  slate,  we  can  draw  lines  upon  it  coinciding  with  AH,  AK,  and  AL. 
If  now  we  measure  off  along  AH  the  part  AB  containing  as  many  inches  as 

c  2 


Fig.  9. 


20 


On  Matter,  Force,  and  Motion. 


[33- 


P  contains  pounds,  and  along  AK  the  part  AC  containing  as  many  inches  as 
O  contains  pounds,  and  complete  the  parallelogram  ABCD,  it  will  be  found 
that  the  diagonal  AD  is  in  the  same  line  as  AL,  and  contains  as  many  inches 
as  R  weighs  pounds.  Consequently,  the  resultant  of  P  and  O  is  represented 
by  AD.  Of  course,  any  other  units  of  length  and  force  might  have  been 
employed.  Now  it  will  be  found  that  when  P,  Q,  and  R  are  changed  in 
any  way  whatever,  consistent  with  equilibrium,  the  same  construction  can  be 
made — the  point  A  will  have  different  positions  in  the  different  cases  ;  but 
when  equilibrium  is  established,  and  the  parallelogram  ABCD  is  constructed, 
it  will  be  found  that  AD  is  vertical,  and  contains  as  many  units  of  length  as 
R  contains  units  of  force,  and  consequently  it  represents  a  force  equal  and 
opposite  to  R — that  is,  it  represents  the  resultant  of  P  and  O. 

34.  Resultant  of  any  number  of  forces    acting-  in  one  plane  on  a 
point. — Let  the  forces  P,  O,  R,  S  (fig.  10)  act  on  the  point  A,  and  let  them 

be  represented  by  the  lines  AB,  AC,  AD,  AE,  as 
shown  in  the  figure.  First,  complete  the  parallelo- 
gram ABFC  and  join  AF  ;  this  line  represents  the 
resultant  of  P  and  Q..  Secondly,  complete  the 
parallelogram  AFGD  and  join  AG  ;  this  line  re- 
presents the  resultant  of  P,  0,  R.  Thirdly,  com- 
plete the  parallelogram  AGHE  and  join  AH  ;  this 
line  represents  the  resultant  of  P,  Q,  R,  S.  It  is 
manifest  that  the  construction  can  be  extended  to 
any  number  of  forces.  A  little  consideration  will 
show  that  the  line  AH  might  be  determined  by  the 
following  construction  :— Through  B  draw  BF 
parallel  to,  equal  to,  and  towards  the  same  part  as  AC ;  through  F  draw 
FG  parallel  to,  equal  to,  and  towards  the  same  part  as  AD ;  through  G  draw 
GH  parallel  to,  equal  to,  and  towards  the  same  part  as  AE  ;  join  AH,  then 
AH  represents  the  required  resultant.  >/ 

35.  Triangle  of  Forces. — If  the  resultant  of  the  forces  is  zero,  they  have 
no  joint  tendency  to  move  the  point,  and  consequently  are  in  equilibrium. 

The  case  of  three  forces  acting  on  a  point  is  of  such  importance  that  we 
may  give  a  brief  statement  of  it.  Let  P,  Q,  R  (fig.  12)  be  three  forces  in 
equilibrium  on  the  point  O.  From  any  point  B  draw  BC 
parallel  to  and  towards  the  same  part  as  OP,  from  C  draw 
CA  parallel  to  and  towards  the  same  part  as  OO,  and 
take  CA  such  that  P  :  Q::  BC  :  CA ;  then,  on  joining 
AB,  the  third  force  R  must  act  along  OR  parallel  to  and 
towards  the  same  part  as  AB,  and  must  be  proportional 
in  magnitude  to  AB.  This  construction  is  frequently 
called  the  Triangle  of  Forces.  It  is  evident  that  while 
the  sides  of  the  triangle  are  severally  proportional  to  P, 
Q,  R,  the  angles  A,  B,  C  are  supplementary  to  QOR, 
ROP,  POQ  respectively  ;  consequently,  "every  trigono- 
metrical relation  existing  between  the  sides  and  angles  of  ABC  will  equally 
exist  between  the  forces  P,  Q,  R,  and  the  supplements  of  the  angles  between 
their  directions.  Thus  in  the  triangle  ABC  it  is  known  that  the  sides  are 
proportional  to  the  sines  of  the  opposite  angles  ;  now,  since  the  sines  of  the 


Fig.  ii. 


-37]       Composition  and  Resolution  of  Parallel  Forces.  2 1 

angles  are  equal  to  the  sines  of  their  supplements,  we  at  once  conclude  that 
when  three  forces  are  in  equilibrium,  each  is  proportional  to  the  sine  of  the 
angle  between  the  directions  of  the  other  two. 

y  36.  Moments  of  Forces. — Let  P  (fig.  12)  denote  any  force  acting  from  B 
to  P,  take  A  any  point,  let  fall  AN  a  perpendicular  from  A  on  BP.  The 
product  of  the  number  of  units  of  force  in  P,  and  the  number  of  units  of 
length  in  AN,  is  called  the  moment  of  P  with  respect  to  A.  Since  the  force 
P  can  be  represented  by  a  straight  line,  the  moment  of  P  can  be  represented 
by  an  area.  In  fact,  if  BC  is  the  line  representing  P,  the  moment  is  properly 
represented  by  twice  the  area  of  the  triangle  ABC.  The  perpendicular  AN 
is  sometimes  called  the  arm  of  the  pressure.  Now  if  a  watch  were  placed 
with  its  face  upwards  on  the  paper,  the  force  P  would  cause  the  arm  AN  to 
turn  round  A  in  the  contrary  direction  to  the  hands  of  the 
watch.  Under  these  circumstances,  it  is  usual  to  con- 
sider the  moment  of  P  with  respect  to  the  point  A  to  be 
positive.  If  P  acted  from  C  to  B,  it  would  turn  NA  in 
the  same  direction  as  the  hands  of  the  watch,  and  now  its 
moment  is  reckoned  negative. 

It  is  a  simple  geometrical  consequence  of  the  paral- 
lelogram of  forces  (33)  that  the  moment  of  the  resultant 
equals  the  sum  of  the  moments  of  the  component  forces,  regard  being  had  to 
the  signs  of  the  moments. 

If  the  point  about  which  the  moments  are  measured  be  taken  in  the  direc- 
tion of  the  resultant,  its  moment  with  respect  to  that  point  will  be  zero  ;  and 
consequently  the  sum  of  the  moments  with  respect  to  such  point  will  be  zero. 

37.  Composition  and  resolution  of  parallel  forces. — The  case  of  the 
equilibrium  of  three  parallel  forces  is  merely  a  particular  case  of  the  equili- 
brium of  three  forces  acting  on  a  point.  In  fact,  let 
P  and  Q  be  two  forces  whose  directions  pass  through 
the  points  A  and  B,  and  intersect  in  O  ;  let  them  be 
balanced  by  a  third  force  R  whose  direction  produced 
intersects  the  line  AB  in  C.  Now  suppose  the  point 
O  to  move  along  AO,  gradually  receding  from  A,  the 
magnitude  and  direction  of  R  will  continually  change, 
and  also  the  point  C  will  continually  change  its 
position,  but  will  always  lie  between  A  and  B.  In  the 
limit  P  and  Q  become  parallel  forces,  acting  towards 
the  same  part  balanced  by  a  parallel  force  R  acting 
towards  the  contrary  part  through  a  point  X  between 
A  and  B.  The  question  is  : — First,  in  this  limiting 


Fig.  13. 


case,  what  is  the  value  of  R  ;  secondly,  what  is  the  position  of  X  ?  Now  with 
regard  to  the  first  point  it  is  plain  that  if  a  triangle  abc  be  drawn  as  in  art. 
35,  the  angles  a  and  b  in  the  limit  will  vanish,  and  c  will  become  180°, 
consequently  ab  ultimately  equals  ac  +  cb  ; 


or 


R  =  P  +  Q. 

With  regard  to  the  second  point  it  follows  from  last  article  (36)  that  the 
moments  of  P  and  Q  about  C  are  always  equal,  whence 

.      AX:XB::Q:P, 


22  On  Matter,  Force,  and  Motion.  [37- 

a  proportion  which  determines  the  position  of  X.    Hence  the  following  rules 
for  the  composition  of  any  two  parallel  forces,  viz. — 

I.  When  two  parallel  forces  P  and  O  act  towards  the  same  part,  at  rigidly 
connected  points  A  and  B,  their  resultant  is  a  parallel  force  acting  towards 
the  same  part,  equal  to  their  sum,  and  its  direction  divides  the  line  AB 
into  two  parts  AC  and  CB  inversely  proportional  to  the  forces  P  and  O. 

II.  When  two    parallel  forces   P  and   Q  act  towards    contrary  parts 
at  rigidly  connected  points  A   and    B,    of  which   P  is    the   greater,    their 
resultant  is  a  parallel  force  acting  towards  the  same  part  as  P,  equal  to  the 
excess  of  P  over  Q,  and  its  direction  divides  BA  produced  in  a  point  C  such 
that  CA  and  CB  are  inversely  proportional  to  P  and  Q. 

In  each  of  the  above  cases  if  we  were  to  apply  R  at  the  point  C,  in 
opposite  directions  to  those  shown  in  the  figure,  it  would  plainly  (by  the  above 
theorem)  balance  P  and  O,  and  therefore  when  it  acts  as  shown  in  figs.  14 
and  15  it  is  the  resultant  of  P  and  Q  in  those  cases  respectively.  It  will,  of 
course,  follow  that  the  force  R  acting  at  C  can  be  resolved  into  P  and  Q 
acting  at  A  and  B  respectively. 


Fig.  14-.  Fig.  15. 

If  the  second  of  the  above  theorems  be  examined,  it  will  be  found  that 
no  force  R  exists  equivalent  to  P  and  Q  when  these  forces  are  equal.  Two 
such  forces  constitute  a  couple,  which  may  be  defined  to  be  two  equal  parallel 
forces  acting  towards  contrary  parts  ;  they  possess  the  remarkable  property 
that  they  are  incapable  of  being  balanced  by  any  single  force  whatsoever. 

In  the  case  of  more  than  two  parallel  forces  the  resultant  of  any  two  can 
be  found,  then  of  that  and  a  third,  and  so  on  to  any  number  ;  it  can  be 
shown  that  however  great  the  number  of  forces  they  will  either  be  in  equili- 
brium or  will  reduce  to  a  single  resultant  or  to  a  couple. 

38.  Centre  of  parallel  forces.— On  referring  to  figs.  14  and  15,  it  will 
be  remarked  that  if  we  conceive  the  points  A  and  B  to  be  fixed  in  the 
directions  AP  and  BQ  of  the  forces  P  and  Q,  and  if  we  suppose  those 
directions  to  be  turned  round  A  and  B,  so  as  to  continue  parallel  and  to 
make  any  given  angle  with  their  original  directions,  then  the  direction  of 
their  resultant  will  continue  to  pass  though  C  ;  that  point  is  therefore  called 
the  centre  of  the  parallel  forces  P  and  Q. 

It  appears  from  investigation,  that  whenever  a  system  of  parallel  forces 
reduces  to  a  single  resultant,  those  forces  will  have  a  centre ;  that  is  to  say, 
if  we  conceive  each  of  the  forces  to  act  at  a  fixed  point,  there  will  be  a  point 


-40] 


The  Lever. 


through  which  the  direction  of  their  resultant  will  pass  when  the  directions 
of  the  forces  are  turned  through  any  equal  angles  round  their  points  of 
application  in  such  a  manner  as  to  retain  the  parallelism  of  their  directions. 
The  most  familiar  example  of  a  centre  of  parallel  forces  is  the  case  in 
which  the  forces  are  the  weights  of  the  parts  of  a  body  ;  in  this  case  the 
forces  all  acting  towards  the  same  part  will  have  a  resultant,  viz.  their  sum  ; 
and  their  centre  is  called  the  centre  of  gravity  of  the  body. 

39.  Equality  of  action  and  reaction. — We  will  proceed   to  exemplify 
some  of  the  principles  now  laid  down  by  investigating  the  conditions   of 
equilibrium  of  bodies  in  a  few  simple  cases  ;  but  before  doing  so  we  refer 
again  to  the  law  stated  in  art.  (29)  and  which  holds  good  whenever  a  mutual 
action  is  called  into  play  between  two  bodies.     Reaction  is  always  equal  and 
contrary  to  action :  that  is  to  say,  the  mutual  actions  of  two  bodies  on  each 
other  are  always  forces  equal  in  amount  and  opposite  in  direction,  and  is 
equally  true  when  the  bodies  are  in  motion  as  well  as  when  they  are  at  rest. 
A  very  instructive  example  of  this  law  has  already  been  given  (33),  in  which 
the  action  on  the  spring  CD   (fig.  7)  is  the  weight  W  transmitted  by  the 
spring  to  C,  and  balanced  by  the  reaction  of  the  ground  transmitted  from  B 
to  D.     Under  these  circumstances  the  spring  is  said  to  be  stretched  by  a 
force  W.     If  the  spring  were  removed,  and  the  thread  were  continuous  from 
A  to  B,  it  is  clear  that  any  part  of  it  is  stretched  by  two  equal  forces,  viz.  an 
action  and  reaction,  each  equal  to  W,  and  the  thread  is  said  to  sustain  a 
tension  W.     When  a  body  is  urged  along  a  smooth  surface,  the  mutual 
action  can  only  take  place  along  the  common  perpendicular  at  the  point  of 
contact.     If,  however,  the  bodies  are  rough,  this  restriction  is  partially  re- 
moved, and  now   the  mutual  action  can  take  place  in  any  direction  not 
making  an  angle  greater  than  some  determinate  angle  with  the  common 
perpendicular.      This  determinate  angle  has  different  values  for  different 
substances,  and  is  sometimes  called  the  limiting  angle  of  resistance,  some- 
times the  angle  of  repose. 

40.  The  lever  is  a  name  given  to  any  bar  straight  or  curved,  AB  (fig.  16) 
resting  on  a  fixed  point  or  edge  c  called  the  fulcrum.     The  forces  acting  on 
the  lever  are  the  weight  or  resistance  O, 

the  power  P,  and  the  reaction  of  the 
fulcrum.  Since  these  are  in  equilibrium, 
the  resultant  of  P  and  Q  must  act  through 
c,  for  otherwise  they  could  not  be  balanced 
by  the  reaction.  Draw  cb  at  right  angles 
to  QB  and  ca  to  PA  produced ;  then 
observing  that  P  x  ca,  and  Q  x  cb  are  the 
moments  of  P  and  Q  with  respect  to  c, 
and  that  they  have  contrary  signs,  we 
have  by  (36), 

P  x  ca  -=  O  y  cb  ; 

an  equation  commonly  expressed  by  the 
rule,  that  in  the  lever  the  power  is  to  the 
weight  in  the  inverse  ratio  of  their  arms. 

Levers  are  divided  into  three  kinds,  according  to  the  position  of  the 


On  Matter,  Force,  and  Motion. 


[40- 


fulcrum  with  respect  to  the  points  of  application  of  the  power  and  the  weight. 
In  a  lever  of  the  first  kind  the  fulcrum  is  between  the  power  and  resistance, 
as  in  fig.  1 6,  and  as  in  a  poker  and  in  the  common  steelyard  ;  a  pair  of 
scissors  and  a  carpenter's  pincers  are  double  levers  of  this  kind.  In  a  lever 
of  the  second  kind  the  resistance  is  between  the  power  and  the  fulcrum,  as  in 
a  wheelbarrow,  or  a  pair  of  nutcrackers,  or  a  door  ;  in  a  lever  of  the  third 
kind  the  power  is  between  the  fulcrum  and  the  resistance,  as  in  a  pair  of 
tongs  or  the  treadle  of  a  lathe.  ' 

41.  Pulleys. — The  pulley  is  a  hard  circular  disc  of  wood  or  of  metal,  in 
the  edge  of  which  is  a  groove,  and  which  can  turn  freely  on  an  axis  in  the 
centre.  Pulleys  are  either  fixed,  as  in  fig.  17,  where  the  stirrup  or  fork  is 
rigidly  connected  with  some  immovable  body,  and  where  the  axis  rotates  in 
the  stirrup  ;  or  it  may  be  movable,  as  in  fig.  18,  where  the  axis  is  fixed  to 
the  fork,  and  it  passes  through  a  hole  in  the  centre  of  the  disc.  The  rope 
which  passes  round  the  pulley  in  fig.  1 7,  supports  a  weight  at  one  end  •  while 
at  the  other  a  pull  is  applied  to  hold  this  weight  in  equilibrium. 

We  may  look  upon  the  power  and  the  resistance  as  acting  at  the  circum- 
ference of  the  circle  ;  hence  as  the  radii  are  equal,  if  we  consider  the  pulley 

as  a  lever,  the  two  arms 
are  equal,  and  equilibrium 
will  prevail  when  the  power 
and  the  resistance  are  equal. 
The  fixed  pulley  affords  thus 
no  mechanical  advantage, 
but  is  simply  convenient  in 
changing  the  direction  of 
the  application  of  a  force. 

In  the  case  of  the  mov- 
able pulley  one  end  of  the 
rope  is  suspended  to  a  fixed 
point  in  a  beam,  and  the 
weight  is  attached  to  the 
hook  on  which  the  pulley 
acts.  The  tension  of  the 
rope  is  everywhere  the  same ; 
one  portion  of  the  weight 
is  supported  by  the  fixed 
part  and  the  other  by  the  power,  and  these  are  equal  to  each  other,  and 
are  together  equal  to  the  weight,  including  the  pulley  itself ;  hence  in  this 
case  P  =  i  Q. 

If  several  pulleys  are  joined  together  on  a  common  axis  in  a  special 
sheath,  which  is  fixed,  and  a  rope  passes  round  all  those  and  also  round  a 
similar  but  movable  combination  of  pulleys,  such  an  arrangement,  which  is 
represented  in  fig.  19,  is  called  a  block  and  tackle. 

If  we  consider  the  condition  of  the  rope  it  will  be  found  to  have  every- 
where  the   same  tension  ;    the  weight  Q  which  is   attached  to  the  hook 
common  to  the  whole  system  is  supported  by  the  six  portions  of  the  rope  ;  . 
hence  each  of  these  portions  will  sustain  one  sixth  of  the  weight ;  the  force 
which  is  applied  at  the  free  end  of  the  rope  which  passes  over  the  upper 


Fig.  17. 


Fig.  18. 


-42]  Wheel  and  Axle.  2$ 

pulley,  and  which  determines  the  tension,  will  have  the  same  value  ;  that  is 
to  say,  it  will  support  one  sixth  of  the  weight. 

The  relation  between  power  and  resistance  in  a  block  and  tackle  is 

expressed  by  the  equation  P  =  -^,  in  which  P  is  the  power,  Q  the  weight, 


and  11  the  number  of  cords  by  which  the  weight  is  supported. 

42.  The  wheel  and  axle. — The  older  form  of  this  machine,  fig.  20,  is 
that  of  an  axle,  to  which  is  rigidly  fixed,  concentric  with  it,  a  wheel  of  larger 
diameter.  The  power  is  applied  tangentially  on  the  wheel,  and  the  resistance 
tangentially  to  the  axle,  as  for  instance  in  the  treadmill  and  water-wheel. 
Sometimes,  as  in  the  case  of  the  capstan,  the  power  is  applied  to  spokes 
fixed  in  the  axle,  which  represent  semi-diameters  of  the  wheel ;  in  other 
cases,  as  in  the  windlass, 
the  handle  is  rigidly  fixed 
to  the  axis. 

In  all  its  modifications 
we  may  regard  the  wheel 
and  axle  as  an  application 
of  the  lever,  the  arms  of 
which  are  the  radii  of  the 
wheel  and  axle  respectively ; 
and  in  all  cases  equilibrium 
exists  where  the  power  is 
to  the  resistance  as  the 
radius  of  the  axle  is  to  the 
radius  of  the  wheel.  Thus 
in  fig.  20,  ¥\Q  —  ab'.ac,  or 
P  x  ac  =  O  x  ab. 

Frequent  applications 
of  wheels  of  different  dia- 
meters are  met  with  in 
which  the  motion  of  one 
wheel  is  transmitted  to  an- 
other, either  by  means  of 
teeth  fitting  in  each  other 
on  the  circumference  of  the 
wheels,  as  in  fig.  21,  or  by 
means  of  bands  passing  over 
the  two  wheels,  as  in  the 
illustration  of  Ladd's  Mag- 
neto-Electrical Machine  (see 
Book  viii.). 

In  fig.  21,  which  repre- 
sents the  essential  parts  of  a  crab  winch,  in  order  to  raise  the  weight  Q 
a  power  p  must  be  applied  at  the  circumference  of  the  wheel   such  that 

P  =  Q  js '  'm  which  r  and  R  are  the  radii  of  the  axle  b  and  of  the  toothed 

wheel  a  respectively. 

The  rotation  of  the  wheel  a  is  affected  by  means  of  the  smaller  wheel  c  or 


26 


On  Matter ',  Force,  and  Motion. 


[42- 


crab,  the  teeth  of  which  fit  in  those  of  a.     But  if  this  wheel  c  is  to  exert  at 
its  circumference  a  power  p,  the  power  P  which  is  applied  at    the  end  of 

the  handle  must  be  P  =  —  p,  in  which  r'  is  the  radius  of  c,  R'  the  length  of 
a  lever  at  the  end  of  which  P  acts,  and  consequently 

P  =  -^Q. 


The  radius  of  the  wheel  c  is  to  that  of  the  wheel  a  as  their  respective  circum- 
ferences ;  and,  as  the  teeth  of  each  are  of  the  same  size,  the  circumferences 
will  be  as  the  number  of  teeth. 

Trains  of  wheelwork  are  used,  not  only  in  raising  great  weights  by  the 
exertion  of  a  small  power  ;  as  in  screw  jacks,  cranes,  crab  winches,  &c.,  but 
also  in  clock  and  watch  works,  and  in  cases  in  which  changes  in  velocity  or 
in  power  or  even  in  direction  are  required.  Numerous  examples  will  be  met 
with  in  the  various  apparatus  described  in  this  work. 

43.  Inclined  Plane.  —  The  properties  and  laws  of  the  inclined  plane  may 
be  conveniently  demonstrated  by  means  of  the  apparatus  represented  in 
fig.  22.  RS  represents  the  section  of  a  smooth  piece  of  hard  wood  hinged  at 
R  ;  by  means  of  a  screw  it  can  be  clamped  at  any  angle  x  against  the  arc- 

shaped  support,  by  which  at  the 
same  time  the  angle  can  be  mea- 
sured ;  a  is  a  cylindrical  roller, 
to  the  axis  of  which  is  attached 
a  string  passing  over  a  pulley 
to  a  scale-pan  P. 

It  is  thus  easy  to  ascertain 
by  direct  experiments  what 
weights  R  must  be  placed  in  the 
pan  P  in  order  to  balance  a  roller 
of  any  given  weight,  or  to  cause 
it  to  move  with  a  given  angle  of 
^^  inclination. 

The  line  RS  represents  the 
length,  ST  the  height,  and  RT  the  base  or  inclined  plane. 

In  'ascertaining  the  theoretical  conditions  of  equilibrium  we  have  a  useful 
application  of  the  parallelogram  of  forces.  Let  the  line  ab,  fig.  22,  represent 
the  force  which  the  weight  W  of  the  cylinder  exerts  acting  vertically  down- 
wards ;  this  may  be  decomposed  into  two  others  ;  one,  ad,  acting  at  right 
angles  against  the  plane,  and  representing  the  pressure  which  the  weight 
exerts  against  the  plane  ;  and  which  is  counterbalanced  by  the  reaction  of 
the  plane  ;  the  other,  ac,<  represents  the  component  which  tends  to  move  the 
weight  down  the  plane,  and  this  component  has  to  be  held  in  equilibrium  by 
the  weight  P,  equal  to  it  and  acting  in  the  opposite  direction. 

It  can  be  readily  shdwn  that  the  triangle  abc  is  similar  to  the  triangle 
SRT,  and  that  the  sides  ac  and  ab  are  in  the  same  proportion  as  the  sides 
ST  and  SR.  But  the  line  ac  represents  the  power,  and  the  line  ab  the 
weight  ;  hence 

ST  :  SR  =  P  :  W  : 


-43]  Inclined  Plane.  27 

that  is,  on  an  inclined  plane,  equilibrium  obtains  when  the  power  is  to  the 
weight  as  the  height  of  the  inclined  plane  to  its  length. 

Since  the  ratio  —  —  is  the  sine  of  the  angle  X,  we  may  also  state  the  prin- 
SR 

ciplethus:  P  =  Wsinr. 

The  component  da  or  be,  which  represents  the  actual  pressure  against 
the  plane,  is  equal  to  W  cos  x ;  that  is,  the  pressure  against  the  plane  is  to 
the  weight  as  the  base  is  to  the  length  of  the  inclined  plane. 

In  the  above  case  it  has  been  considered  that  the  power  acts  parallel  to 
the  inclined  plane.  It  may  be  applied  so  as  to  act  horizontally.  It  will  then 
be  seen  from  fig.  23  that  the  weight  W  may  be  decomposed  into  two  forces, 
one  of  which,  ab,  acts  at  right  angles  to  the  plane,  and  the  other,  ac,  parallel 
to  the  base.  It  is  this  latter  which  is  to  be  kept  in  equilibrium  by  the  power. 
From  the  similarity  of  the  two  triangles  acb  and  STR,  ac :  fc=ST:  TR 
=  h  :  b  ;  but  be  is  equal  to  W,  and  ac  is  equal  to  P,  hence  the  power  which 
must  be  applied  at  b  to  hold  the  weight  W  in  equilibrium  is  as  the  height 
of  the  inclined  plane  is  to  the  base,  or  as  the  tangent  of  the  angle  of  inclina- 
tion x  ;  that  is,  P  =  W  tan  x  The  pressure  upon  the  plane  in  this  case  may 

be  easily  shown  to  be  ab  = 

cos  x 

that  is   = .    This  is  sometimes 

cos  x 

called  the   relative  weight  on  the 
plane. 

If   the   force     P   which    is    to 

counterbalance  W  is  not  parallel  to  

the  plane,  but  forms  an  angle,  E,  with       •& 

it,  this  force  can  be  decomposed  into 

one  which  is  parallel  to  it,  and  one  which  is  at  right  angles.     Of  these  only 

the  first  is  operative,  and  is  equal  to  P  cos  E. 

In  most  cases^of  the  use  of  the  inclined  plane,  such  as  in  moving  carriages 
and  waggons  along  roads,  in  raising  casks  into  waggons  or  warehouses,  the 
power  is  applied  parallel  to  the  inclined  plane.  An  instance  of  a  case  in 
which  a  force  acts  parallel  to  the  base  is  met  with  in  the  screw. 

Owing  to  the  unevenness  of  the  surfaces  in  actual  use,  the  laws  of  equili- 
brium and  of  motion  on  an  inclined  plane  undergo  modification.  The_/>7<r- 
tion,  for  instance,  which  comes  into  play  amounts  on  ordinary  roads  to  from 
T\  to  i,  and  on  railways  to  from  T|y  to  ^  of  the  relative  weight.  This  must 
be  looked  upon  as  a  hindrance  to  be  continually  overcome,  and .  must  be 
deducted  from  the  force  required  to  keep  a  body  from  falling  down  an 
inclined  plane,  or  must  be  added  to  it  in  the  case  in  which  a  body  is  to  be 
moved  up  the  plane.  Hence  the  use  of  the  inclined  plane  in  unloading  heavy 
casks  into  cellars,  &c.  * 

A  body  which  cannot  roll,  does  not  move  on  the  inclined  plane,  provided 
the  inclination  is  below  a  certain  amount  (39).  The  determination  of  this 
limiting  angle  of  resistance,  at  which  a  body  on  an  inclined  plane  just  begins 
to  move,  may  serve  as  a  rough  illustration  of  a  mode  of  ascertaining  the 
'  coefficient  of  friction.' 


28 


On  Matter \  Force,  and  Motion. 


[43- 


For  in  the  case  in  which  the  power  is  applied  parallel  to  the  plane,  the 
component  of  the  weight  which  presses  aganst  the  plane  or  the  actual  load, 
L,  is  W  cos  x ;  and  the  component  which  tends  to  move  the  body  down  the 
plane  is  equal  to  W  sin  x.  If  the  friction,  R,  is  just  sufficient  to  hold  this  in 

equilibrium,  the  coefficient  of  friction  will  be      = ^1^"=  tan  x. 

L     W  COS.T 

Thus  if  we  place  on  the  plane  a  block  of  the  same  material,  by  gradually 
increasing  the  inclination  it  will  begin  to  move  at  a  certain  angle,  which 
will  depend  on  the  nature  of  the  material ;  this  angle  is  the  limiting  angle 
of  resistance,  and  its  tangent  is  the  coefficient  of  friction  for  that  material. 

44.  The  Wedge. — The  ordinary  form  of  the  wedge  is  that  of  a  three- 
sided  prism  of  iron  or  steel,  one  of  whose  angles  is  very  acute.     Its  most 
frequent  use  is  in  splitting  stone,  timber,  &c.     Fig.  24  represents  in  section 
the  application  of  the  wedge  to  this  purpose.     The  side  ab  is  the  back,  the 
vertex  of  the  angle  acb  which  the  two  faces  ac  and  be  make  with  each  other 
represents  the  edge,  and  the  faces  ac  and  be  the  sides  of  the  wedge.     The 
power  P  is  usually  applied  at  right  angles  to  the  back  ;  and  we  may  look 
upon  the  cohesion  between  the  fibres  of  the  wood  as  representing  the  resist- 
ance to  be  overcome  ;  as  corresponding  to  what  in  other  machines  is  the 

weight.  Suppose  this  to  act  at  right  angles  to  the 
two  faces  of  the  wedge,  and  to  be  represented  by 
the  lines/*?  and  ge  ;  complete  the  parallelogram  gef, 
then  the  diagonal  he  will  represent  the  resultant 
of  the  reaction  of  the  fibres  tending  to  force  the 
wedge  out ;  the  force  which  must  be  applied  to 
hold  this  wedge  in  equilibrium  must  therefore  be 
equal  to  eh.  Now  efh  is  similar  to  the  triangle 
acb)  therefore  ab  :  ac  =  eh  :  ef\  but  these  lines  re- 
present the  pressure  applied  at  the  back  of  the 
wedge,  and  the  pressure  on  the  face  ac,  hence  if  P 
represent  the  former  and  O  the  latter,  there  is 
equilibrium  when  P  :  O  =  ab  \  be,  that  is,  when  the 
power  is  to  the  resistance  in  the  same  ratio  as  the 
back  of  the  wedge  bears  to  one  of  the  sides.  The 
relation  between  power  and  resistance  is  more 
favourable  the  sharper  the  edge,  that  is,  the 
smaller  the  angle  which  the  sides  make  with  each 
other. 

The  action  of  all  sharp  cutting  instruments,  such  as  chisels,  knives, 
scissors,  &c.,  depends  on  the  principle  of  the  wedge.  It  is  also  applied  when 
very  heavy  weights  are  to  be  raised  through  a  short  distance,  as  in  launching 
ships,  and  in  bracing  columns  and  walls  to  the  perpendicular. 

45.  The  Screw. — Let  us  suppose  a  piece  of  paper  in  the  shape  of  a 
right-angled  triangle  aee'  to  be  applied  with  its  vertical  side  ac'er  against  a 
cylinder,  and  parallel  to  the  axis,  and  to  be  wrapped  round  the  cylinder  ;  the 
hypotenuse  will  describe  a  screw  line  or  helix  on  the  surface  of  the  cylinder 
(fig.  25)  ;  the  points  ab  cde  will  occupy  the  positions  respectively  a  b' c'  d'  e'. 
If  the  dimensions   be  so  chosen  that  the  base  of  the  triangle  cc'  is  equal 
to  the  circumference  of  the  cylinder,  then  the  hypotenuse  abc  becomes  an 


Fig.  24. 


Virtual  Velocity. 


29 


inclined  plane  traced  on  the  surface  of  the  cylinder  ;  the  distance  a  c'  being 
the  height  of  the  plane. 


An  ordinary  screw  consists  of  an  elevation  on  a  solid  cylinder  ;  this 
elevation  may  be  either  square,  as  in  fig.  26,  or  acute,  and  such  screws  are 
called  square  or  sharp  screws  accordingly. 

When  a  corresponding  groove  is  cut  in 
the  hollow  cylinder  or  nut  of  the  same  dia- 
meter as  the  bolt,  this  gives  rise  to  an  in- 
ternal or  companion  screw  or  nut,  fig.  27. 

The  vertical  distance  between  any  two 
threads  of  a  screw  measured  parallel  to  the 

axis  is  called  the  pitch,  and  the  angle  ace'  or  aee'  is  called  the  inclination  of 
the  screw. 

In  practice,  a  raised  screw  is  used  with  its  companion  in  such  a  manner 
that  the  elevations  of  the  one  fit  into,  and  coincide  with,  the  depressions  of 
the  other.  The  screw  is  a  modification  of  the  inclined  plane,  and  the  condi- 
tions of  equilibrium  are  those  which  obtain  in  the  case  of  the  plane.  The 
resistance,  which  is  either  a  weight  to  be  raised  or  a  pressure  to  be  exerted, 
acts  in  the  direction  of  the  vertical,  and  the  power  acts  parallel  to  the  base  ; 
hence  we  have  P  :  R  =  A  :  b,  and  the  length  of  the  base  is  the  circumference 
of  the  cylinder  ;  whence  P  :  R  =  h  :  2nr  ;  r  being  the  radius  of  the  cylinder, 
and  h  the  pitch  of  the  screw. 

The  power  is  usually  applied  to  the  screw  by  means  of  a  lever,  as  in  the 

bookbinders'  press,  &c.,  and  the  principle  of  the  screw  may  be  stated  to  be 

generally  that  the  power  of  the  screw  is  to  the  resistance  in  the  same  ratio 

as  that  of  the  pitch  of  the  screw  to  the  circumference  of  the  circle  through 

•  .which  the  power  acts. 

»v ff*  4^'  virtual  Velocity. —  If  the  point  of  application  of  a  force  be  slightly 
Gisplaced,  the  resolved  part  of  the  displacement  in  the  direction  of  the  force 
is  termed  the  virtual  velocity  of  the  force,  and  is  considered  as  positive  or 
negative,  according  as  it  is  in  the  same  direction  as  the  force,  or  in  the 
opposite  direction.  Thus  in  fig.  28  let  the  point  of 
application  A  of  the  force  P  be  displaced  to  A',  and 
draw  Pi? a  perpendicular  to  AP.  Then  Aa  is  the 
virtual  velocity  of  the  force  P,  and  being,  in  this  case, 
in  the  direction  of  P,  is  to  be  considered  positive. 

The  principle  of  virtual  velocities  asserts  that  if  any 
machine  or  system  be  kept  in  equilibrium  by  any 
number  of  forces,  and  the  machine  or  system  then  re- 
ceive any  very  small  displacement,  the  algebraic  sum  of  the  products  formed 


30  On  Matter,  Force,  and  Motion.  [46- 

by  multiplying  each  force  by  its  virtual  velocity  will  be  zero.  Of  course,  the 
displacement  of  the  machine  is  supposed  to  be  such  as  not  to  break  the 
connection  of  its  parts  ;  thus  in  the  wheel  and  axle  the  only  possible  dis- 
placement is  to  turn  it  round  the  fixed  axle  ;  in  the  inclined  plane  the  weight 
must  still  continue  to  rest  on  the  plane  ;  in  the  various  systems  of  pulleys 
the  strings  must  still  continue  stretched,  and  must  not  alter  in  length,  &c. 

The  complete  proof  of  this  principle  is  beyond  the  scope  of  the  present 
work,  but  we  may  easily  establish  its  truth  in  any  of  the  machines  we  have 
already  considered.  It  will  be  found  in  every  case  that,  if  the  machine 
receive  a  small  displacement,  the  virtual  velocities  of  P  and  W  will  be  of 
opposite  signs,  and  that,  neglecting  the  signs,  P  x  P's  virtual  velocity  =  W  x 
W's. virtual  velocity.  Thus,  to  take  the  case  of  a  bent  lever,  let  P  and  Q  be 
the  forces  acting  at  the  extremities  of  the  arms  of  the  bent  lever  AFB  (fig.  29), 
and  let  the  lever  be  turned  slightly  round  its  fulcrum  F,  bringing  A  to  A',  and 
B  to  B'.  Draw  A' a  and  Wb  perpendicular  to  P  and  Q  respectively  ;  then  Aa 
is  the  virtual  velocity  of  P,  and  B<£  that  of  Q,  the  former  being  positive  and 
the  latter  negative.  Let  Yp,  Yq  be  the  perpendiculars  from  the  fulcrum 
upon  P  and  Q,  or  what  we  have  called  (art.  40)  the  arms  of  P  and  Q.  Now, 
as  the  displacement  is  very  small,  the  angles  FAA',  FBB'  will  be  very  nearly 
right  angles  ;  and,  therefore,  the  right-angled  triangles  A#A',  B<£B'  will 
ultimately  be  similar  to  the  triangles  YpA,  F^B  respectively,  whence 

Act       ¥ p       j   B#       r  y         Ad 
AA/~FA'     l    BlP~FB'    r  Yp  ~ 


triangles  FAA',  FBB'  are  similar, 
as  they  are  both  isosceles,  and 
their  vertical  angles  are  equal,  so 

i      AA'     BB'        ,  Aa     b 

that     —  =     —  ;  whence         = 

FA      FB  Yp     Yq 

or,  as  we  may  put  it,  -  — -  = 

yv  '  p  x  F/ 

Q       £  *  ^  .     Now  the  denominators  of 
Q  x  F? 

Fig.  20.  C*  .... 

these  two  equal  fractions  are  equal, 
if  the  lever  be  in  equilibrium  (art.  40).     Hence  the  numerators  are  equal,  or 

P  x  P's  virtual  velocity  =  Q  x  O's  virtual  velocity. 

As  a  further  and  simpler  example,  take  the  case  of  the  block  and  tackle 
described  in  article  41.  Suppose  the  weight  to  be  raised  through  a  space  h  ; 
then  the  virtual  velocity  of  the  weight  is  h,  and  is  negative.  Now,  as  the 
distance  between  the  block  and  tackle  is  less  than  before  by  the  space  //,  and 
as  the  rope  passes  over  this  space  n  times,  in  order  to  keep  the  rope  still 
tight  the  power  will  have  to  move  through  a  space  equal  to  nh.  This  is  the 
virtual  velocity  of  P,  and  is  positive,  and  as  W  «  nP,  we  see  that 

W  x  W's  virtual  velocity  =  P  x  P's  virtual  velocity. 

46$.  Machines.  —In  many  machines  in  common  use,  two  forces  can  readily 
be  distinguished.  One  is  a  force  applied  in  order  to  drive  the  machine,  and  the 


~46a]  Machines.  3  1 

other  is  a  force  overcome,  and  is  called  the  resistance.  The  force  applied  is 
usually,  though  improperly,  called  the  power.  In  general  these  forces  are  un- 
equal. If  the  machine  moved  without  friction  these  forces  might  be  exactly 
balanced,  in  such  a  way  that  if  either  of  them  were  increased  in  the  slightest 
degree,  the  machine  would  begin  to  move  with  a  uniformly  accelerated  motion. 
If  such  a  machine  thus  balanced  were  to  be  started  by  an  impulse  which 
should  then  cease  to  act,  the  machine  would  move  continuously  at  a  uniform 
rate  until  acted  upon  by  some  other  external  force.  If  we  imagine  a  balanced 
frictionless  machine  to  become  a  machine  with  friction,  then  either  of  the  two 
forces  might  be  varied  between  certain  limits,  without  setting  the  machine 
into  motion.  Hence,  if  the  machine  is  to  move  uniformly,  the  force  applied  in 
driving  it  must  be  greater  than  would  be  necessary  to  give  uniform  motion  to 
a  frictionless  machine.  The  force  applied,  P,  and  the  resistance  overcome, 
R,  may  be  expressed  in  pounds  weight,  which  may  be  converted  into  absolute 
units  by  multiplying  by  the  value  of^at  the  place.  While  P  moves  over  a 
certain  distance^,  R  moves  over  a  distance  r.  These  distances  can  be  deter- 
mined by  measurement.  The  ratio  of  r  \.Q  p  can  often  be  seen  by  simple  in- 
spection, since  its  value  depends  upon  the  gearing  or  construction  of  the 
machine. 

If  the  force  P  is  exerted  over  a  distance  /,  the  work  applied  is  P/  foot- 
pounds. While  this  work  is  being  applied  to  the  machine,  a  certain  amount 
of  work,  Rr,  is  transmitted  through  the  machine,  and  is  done  upon  the  resist- 
ance. Experiment  shows  that  the  work  applied  P/  is  always  greater  than 
the  work  Rr  transmitted  through  the  machine.  This  difference  represents 
the  work  w^hich  is  required  to  move  the  parts  of  the  machine  upon  each 
other,  and  is  called  internal  work.  If  the  internal  work  is  represented  by  I, 
the  condition  for  uniform  action  of  a  machine  is  given  by  the  equation 


It  will  be  assumed  that  a  small  force  P//x  is  applied,  sufficient  to  move 
the  machine  uniformly  when  unloaded.  This  value  of  P//x  is  not  included 
in  P.  In  this  case,  the  work  of  friction  is  due  wholly  to  the  load  which  the 
machine  carries,  and  I  becomes  zero  when  R  =  0.  The  quantity  I  is  of  the 
same  nature  as  the  other  two  quantities  in  the  equation,  being  the  product  of 
a  certain  force  of  friction  into  a  certain  distance,  but  in  general  these  factors 
cannot  be  determined  separately.  It  is  found  that  I  diminishes  in  value  as 
the  parts  of  the  machine  in  contact  are  made  smoother,  and  is  further 
diminished  by  oiling  the  bearings  —  that  is  to  say,  the  quantities  P/  and  Rr, 
which  can  be  easily  determined,  become  more  nearly  equal. 

The  equation  may  also  be  put  into  the  following  form  :  — 

P      r 

R  V    where  .'-jL 

It  is  evident  that  the  ratio  -  is  a  constant  quantity,  for  a  given  machine, 

geared  in  a  definite  manner.     Experiment  shows  that  the  ratio         is  also 

R 

practically  constant,  so  that  the  quantity  i  may  also  be  considered  constant 
for  a  given  machine  in  a  definite  condition.     It  would,  however,  be  changed 


32  On  Matter,  Force,  and  Motion.  ^Ga- 

by oiling  the  bearings,  as  this  would  make  it  necessary  to  diminish  P  in 
order  to  preserve  uniform  motion,  and  it  also  depends  upon  the  arrangement 
of  the  machine,  as  will  be  pointed  out  further  on. 

^  47.  Friction. — In  the  cases  of  the  actions  of  machines  which  have  been 
described,  the  resistances  which  are  offered  to  motion  have  not  been  at  all 
considered.  The  surfaces  of  bodies  in  contact  are  never  perfectly  smooth  ; 
even  the  smoothest  present  inequalities  which  can  neither  be  detected  by  the 
touch  nor  by  ordinary  sight ;  hence  when  one  body  moves  over  the  surface 
of  another,  the  elevations  of  one  sink  into  the  depressions  of  the  other,  like 
the  teeth  of  wheels,  and  thus  offer  a  certain  resistance  to  motion  ;  this  is 
what  is  called  friction.  It  must  be  regarded  as  a  force  which  continually 
acts  in  opposition  to  actual  or  possible  motion. 

Friction  is  of  two  kinds  :  sliding,  as  when  one  body  glides  over  another  ; 
this  is  least  when  the  two  surfaces  in  contact  remain  the  same,  as  in  the 
motion  of  an  axle  in  its  bearing  ;  and  rolling  friction,  which  occurs  when  one 
body  rolls  over  another,  as  in  the  case  of  an  ordinary  wheel.  The  latter  is 
less  than  the  former,  for  by  the  rolling  the  inequalities  of  one  body  are  raised 
over  those  of  the  other.  As  rolling  friction  is  considerably  less  than  sliding 
friction,  it  is  a  great  saving  of  power  to  convert  the  latter  into  the  former  ;  as 
is  done  in  the  case  of  the  casters  of  chairs  and  other  furniture,  and  also  in  that 
of  friction  wheels.  On  the  other  hand,  it  is  sometimes  useful  to  change  roll- 
ing into  sliding  friction,  as  when  drags  are  placed  on  carriage  wheels. 

Friction  is  directly  proportional  to  the  pressure  of  the  two  surfaces 
against  each  other.  That  fraction  of  the  pressure  which  must  act  as  moving 
force  merely  to  overcome  friction  is  called  the  coefficient  of  friction. 

Friction  is  independent  of  the  extent  of  the  surfaces  in  contact  if  the  pres- 
sure is  the  same.  Thus,  suppose  a  board  with  a  surface  of  a  square  deci- 
metre resting  on  another  board  to  be  loaded  with  a  weight  of  a  kilogramme. 
If  this  load  be  distributed  over  a  similar  board  of  two  square  decimetres 
surface,  the  total  friction  will  be  the  same,  while  the  friction  per  square 
centimetre  is  one-half,  for  the  pressure  on  each  square  centimetre  is  one-half 
of  what  it  was  before.  Friction  is  diminished  by  polishing  and  by  smearing, 
but  is  increased  by  heat.  It  is  greater  as  a  body  passes  from  the  state  of 
rest  to  that  of  motion  than  during  motion,  but  seems  independent  of  the 
velocity.  The  coefficient  of  friction  depends  on  the  nature  of  the  substances 
in  contact  ;  thus  for  oak  upon  oak  it  is  0*418  when  the  fibres  are  parallel, 
and  0-293  when  they  cross  ;  for  beech  upon  beech  it  is  0-56.  Greasy  sub- 
stances, which  are  not  absorbed  by  the  body,  diminish  friction,  but  increase 
it  if  they  are  absorbed.  Thus  moisture  and  oil  increase,  while  tallow,  soap, 
and  graphite  diminish,  the  friction  of  wooden  surfaces.  In  the  sliding  fric- 
tion of  cast  iron  upon  bronze  the  coefficient  was  found  to  be  0-25  without 
grease  ;  with  oil  it  was  0-17,  fat  p-ii,  soap  0-03,  and  with  a  mixture  of  fat 
and  graphite  0-02.  The  coefficient  of  rolling  friction  for  cast-iron  wheels  on 
iron  rails  as  in  railways  is  about  0*004  5  f°r  ordinary  wheels  on  an  ordinary 
road  it  is  0*04,  hence  a  horse  can  draw  ten  times  as  great  a  load  on  rails  as 
on  an  ordinary  road,  and  this  is  indeed  a  main  use  of  railways.  The  coeffi- 
cient of  steel  upon  smooth  ice,  as  in  skating,  is  from  0*0 1 6  to  0*032. 

Without  friction  on  the  ground,  neither  man  nor  animals,  neither  ordinary 
carriages  nor  railway  carriages,  could  move.  Friction  is  necessary  for  the 


-48]  Resistance  to  Motion  in  a  Fluid  Medium.  33 

transmission  of  power  from  one  wheel  to  another  by  means  of  bands  or 
ropes  ;  and  without  friction  we  could  hold  nothing  in  the  hands. 

48.  Resistance  to  Motion  in  a  Fluid  Medium. — A  body  in  moving 
through  any  medium  such  as  air  or  water  experiences  a  certain  resistance  ; 
for  the  moving  body  sets  in  motion  those  parts  of  the  medium  with  which  it 
is  in  contact,  whereby  it  loses  an  equivalent  amount  of  its  own  motion. 

This  resistance  increases  with  the  surface  of  the  moving  body ;  thus  a 
soap-bubble  or  a  snow-flake  falls  more  slowly  than  does  a  drop  of  water  of 
the  same  weight.  It  also  increases  with  the  density  of 
the  medium  ;  thus  in  rarefied  air  it  is  less  than  in  air 
under  the  ordinary  pressure  ;  and  in  this  again  it  is 
less  than  in  water. 

The  influence  of  this  resistance  may  be  illustrated 
by  means  of  the  apparatus  represented  in  fig.  30, 
which  consists  of  two  vanes,  ww,  fixed  to  a  horizontal 
axis,  xx,  to  which  also  is  attached  a  bobbin  s.  The 
rotation  of  the  vanes  is  effected  by  means  of  the  falling 
of  a  weight  attached  to  the  string  coiled  round  the 
bobbin.  The  vanes  can  be  adjusted  either  at  right 
angles  or  parallel  to  the  axis.  In  the  former  position 
the  vanes  rotate  rapidly  when  the  weight  is  allowed  to 
act ;  in  the  latter,  however,  where  they  press  with  their 
entire  surface  against  the  air,  the  resistance  greatly 
lessens  the  rapidity  of  rotation. 

The  resistance  increases  with  the  velocity  of  the 
moving  body,  and  for  moderate  velocities  is  proper-          .      „. 
tional  to  the  square  ;  for,  supposing  the  velocities  of  a 

body  made  twice  as  great,  it  must  displace  twice  as  much  matter,  and  must 
also  impart  to  the  displaced  particles  twice  the  velocity.  For  high  veloci- 
ties the  resistance  in  a  medium  increases  in  a  more  rapid  ratio  than  that  of 
the  square,  for  some  of  the  medium  is  carried  along  with  the  moving  body, 
and  this,  by  its  friction  against  the  other  portions  of  the  medium,  causes  a 
loss  of  velocity. 

It  is  this  resistance  which  so  greatly  increases  the  difficulty  and  cost  of 
attaining  very  high  speed  in  steam-vessels.  Use  is  made,  on  the  other  hand, 
of  this  resistance  in  parachutes  (fig.  165)  and  in  the  wind-vanes  for  diminish- 
ing the  velocity  of  falling  bodies  (fig.  54),  the  principle  of  which  is  illustrated 
by  the  apparatus,  fig.  30.  Light  bodies  fall  more  slowly  in  air  than  heavy 
ones  of  the  same  surface,  for  the  moving  force  is  smaller  compared  with  the 
resistance.  The  resistance  to  a  falling  body  may  ultimately  equal  its  weight ; 
it  then  moves  uniformly  forward  with  the  velocity  which  it  has  acquired. 
Thus,  a  rain-drop  falling  from  a  height  of  3,000  feet  should,  when  near  the 
ground,  have  a  velocity  of  nearly  440  feet,  or  that  of  a  musket-shot ;  owing, 
however,  to  the  resistance  of  the  air,  its  actual  velocity  is  probably  not  more 
than  30  feet  in  a  second.  On  railways  the  resistance  of  the  air  is  appreciable ; 
with  a  carriage  exposing  a  surface  of  22  square  feet,  it  amounts  to  16  or  17 
pounds  when  the  speed  of  the  train  is  16  feet  a  second,  or  n  miles  an  hour. 

By  observing  the  rate  of  diminution  in  the  number  of  oscillations  of  a 
horizontal  disc  suspended  by  a  thread  when  immersed  in  water,  Meyer  de- 

D 


34  On  Matter,  Force,  and  Motion.  [48- 

termined  the  coefficient  of  the  frictional  or  internal  resistance  of  water,  and 
found  that  at  10°  it  was  equal  to  0*01567  gramme  on  a  square  centimetre  ; 
and  for  air  it  was  about  ~j  as  much. 

49.  Uniformly  Accelerated   Rectilinear  Motion. — Let  us   suppose  a 
•/      body  containing  m  units  of  mass  to  move  from  rest  under  the   action  of  a 
force  of  F  units,  the  body  will  move  in  the  line  of  action  of  the  force,  and 
will  acquire  in  each  second  an  additional  velocity /given  by  the  equation 

consequently,  if  v  is  its  velocity  at  the  end  of  t  seconds,  we  have 

v=/t.  (i) 

To  determine  the  space  it  will  describe  in  t  seconds,  we  may  reason  as 
follows  : — The  velocity  at  the  time  t  being  ft,  that  at  a  time  /  +  r  will  bey 
(*  +  T).  If  the  body  moved  uniformly  during  the  time  r  with  the  former 
velocity  it  would  describe  a  space  s  equal  to  fir  ;  if  with  the  latter  velocity, 
a  space  s1  equal  to/(^  +  r)r.  Consequently, 

sl :  s::  t  +  r  :t\ 

therefore,  when  r  is  indefinitely  small,  the  limiting  values  of  s  and  jx  are 
equal.  Now,  since  the  body's  velocity  is  continually  increasing  during  the 
time  T,  the  space  actually  described  is  greater  than  s  and  less  than  sr  But 
since  the  limiting  values  of  s  and  j,  are  equal,  the  limiting  value  of  the  space 
described  is  the  same  as  that  of  s  or  sr  In  other  words,  if  we  suppose  the 

whole  time  of  the  body's  motion  to  be  divided 
into  any  number  of  equal  parts,  if  we  determine 
the  velocity  of  the  body  at  the  beginning  of  each 
of  these  parts,  and  if  we  ascertain  the  spaces 
described  on  the  supposition  that  the  body 
moves  uniformly  during  each  portion  of  time, 
the  limiting  value  of  the  sum  of  these  spaces 
will  be  the  space  actually  described  by  the  body. 
r  Draw  a  line  AC  (fig.  31),  and  at  A  construct  an 

angle  CAB,    whose   tangent   equals  /;    divide 

AC  into  any  number  of  equal  parts  in  D,  E,  F,...and  draw  PD,  QE,  RF,... 
BC  at  right  angles  to  AC  ;  then  since  PD  =  AD  x/  QE  =  AE  x/  RF  =  AF  x/ 
BC  =  AC  x/  &c.,  PD  will  represent  the  velocity  of  the  body  at  the  end  of 
the  time  represented  by  AD,  and  similarly  QE,  RF,...BC,  will  represent  the 
velocity  at  the  end  of  the  times  AE,  AF,...AC.  Complete  the  rectangles  De, 
E/  F^-...  These  rectangles  represent  the  space  described  by  the  body  on 
the  above  supposition  during  the  second,  third,  fourth,... portions  of  the  time. 
Consequently,  the  space  actually  described  during  the  time  AC  is  the  limit 
of  the  sum  of  the  rectangles  ;  the  limit  being  continually  approached  as  the 
number  of  parts  into  which  AC  is  divided  is  continually  increased.  But  this 
limit  is  the  area  of  the  triangle  ABC  :  that  is  £AC  x  CB  or  ^AC  x  AC  x/ 
Therefore,  if  AC  represents  the  time  /  during  which  the  body  describes  a 
space  s,  we  have 

s  =  $/t2-  (2) 

Since  this  equation  can  be  written 


T/l 


-50]  Motion  on  an  Inclined  Plane.  35 

we  find,  on  comparison  with  equation  (i),  that 

«"  =  2/J.  (3) 

To  illustrate  these  equations,  let  us  suppose  the  accelerative  effect  of  the 
force  to  be  6  ;  that  is  to  say,  that,  in  virtue  of  the  action  of  the  force,  the  body 
acquires  in  each  successive  second  an  additional  velocity  of  6  feet  per  second, 
and  let  it  be  asked  what,  on  the  supposition  of  the  body  moving  from  rest, 
will  be  the  velocity  acquired  and  the  space  described  at  the  end  of  12 
seconds  ;  equations  I  and  2  enable  us  to  answer  that  at  that  instant  it  will  be 
moving  at  the  rate  of  72  feet  per  second,  and  will  have  described  432  feet. 

The  following  important  result  follows  from  equation  2.  At  the  end  of 
the  first,  second,  third,  fourth,  &c.,  second  of  the  motion  the  body  will  have 
described  £/j  £/x  4,  i/x  9,  £/x  16,  &c.,  feet  ;  and  consequently  during  the 
first,  second,  third,  fourth,  &c.  second  of  the  motion  will  have  described  \f, 
i/x  3>  2/x  S->  i/x  7>  &c->  feet>  namely  spaces  in  arithmetical  progression. 

The  results  of  the  above  article  can  be  stated  in  the  form  of  laws  which 
.apply  to  the  state  of  a  body  moving  from  a  state  of  rest  under  the  action  of 
a  constant  force  :  — 

I.  The  velocities  are  proportional  to  the  times  during  which  the  motion 
has  lasted. 

II.  The  spaces  described  are  proportional  to  the  squares  of  the  times  em- 
ployed in  their  description. 

III.  The  spaces  described  are  proportional  to  the  squares  of  the  velocities 
acquired  during  their  description. 

IV.  The  spaces  described  in  equal  successive  periods  of  time  increase  by  a 
.constant  quantity. 

Instead  of  supposing  the  body  to  begin  to  move  from  a  state  of  rest,  we 
may  suppose  it  to  have  an  initial  velocity  V,  in  the  direction  of  the  force.  In 
this  case  equations  i,  2,  and  3  can  be  easily  shown  to  take  the  following 
forms,  respectively  :— 


If  the  body  move  in  a  direction  opposite  to  that  of  the  force,  f  must  be 
reckoned  negative. 

The  most  important  exemplification  of  the  laws  stated  in  the  present 
article  is  in  the  case  of  a  body  falling  freely  in  vacuo.  Here  the  force  causing 
the  acceleration  is  that  of  gravity,  and  the  acceleration  produced  is  denoted 
by  the  letter  g  :  it  has  already  been  stated  (29)  that  the  numerical  value  of 
g-is  32-1912  at  London,  when  the  unit  of  time  is  a  second  and  the  unit  of 
length  a  foot.  Adopting  the  metre  as  unit  of  length,  the  value  of  g  at 
London  is  9-8117. 

50.  motion  on  an  Inclined  Plane.  —  Referring  to  (43),  suppose  the  force 
P  not  to  act  ;  then  the  mass  M  is  acted  on  by  an  unbalanced  force  M^  sin 
x,  in  the  direction  SR,  consequently  the  acceleration  down  the  plane  is  g 
sin  .r,  and  the  motion  becomes  a  particular  case  of  that  discussed  in  the 
last  article.  If  it  begins  to  move  from  rest,  it  will  at  the  end  of  /  seconds 
acquire  a  velocity  v  given  by  the  equation 

v  =gt  sin  ;r, 

D  2 


36  On  Matter,  Force,  and  Motion.  [50— 

and  will  describe  a  length  s  of  the  plane  given  by  the  equation 


Also,  if  v  is  the  velocity  acquired  while  describing  s  feet  of  the  plane, 

v*  —  2gs  sin  x. 

Hence  (fig.  22)  if  a  body  slides  down  the  plane  from  S  to  R  the  velocity 
which  it  acquires  at  R  is  equal  to  V^g  -  RS  sin  R  or  \/2g .  ST  ;  that  is  to  say, 
the  velocity  which  the  body  has  at  R,  does  not  depend  on  the  angle  _r,  but 
only  on  the  perpendicular  height  ST.  The  same  would  be  true  if  for  RS 
we  substituted  any  smooth  curve,  and  hence  we  may  state  generally,  that 
when  a  body  moves  along  any  smooth  line  under  the  action  of  gravity,  the 
change  of  velocity  it  experiences  in  moving  from  one  point  to  another  is  that 
due  to  the  vertical  height  of  the  former  point  above  the  latter. 

51.  motion  of  Projectiles. — The  equations  given  in  the  above  article 
apply  to  the  case  of  a  body  thrown  vertically  upwards  or  downwards  with  a 
certain  initial  velocity.  We  will  now  consider  the  case  of  a  fyeavy  body 
thrown  in  a  horizontal  direction.  Let  «,  fig.  32,  be  such  a  body  thrown  with 
an  initial  velocity  of  v  feet  in  a  second,  and  let  the  line  ab  represent  the  space 
described  in  any  interval ;  then  at  the  end  of 
the  2,  3,  4...  equal  interval,  the  body,  in  virtue 
of  its  inertia,  will  have  reached  the  points  c  d  e^ 
&c.  But  during  all  this  time  the  body  is  under 
the  influence  of  gravity,  which  if  it  alone  acted, 
would  cause  the  body  to  fall  through  the  dis- 
tances represented  on  the  vertical  line  ;  these  are 
determined  by  the  successive  values  of  \gf~, 
which  is  the  formula  for  the  space  described 
by  a  freely  falling  body  (50).  The  effect  of  the 
combined  action  of  the  two  forces  is  that  at  the 
end  of  the  first  interval,  &c.,  the  body  will  be 
at  bf,  at  the  end  of  the  second  interval  at  c*,  of 
the  third  at  df,  &c.,  the  spaces  bb',  ccf,  dd... 
being  proportional  to  the  squares  of  ab,  ac,  ad, 
respectively,  and  the  line  joining  these  points, 
represents  the  path  of  the  body.  By  taking  the 
intervals  of  time  sufficiently  small  we  get  a  regu- 


Fig.  32- 


larly  curved  line  of  the  form  known  as  the  parabola. 

If  the  direction  in  which  the  body  is  thrown  makes  an  angle  of  a  with 


Fig.  33- 

the  horizon  (fig.  33),  then  after  t  seconds  it  would  have  travelled  a  distance* 
ab  =  vt,  where  v  is  the  original  velocity ;  during  this  time,  however,  it  will  have: 


-53]  Motion  in  a  Circle  —  Centrifugal  Force.  37 

fallen  through  a  distance  be  =  ^gP  ;  the  height  which  it  will  have  actually 
reached  is  =  bd-  be  •-=  vt  sin  a  -  %gf~  ;  and  the  horizontal  distance  will  be 
.ad=ab  cos  a=--vt  cos  a.  The  range  of  the  body,  or  the  greatest  distance 
through  which  it  is  thrown,  will  be  reached  when  the  height  is  again  =  0  ;  that 

is,  when-2//  sin  a-  2^  =  0,  from  which  /  =  —       —       Introducing    this   value 

£> 

of  /  into  the  quotation  for  the  distance  d,  we  have  d=2l'v  sm  a  cos  a,  which 

£ 
by  a  trigonometrical  transformation  =  —         —  .       The    greatest    height    is 

o 

attained  in  half  the  time  of  flight,  or  when  ?*•—     —  ,  from  which  we  get 


It  follows  from  the  formula  that  the  height  is  greatest  when  sin  a  is 
greatest,  which  is  the  case  when  it  =  90°,  or  when  the  body  is  thrown  vertically 
upwards  ;  the  range  is  greatest  where  sin  20.  is  a  maximum,  that  is,  when 
2a  =  90°  or  a  =  45°. 

In  these  formulae  it  has  been  assumed  that  the  air  offers  no  resistance. 
This  is,  however,  far  from  the  case,  and  in  practice,  particularly  if  the  velo- 
city of  projection  is  very  great,  the  path  differs  from  that  of  a  parabola. 
Pig.  33  approximately  represents  the  path,  allowing  for  the  resistance  of  the 
air.  The  divergence  from  'the  true  theoretical  path  is  affected  by  the  fact 
-that  in  the  modern  rifled  arms  the  projectiles  are  not  spherical  in  shape  ; 
and  also  because,  along  with  their  motion  of  translation,  they  have,  in  con- 
sequence of  the  rifling,  a  rotatory  motion  about  their  axis.  »/.  ^^r4^^ 

52.  Composition  of  Velocities.  —  The  principle  for  the  composition  of 
velocities  is  the  same  as  that  for  the  composition  of  forces  :  this  follows  evi- 
dently from  the  fact  that  forces  are  measured  by  the  momentum  they  com- 
municate, and  are  therefore  to  one  another  in  the  same  ratio  as  the  velocities 
they  communicate  to  the  same  body.     Thus  (fig.  5,  art.  30),  if  the  point  has 
at  any  instant  a  velocity  AB  in  the  direction  AP,  and  there  is  communicated 
to  it  a  velocity  AC  in  the  direction  AQ,  it  will  move  in  the  direction  AR  with 
.a  velocity  represented  by  AD.     And  conversely,  the  velocity  of  a  body  re- 
presented by  AD  can  be  resolved  into  two  component  velocities  AB  and  AC. 
This  suggests  the  method  of  determining  the  motion  of  a  body  when  acted 
•on  by  a  force  in  a  direction  transverse  to  the  direction  of  its  velocity  ;  namely, 
suppose  the  time  to  be  divided  into  a  great  number  of  intervals,  and  suppose 
the  velocity  actually  communicated  by  the  force  to  be  communicated  at  once, 
±hen  by  the  composition  of  velocities  we  can  determine  the  motion  during 
each  interval,  and  therefore  during  the  whole  time  ;  the  actual  motion  is  the 
limit  to  which  the  motion,  thus  determined,  approaches  when  the  number  of 
intervals  is  increased. 

53.  Motion  in  a  Circle  —  Centrifugal  Force.  —  When  a  body  is  once  in 
motion,   unless  it  be  acted  upon  by   some  force,  it   will   move   uniformly 
forward  in  a  straight  line  with  unchanged  velocity  (26).    If,  therefore,  a  body 
moves  uniformly  in  any  other  path  than  a  straight  line  —  in  a  circle,  for 
instance  —  this  must  be  because  some  force  is  constantly  at  work  which 
continuously  deviates  it  from  this  straight  line, 


On  Matter,  Force,  and  Motion. 


[53- 


We  have  already  seen  an  example  of  this  in  the  case  of  the  motion 
of  projectiles  (51),  and  will  now  consider  it  in  the  case  of  central  motion, 
or  motion  in  a  circle,  of  which  we  have  an  example  in  the  motion  of  the 
celestial  bodies  or  in  the  motion  of  a  sling. 

In  the  latter  case,  if  the  string  is  cut,  the  stone,  ceasing  to  be  acted  upon 
by  the  tension  of  the  string,  will  move  in  a  straight  line  with  the  velocity 
which  it  already  possesses — that  is,  in  the  direction -«f  the  tangent  to  the  curve 
at  the  point  where  the  stone  was  when  the  string  was  cut.  The  tension  of 
the  string,  the  effect  of  which  is  to  pull  the  stone  towards  the  centre  of  the 
circle,  and  to  cause  the  stone  to  move  in  its  circular  path,  is  called  the  centri- 
petal or  central  force  ;  the  reaction  of  the  stone  upon  the  string,  which  is 
equal  and  opposite  to  this  force,  is  called  its  centrifugal  force.  The  amount 
of  these  forces  may  be  arrived  at  as  follows  : — 

Let  us  suppose  a  body  moving  in  a  circle  with  given  uniform  velocity 
to  be  at  the  point  a  (fig.  34) ;  then,  had  it  not  been  acted  on  by  a  force  in 
the  direction  ac,  it  would,  in  a  small  succeeding  interval  of  time  /,  have 
continued  to  move  in  the  direction  of  the  tangent  at  a,  and  have  passed 
through  a  distance  which  we  will  represent  by  ab.  In  consequence,  how- 
ever, of  this  force  it  has  not  followed  this  direction,  but  has  arrived  at  the 
point  d  on  the  curve;  hence  the  force  has  made  it 
traverse  the  distance  bd  =  ae  in  this  interval.  If 
f  be  the  acceleration  with  which  the  body  is  drawn 
towards  the  centre,  ae  =  j>ft~,  and  if  ad  be  very  small, 
it  may  be  taken  as  equal  to  ab  or  z//,  where  z/  is  the 
velocity  of  the  moving  body.  Now  if  an  is  the 
diameter  of  the  circle,  the  triangle  adn  is  inscribed 
in  a  semicircle  and  is  right-angled,  whence  ad~  = 
ae  x  an  =  ae  x  2r.  Substituting  their  values  for  ad 
and  ae  in  this  equation,  we  find  that  v~f~  =  ^ft  x  2r, 

from  which  f  =  — ;  that  is,  in  order  that  a  body  with 

a  certain  velocity  may  move  in  a  circle,  it  must 
be  drawn  to  the  centre  by  a  force  which  is  directly 
as  the  square  of  the  velocity  with  which  the  body 
moves,  and  which  is  inversely  as  the  radius  of  the 
circle.  In  order  to  express  this  in  the  ordinary  units 
of  weight,  we  must  multiply  the  above  expression 

mv2         Wz/~ 

by   the   mass,    which    gives    F  =  — ~    or  — !        To 

r  gr 

keep  the  body  in  a  circle  an  attraction  towards  the 
centre  is  needed,  which  is  constantly  equal  to  -— , 

and  this  attraction  is  constantly  neutralised  by  the 
centrifugal  force. 

The  above  expression  may  be  put  in  a  form  which 
is   sometimes    more    convenient.     If  T  be   the   time 
in  seconds    required  to   traverse  the  circumference   inr  with  the  velocity 

47rVa  f  T-  r,  T-      4/«7rV    4\VW 

vt  then  z/3  =  ^=3-  >  from  which  r  =  ^-^-  =  - — =^— 

If  a  rigid  body  rotates  about  a  fixetf  axis,  all  parts  of  the  body  describe 


Fig.  34- 


-54]  'Motion  in  a  Vertical  Circle.  39 

circumferences  of  various  diameters,  but  all  in  the  same  time.  The  velocity 
of  the  motion  of  individual  particles  increases  with  the  distance  from  the  axis 
of  rotation.  By  angular  'velocity  is  understood  the  velocity  of  a  poini^at  unit 
distance  from  the  axisJof  rotation.  If  this  is  denoted  by  o>,  the  velocity  v  of  a 

point  at  a  distance  frffn  the  axis  is  o>r,  .from  "winch  <u  =     =  -—  and_/=rar. 

The  existence  of  ceiihrifugal  force  j^nay  b£  demonstrated  by  means  of 
numerous  experiments,  such  as  the  centrifugal  railway.  If  a  small  can  of 
water  hung  by  the  handle  to  a  string  be  rapidly  rotated  in  a  vertical  circle, 
no  water  will  fall  out,  for,  at  a  suitable  velocity,  the  liquid  will  press  against 
the  bottom  of  the  vessel  with  a  force  at  right  angles  to  the  circle,  and  greater 
than  its  own  weight. 

54.  Motion  in  a  Vertical  Circle.  —  Let  ACBD  be  a  circle  whose  plane 
is  vertical  and  radius  denoted  by  r.  Suppose  a  point  placed  at  A,  and 
allowed  to  slide  down  the  curve,  what  velocity  will  it  have  acquired  on 
reaching  any  given  point  P  ?  Draw  the  vertical  diameter  CD,  join  CA,  CP, 
and  draw  the  horizontal  lines  AMB  and  PNP'.  Now,  assuming  the  curve 
to  be  smooth,  the  velocity  acquired  in  falling  from  A  to  P  is  that  due  to  MN, 
the  vertical  height  of  A  above  P  (51)  ;  if,  therefore,  v  denote  the  velocity  of 
the  point  at  P,  we  shall  have 


Now  by  similar  triangles  DCP,  PCN  we  have 

DC  :  CP::CP  :  CN  ; 
consequently,  if  we  denote  by  s  the  chord  CP, 


In  like  manner  if  a  denote  the  chord  CA, 


therefore  2rUN=a2-  s2, 

and  */2  =  ^(a2-.y2). 

Now  v  will  have  equal  values  when  s  has  the  same  value,  whether  positive 
or  negative,  and  for  any  one  value  of  s  there  are  two  equal  values  of  v,  one 
positive  and  one  negative.  That  is  to  say,  since  CP'  is  equal  to  CP,  the 
body  will  have  the  same  velocity  at  P'  that  it  has  at  P,  and  at  any  point  the 
body  will  have  the  same  velocity  whether  it  is  going  up  the  curve  or  down 
the  curve.  Of  course  it  is  included  in  this  statement  that  if  the  body  begins 
to  move  from  A  it  will  just  ascend  to  a  point  B  on  the  other  side  of  C,  such 
that  A  and  B  are  in  the  same  horizontal  line.  It  will  also  be  seen  that  at  C 
the  value  of  s  is  zero  ;  consequently,  if  V  is  the  velocity  acquired  by  the 
body  in  falling  from  A  to  C,  we  have 

V  = 

and,  on  the  other  hand,  if  the  body  begins  to  move  from  C  with  a  velocity  V 
it  will  reach  a  point  A  such  that  the  chord  AC  or  a  is  given  by  the  same 
equation.  In  other  words,  the  velocity  at  the  lowest  point  is  proportional  to 
the  chord  of  the  arc  described. 


I 


40 


On  Matter,  Force,  and  Motion. 


[55- 


55.  Motion  of  a  Simple  Pendulum.  —  By  a  simple  pendulum  is  meant  a 
heavy  particle  suspended  by  a  fine  thread  from  a  fixed  point,  about  which  it 
oscillates  without  friction.  So  far  as  its  changes  of  velocity  are  concerned 
they  will  be  the  same  as  those  of  the  point  in  the  previous  article,  for  the 
tension  of  the  thread,  acting  at  each  position  in  a  direction  at  right  angles  to 
that  of  the  motion  of  the  point,  will  .  no  more  affect  Jts  motion  than  there- 
action  of  the  smooth  curve  affects  that  of  the  point 
in  the  last  article.  The  time  of  an  oscillation  —  that 
is,  the  time  in  which  the  point  moves  from  A  to  B— 
can  be  easily  ascertained  when  the  arc  of  vibration 
is  small  ;  that  is,  when  the  chord  and  the  arc  do  not 
sensibly  differ. 

Thus,  let  AB  (fig.  36)  equal  the  arc  or  chord 
ACB  (fig.  35)  ;  with  centre  C  and  radius  AC  or  a 
describe  a  circle,  and  suppose  a  point  to  describe  the 
circumference  of  that  circle  with  a  uniform  velocity 

Fis-  36-  V  or  *X/C     At  any  instant  let  the  point  be  at  Q, 

join  CQ,  draw  the  tangent  QT,  also  draw  QP  at  right  angles  and  QN 
parallel  to  AB,  then  the  angles  NOT  and  COP  are  equal.    Now  the  velocity 

of  Q  resolved  parallel  to  AB  is  V  cos  TQN  or  *\/£  cos  COP  ;  that  is,  if 
CP  equals  s,  the'velocity  of  Q  parallel  to  AB  is 


But  if  we  suppose  a  point  to  move  along  AB  in  such  a  manner  that  its 
velocity  in  each   position  is  the  same  as  that  of  the  oscillating  body,  its 

velocity  at  P  would   also    equal    A  I  &  (a*  —  s~)  •  and,  therefore,  this   point 

would  describe  AB  in  the  same  time  that  Q  describes  the  semicircumference 
AQB.     If  then  /  be  the  required  time  of  an  oscillation,  we  have 


no.  -7-  a  A  /£  =TT  A  /  r. 
V   r        V  g 


This  result  is  independent  of  the  length  of  the  arc  of  vibration,  provided  its 
amplitude,  that  is  AB,  be  small  —  not  exceeding  4  or  5  degrees,  for  instance. 
It  is  evident  from  the  formula  that  the  time  of  a  vibration  is  directly  pro- 
portional to  the  square  root  of  the  length  of  the  pendulum,  and  inversely 
proportional  to  the  square  root  of  the  accelerating  force  of  gravity. 

As  an  example  of  the  use  of  the  formula  we  may  take  the  following  :  —  It 
has  been  found  that  39*13983  inches  is  the  length  of  a  simple  pendulum 
whose  time  of  oscillation  at  Greenwich  is  one  second  ;  the  formula  at  once 
leads  to  an  accurate  determination  of  the  accelerating  force  of  gravity  g  ;  for 
using  feet  and  seconds  as  our  units  we  have  /=  i,  r  =  3*26165,  and  ?r  stands 
for  the  known  number  3-14159,  therefore  the  formula  gives  us 

g=  (3-I4I59)8  x  3-26765  =  32-1912. 

This  is  the  value  employed  in  (29). 

Other  examples  will  be  met  with  in  the  Appendix. 


-57J  Impulsive  Forces.  41 

56.  Graphic  Representation  of  the  Changes  of  Velocity  of  an  Oscil- 
lating: Body. — The  changes  which  the  velocity  of  a  vibrating  body  under- 
goes may  be  graphically  represented  as  follows  : — Draw  a  line  of  indefinite 
length  and  mark  off  AH  (fig.  37)  to  represent  the  time  of  one  vibration,  HH' 


Fig.  37- 

to  represent  the  time  of  the  second  vibration,  and  so  on.  During  the  first 
vibration  the  velocity  increases  from  zero  to  a  maximum  at  the  half-vibration, 
and  then  decreases  during  the  second  half-vibration  from  the  maximum  to 
zero.  Consequently,  a  curved  line  or  arc  AQH  may  be  drawn,  whose 
ordinate  OM  at  any  point  Q  will  represent  the  velocity  of  the  body  at  the 
time  represented  by  AM.  If  a  similar  curved  line  or  arc  HPH'  be  drawn, 
the  ordinate  PN  of  any  point  P  will  represent  the  velocity  at  a  time  denoted 
by  AN.  But  since  the  direction  of  the  velocity  in  the  second  oscillation  is 
contrary  to  that  of  the  velocity  in  the  first  oscillation,  the  ordinate  NP  must 
be  drawn  in  the  contrary  direction  to  that  of  MQ.  If,  then,  the  curve  be 
continued  by  a  succession  of  equal  arcs  alternately  on  opposite  sides  of  AD, 
the  variations  of  the  velocity  of  the  vibrating  body  will  be  completely  repre- 
sented by  the  varying  magnitudes  of  the  ordinates  of  successive  points  of 
the  curve.  The  last  article  shows  this  to  be  the  curve  of  sines  for  a 
pendulum. 

•pr  57,  Impulsive  Forces. — When  a  force  acts  on  a  body  for  an  inappre- 
ciably short  time,  and  yet  sensibly  changes  its  velocity,  it  is  termed  an  instan- 
taneous or  impulsive  force.  Such  a  force  is  called  into  play  when  one  body 
strikes  against  another.  A  force  of  this  character  is  nothing  but  a  finite 
though  very  large  force,  acting  for  a  time  so  short  that  its  duration  is  nearly, 
or  quite,  insensible.  In  fact,  if  M  is  the  mass  of  the  body,  and  the  force 
•contains  M/ units,  it  will,  in  a  time  /,  communicate  a  velocity  ft\  now,  how- 
ever small  /  may  be,  M/  and  therefore/  may  be  so  large  that  ft  may  be  of 
.sensible  or  even  considerable  magnitude.  Thus  if  M  contains  a  pound  of 
matter,  and  if  the  force  contains  ten  thousand  units,  though  t  were  so  short 
as  to  be  only  the  j~  of  a  second,  the  velocity  communicated  by  the  force 
would  be  one  of  10  feet  per  second.  It  is  also  to  be  remarked  that  the  body 
will  not  sensibly  move  while  this  velocity  is  being  communicated  ;  thus,  in 
the  case  supposed,  the  body  would  only  move  through  ^f£*  or  the  ~~  of  a 
foot  while  the  force  acts  upon  it. 

When  one  body  impinges  on  another,  it  follows  from  the  law  of  the 
equality  of  action  and  reaction  (39)  that  whatever  force  the  first  body  exerts 
upon  the  second,  the  second  will  exert  an  equal  force  upon  the  first  in  the 
opposite  direction.  Now  forces  are  proportional  to  the  momenta  generated 
in  the  same  time  ;  consequently,  these  forces  generate,  during  the  whole  or 
any  part  of  the  time  of  impact,  in  the  bodies  respectively,  equal  momenta 
with  contrary  signs  ;  and  therefore  the  sum  of  the  momenta  of  the  two  bodies 
will  remain  constant  during  and  at  the  end  of  the  impact.  It  is  of  course 
understood  that  if  the  two  bodies  move  in  contrary  directions  their  momenta 
have  opposite  signs,  and  the  sum  is  an  algebraical  sum.  In  order  to  test  the 


42  On  Matter,  Force,  and  Motion.  [57- 

physical  validity  of  this  conclusion,  Newton  made  a  series  of  experiments, 
which  may  be  thus  briefly  described — Two  balls  A  and  B  (fig.  38)  are  hung 

from  points  C,  D  in  the  same  horizontal 
line  by  threads  in  such  a  manner  that 
their  centres  A  and  B  are  in  the  same 
horizontal  line.  With  centre  C  and  ra- 
dius CA  describe  a  semicircle  EAF, 
and  with  centre  D  and  radius  DB 
describe  a  semicircle  GBH,  on  the 
wall  in  front  of  which  the  balls  hang. 
38>  Let  A  be  moved  back  to  R,  and  be 

allowed  to  descend  to  A  ;  it  there  im- 
pinges on  B  ;  both  A  and  B  will  now  move  along  the  arcs  AF  and  BH 
respectively  ;  let  A  and  B  come  to  their  highest  points  at  r  and  k  respectively. 
Now  if  V  denote  the  velocity  with  which  A  reaches  the  lowest  point,  v  and  u 
the  velocities  with  which  A  and  B  leave  the  lowest  points  after  impact,  and 
r  the  radius  AC,  it  follows  from  (54)  that 


V  =  chd  AR  A       ,  v  =  chd  Ar  *,  and  u  -  chd  B£ 

therefore  if  A  and  B  are  the  masses  of  the  two  balls,  the  momentum  at  the 
instant  before  impact  was  proportional  to  A  x  chd  AR,  and  the  momentum 
after  impact  was  proportional  to  A  x  chd  Ar  +  B  x  chd  B>£.  Now  when  the 
positions  of  the  points  R,  r,  and  k  had  been  properly  corrected  for  the 
resistance  of  the  air,  it  was  found  that  these  two  expressions  were  equal  to 
within  quantities  so  small  that  they  could  be  properly  referred  to  errors  of 
observation.  The  experiment  succeeded  equally  under  every  modification, 
whether  A  impinged  on  B  at  rest  or  in  motion,  and  whatever  the  materials  of 
A  and  B  might  be. 

58.  Direct  Collision  of  Two  Bodies.  —  Let  A  and  B  be  two  bodies 
moving  with  velocities  V  and  U  respectively,  along  the  same  line,  and  let 
their  mutual  action  take  place  in  that  line  ;  if  the  one  overtake  the  other, 
what  will  be  their  respective  velocities  at  the  instant  after  impact  ?  We  will 
answer  this  question  in  two  extreme  cases. 

i.  Let  us  suppose  the  bodies  to  be  quite  inelastic.  In  this  case,  when  A 
touches  B,  it  will  continue  to  press  against  B  until  their  velocities  are 
equalised,  when  the  mutual  action  ceases.  For  whatever  deformation  the 
bodies  may  have  undergone,  they  have  no  tendency  to  recover  their  shapes. 
If,  therefore,  x  is  their  common  velocity  after  impact,  we  shall  have  A;r+  B;r 
their  joint  momentum  at  the  end  of  impact,  but  their  momentum  before 
impact  was  AV  +  BU.  Whence 


an  equation  which  determines  x. 

ii.  Let  us  suppose  the  bodies  perfectly  elastic.  In  this  case  they  recover 
their  shapes,  with  a  force  exactly  equal  to  that  with  which  they  were  com- 
pressed. Consequently  the  whole  momentum  lost  by  the  one,  and  gained  by 
the  other,  must  be  exactly  double  of  that  lost  while  compression  took  place  ; 
that  is,  up  to  the  instant  at  which  their  velocities  were  equalised.  But  these 


-59]  Work:  Meaning  of  the  Term.  43 

are  respectively  AV  —  A^-and  B;r-  BU  ;  therefore,  if  v  and  u  are  the  required 

final  velocities, 

A7/  =  AV-2(AV-A;r)  orv=  -V  +  2r 
¥>u  =  BU  +  2(B,r-  B£  )  or  z/  =  2.r-  U, 

hence 


and 

(A  +  B)z/  -  2AV  -  (A  -  B)U.  JJr 

The  following  conclusion  from  these  equations  may  be  noticed  :  suppose  a 
ball  A,  moving  with  a  velocity  V,  to  strike  directly  an  equal  ball  B  at  rest. 
In  this  case  A  =  B  and  U  =  o,  consequently  v  =  o  and  u  =  V  ;  that  is,  the 
former  ball  A  is  brought  to  rest,  and  the  latter  B  moves  on  with  a  velocity  V. 
If  now  B  strike  on  a  third  equal  ball  C  at  rest,  B  will  in  turn  be  brought 
to  rest,  and  C  will  acquire  the  velocity  V.  And  the  same  is  true  if  there  is 
a  fourth,  or  fifth,  or  indeed  any  number  of  balls.  This  result  may  be  shown 
with  ivory  balls,  and  is  a  very  remarkable  experiment. 

59.  Work:  Meaningr  of  the  Term.  —  It  has  been  pointed  out  (19,  26) 
that  a  moving  body  has  no  power  of  itself  to  change  either  the  direction  or 
the  speed  of  its  motion,  and  that,  if  any  such  change  takes  place,  it  is  a  proof 
that  the  body  is  acted  upon  by  some  external  force.  But  although  change  of 
motion  thus  always  implies  the  action  of  force,  forces  are  often  exerted  with- 
out causing  any  change  in  the  motion  of  the  bodies  on  which  they  act.  For 
instance,  when  a  ship  is  sailing  at  a  uniform  speed,  the  force  exerted  on  it  by 
the  wind  causes  no  change  in  its  motion,  but  simply  prevents  such  a  change 
being  produced  by  the  resistance  of  the  water  ;  or,  when  a  railway-train  is 
running  with  uniform  velocity,  the  force  of  the  engine  does  not  change,  but 
only  maintains  its  motion  in  opposition  to  the  forces,  such  as  friction  and  the 
resistance  of  the  air,  which  tend  to  destroy  it. 

These  two  classes  of  cases  —  namely,  first,  those  in  which  forces  cause  a 
change  of  motion  ;  and  secondly,  those  in  which  they  prevent,  wholly  or  in 
part,  such  a  change  being  produced  by  other  forces  —  include  all  the  effects 
to  which  the  action  of  forces  can  give  rise.  When  acting  in  either  of  these 
ways,  a  force  is  said  to  do  work  :  an  expression  which  is  used  scientifically 
in  a  sense  somewhat  more  precise,  but  closely  accordant  with  that  in  which 
it  is  used  in  common  language.  A  little  reflection  will  make  it  evident  that,. 
in  all  cases  in  which  we  are  accustomed  to  speak  of  work  being  done  — 
whether  by  men,  horse-power,  or  steam-power,  and  however  various  the  pro- 
ducts may  be  in  different  cases  —  the  physical  part  of  the  process  consists 
solely  in  producing  or  changing  motion,  or  in  keeping  up  motion  in  opposition 
to  resistance,  or  in  a  combination  of  these  actions.  The  reader  will  easily 
convince  himself  of  this  by  calling  to  mind  what  the  definite  actions  are  which 
constitute  the  work  done  by  (say)  a  navvy,  a  joiner,  a  mechanic,  a  weaver  ;  that 
done  by  a  horse,  whether  employed  in  drawing  a  vehicle,  or  in  turning  a  gin  ; 
or  that  of  a  steam-engine,  whether  it  be  used  to  drag  a  railway-train  or  to 
drive  machinery.  In  all  cases  the  work  done  is  reducible,  from  a  mechanical 
point  of  view,  to  the  elements  that  have  been  mentioned,  although  it  may  be 
performed  on  different  materials,  with  different  tools,  and  with  different 
degrees  of  skill. 


44  On  Matter,  Force,  and  Motion.  [59- 

It  is,  moreover,  easy  to  see  (comp.  53)  that  any  possible  change  or 
motion  may  be  represented  as  a  gain  by  the  moving  body  of  an  additional 
(positive  or  negative)  velocity  either  in  the  direction  of  its  previous  motion, 
or  at  right  angles  to  it ;  but  a  body  which  gains  velocity  is  (27)  said  to  be 
accelerated.  Hence,  what  has  been  said  above  may  be  summed  up  as 
follows  : —  When  a  force  produces  acceleration,  or  when  it  maintains  motion 
unchanged  in  opposition  to  resistance,  it  is  said  to  do  WORK. 

60.  Measure  of  Work. — In  considering  how  work  is  to  be  measured,  or 
how  the  relation  between  different  quantities  of  work  is  to  be  expressed 
numerically,  we  have,  in  accordance  with  the  above,  to  consider  first,  work  oj 
acceleration ;  and  secondly,  work  against  resistance.  But  in  order  to  make 
the  evaluation  of  the  two  kinds  of  work  consistent,  we  must  bear  in  mind 
that  one  and  the  same  exertion  of  force  will  result  in  work  of  either  kind 
according  to  the  conditions  under  which  it  takes  place  :  thus,  the  force  of 
gravity  acting  on  a  weight  let  fall  from  the  hand  causes  it  to  move  with  a 
continually  accelerated  velocity  until  it  strikes  the  ground  ;  but  if  the  same 
weight,  instead  of  being  allowed  to  fall  freely  through  the  air,  be  hung  to  a 
cord  passing  round  a  cylinder  by  means  of  which  various  degrees  of  friction 
can  be  applied  to  hinder  its  descent,  it  can  be  made  to  fall  with  a  very  small 
and  practically  uniform  velocity.  Hence,  speaking  broadly,  it  may  be  said 
that,  in  the  former  case,  the  work  done  by  gravity  upon  the  weight  is  work  of 
acceleration  only,  while  in  the  latter  case  it  is  work  against  resistance  (friction) 
only.  But  it  is  very  important  to  note  that  an  essential  condition,  without 
which  a  force,  however  great,  cannot  do  work  either  of  one  kind  or  the  other, 
is  that  the  thing  acted  on  by  it  shall  move  while  the  force  continues  to  act. 
This  is  obvious,  for  if  no  motion  takes  place  it  clearly  cannot  be  either 
accelerated  or  maintained  against  resistance.  The  motion  of  the  body  on 
which  a  force  acts  being  thus  necessarily  involved  in  our  notion  of  work 
being  done  by  the  force,  it  naturally  follows  that,  in  estimating  how  much 
work  is  done,  we  should  consider  how  much — that  is  to  say,  how  far — the 
body  moves  while  the  force  acts  upon  it.  This  agrees  with  the  mode  of 
estimating  quantities  of  work  in  common  life,  as  will  be  evident  if  we  consider 
a  very  simple  case — for  instance,  that  of  a  labourer  employed  to  carry  bricks 
up  to  a  scaffold  :  in  such  a  case  a  double  number  of  bricks  carried  would 
represent  a  double  quantity  of  work  done,  but  so  also  would  a  double  height 
of  the  scaffold,  for  whatever  amount  of  work  is  done  in  raising  a  certain 
number  to  a  height  of  twenty  feet,  the  same  amount  must  be  done  again  to 
raise  them  another  twenty  feet,  or  the  amount  of  work  done  in  raising  the 
bricks  forty  feet  is  twice  as  great  as  that  done  when  they  are  raised  only 
twenty  feet.  It  is  also  to  be  noted  that  no  direct  reference  to  time  enters  into 
the  conception  of  a  quantity  of  work  :  if  we  want  to  know  how  much  work  a 
labourer  has  done,  we  do  not  ask  how  long  he  has  been  at  woflc,  but  what  he 
has  done — for  instance,  how  many  bricks  he  has  carried,  and  to  what  height ; 
.and  our  estimate  of  the  total  amount  of  work  is  the  same  whether  the  man 
has  spent  hours  or  days  in  doing  it. 

The  foregoing  relations  between  force  and  work  may  be  put  into  definite 
mathematical  language  as  follows  : — If  the  point  of  application  of  a  force 
moves  in  a  straight  line,  and  if  the  part  of  the  force  resolved  along  this  line 
acts  in  the  direction  of  the  motion,  the  product  of  that  component  and  the 


-60]  Measure  of  Work.  45 

length  of  the  line  is  the  work  done  by  the  force.  If  the  component  acts  in 
the  opposite  direction  to  the  motion,  the  component  may  be  considered  as 
a  resistance,  and  the  product  is  work  done  against  the  resistance.  Thus,  in 
(43),  if  we  suppose  a  to  move  up  the  plane  from  R  to  S,  the  work  done  by  P 
is  P  x  RS  :  the  work  done  against  the  resistance  W  is  W  sin  x  x  RS.  It 
will  be  observed  that  if  the  forces  are  in  equilibrium  during  the  motion,  so 
that  the  velocity  of  a  is  uniform,  P  equals  W  sin  x,  and  consequently  the 
work  done  by  the  power  equals  that  done  against  the  resistance.  Also,  since 
RS  sin  x  equals  ST,  the  work  done  against  the  resistance  equals  W  x  ST. 
In  other  words,  to  raise  W  from  R  to  S  requires  the  same  amount  of  work 
as  to  raise  it  from  T  to  S. 

If,  however,  the  forces  are  not  in  equilibrium,  the  motion  of  a  will  not  be 
uniform,  but  accelerated  ;  the  work  done  upon  it  will  nevertheless  still  be 
represented  by  the  product  of  the  force  into  the  distance  through  which  it 
acts.  In  order  to  ascertain  the  relation  between  the  amount  of  work  done 
and  the  change  produced  by  it  in  the  velocity  of  the  moving  mass,  we  must 
recall  one  or  two  elementary  mechanical  principles.  Let  F  be  the  resultant 
force  resolved  along  the  direction  of  motion,  and  S  the  distance  through 
which  its  point  of  application  moves  :  then,  according  to  what  has  been  said, 
the  work  done  by  the  force  =  FS.  Further,  it  has  been  pointed  out  (29)  that 
a  constant  force  is  measured  by  the  momentum  produced  by  it  in  a  unit  ,of 
time  :  hence,  if  T  be  the  time  during  which  the  force  acts,  V  the  velocity  of 
the  mass  M  at  the  beginning  of  this  period,  and  V,  the  velocity  at  the  end, 
the  momentum  produced  during  the  time  T  is  M  Vx  —  M  V,  and  consequently 
the  momentum  produced  in  a  unit  of  time,  or,  in  other  words,  the  measure 
of  the  force,  is 

F_M(V1-V)> 

The  distance  S  through  which  the  mass  M  moves  while  its  velocity 
changes  from  the  value  V  to  the  value  Vl  is  the  same  as  if  it  had  moved 
during  the  whole  period  T  with  a  velocity  equal  to  the  average  value  of  the 
varying  velocity  which  it  actually  possesses.  But  a  constant  force  acting 
upon  a  constant  mass  causes  its  velocity  to  change  at  a  uniform  rate  ;  hence, 
in  the  present  case,  the  average  velocity  is  simply  the  arithmetical  mean  of 
the  actual  and  final  velocities  : 


Combining  this  with  the  last  equation,  we  get  as  the  expression  for  the 
work  done  by  the  force  F  : 


or,  in  words,  when  a  constant  force  acts  on  a  mass  so  as  to  change  its 
velocity,  the  work  done  by  the  force  is  eqital  to  half  the  product  of  the  mass 
into  the  change  of  the  square  of  the  velocity. 

•  The  foregoing  conclusion  has  been  arrived  at  by  supposing  the  force  F 
to  be  constant,  but  it  is  easy  to  show  that  it  holds  good  equally  if  F  is  the 
average  magnitude  of  a  force  which  varies  from  one  part  to  another  of  the 
total  distance  through  which  it  acts.  To  prove  this,  let  the  distance  S  be 
subdivided  into  a  very  great  number  n  of  very  small  parts,  each  equal  to  s, 


46  On  Matter,  Force,  and  Motion.  [60- 

so  that  ns  =  S.  Then,  by  supposing  s  to  be  sufficiently  small,  we  may  with- 
out any  appreciable  error  consider  the  force  as  constant  within  each  of  these 
intervals,  and  as  changing  suddenly  as  its  point  of  application  passes  from 
-one  interval  to  the  next.  Let  F15  F2,  F3  .  .  .  .  F«,  be  the  forces  acting 
throughout  the  ist,  2nd,  3rd  ....  72th  interval  respectively,  and  let  the 
velocity  at  the  end  of  the  same  intervals  be  vl9  v^  v3,  .  .  .  .  vn  (  =  VX) 
respectively  ;  then,  for  the  work  done  in  the  successive  intervals,  we  have  : 


•or,  for  the  total  work, 


where  the   quantity  of  the   left-hand   side  of  the  equation  may    also   be 
written  Fi  +  F2+   •  •    +F".».y  =  FS,  if  we  put  F  to  stand  for  the  average  (or 

arithmetical  mean)  of  the  forces  F15  F2,  &c. 

An  important  special  case  of  the  application  of  the  above  formula  arises 
when  either  the  initial  or  the  final  velocity  of  the  mass  M  is  nothing  ;  that 
is  to  say,  when  the  effect  of  the  force  is  to  make  a  body  pass  from  a  state 
of  rest  into  one  of  motion,  or  from  a  state  of  motion  into  one  of  rest.  The 
general  expression  then  assumes  one  of  the  following  forms,  namely  :  — 


-FS=MV2; 

the  first  of  which  denotes  the  quantity  of  work  which  must  be  done  on  a  body 
•of  mass  M  in  order  to  give  to  it  the  velocity  Vt,  while  the  second  expresses 
the  work  that  must  be  done  in  order  to  bring  the  same  mass  to  rest  when  it 
is  moving  with  the  velocity  V0,  the  negative  sign  in  the  latter  case  showing 
that  the  force  here  acts  in  opposition  to  the  actual  motion,  and  is  therefore 
to  be  regarded  as  a  resistance. 

In  practice,  the  case  which  most  frequently  occurs  is  where  work  of  ac- 
•celeration  and  work  against  resistance  are  performed  simultaneously.  Thus, 
recurring  to  the  inclined  plane  already  referred  to  in  art.  43  ;  if  the  force  P 
(where  P  is  the  constant  force  with  which  the  string  pulls  W  up  the  plane) 
be  greater  than  W  sin  x,  the  body  W  will  move  up  the  incline  with  a  con- 
tinually increasing  velocity,  and  if  the  point  of  application  of  P  be  displaced 
from  R  to  S,  the  total  amount  of  work  done,  namely,  P  x  RS,  consists  of  a 
portion  =  W  sin  x  RS,  done  against  the  resistance  of  the  weight  W,  and  of  a 
portion  =  (P  —  W  sin  x)  RS  expended  in  accelerating  the  weight.  Hence,  to 
determine  the  velocity  v  with  which  W  arrives  at  the  top  of  the  incline  we 
have  the  equation 


-61a]  Systems  of  Units.  47 

for  the  portion  of  P  which  is  in  excess  of  what  is  required  to  produce  equili- 
brium with  the  weight  W,  namely,  F  -  W  sin  ;tr,  corresponds  to  the  resultant 
force  F  supposed  in  the  foregoing  discussion,  and  RS  to  the  distance  through 
which  this  resultant  force  acts. 

61.  Unit  of  Work.  Power. — For  strictly  scientific  purposes  a  unit  of  work 
is  taken  to  be  the  work  done  by  a  unit  of  force  when  its  point  of  application 
moves  through  one  foot  in  the  direction  of  its  action  ;  but,  as  a  convenient 
and  sufficiently  accurate  standard  for  practical  purposes,  the  quantity  of  work 
which  is  done  in  lifting  I  pound  through  the  height  of  I  foot  is  commonly 
adopted  as  the  unit,  and  this  quantity  of  work  is  spoken  of  as  one  '  foot- 
pound.' It  is,  however,  important  to  observe  that  the  foot-pound  is  not  per- 
fectly invariable,  since  the  weight  of  a  pound,  and  therefore  the  work  done 
in  lifting  it  through  a  given  height,  differs  at  different  places,  being  a  little 
greater  near  the  Poles  than  near  the  Equator. 

On  the  metrical  system  the  kilogrammetre  is  the  unit ;  it  is  the  work 
done  when  a  weight  of  a  kilogramme  is  raised  through  a  height  of  a 
metre.  This  is  equal  to  7*24  foot-pounds,  and  one  foot-pound  =  '1381  of  a 
kilogrammetre. 

In  estimating  the  usefulness  of  any  motor  it  becomes  necessary  to  know 
the  time  required  by  it  for  doing  a  given  amount  of  work.  The  amount  of 
work  per  second  is  the  power  of  the  motor.  The  unit  of  power  is  the 
power  required  to  do  a  unit  of  work  in  a  unit  of  thne.  For  measuring  the 
power  of  engines  the  unit  used  is  the  horse-power,  which  represents  a  rate 
of  work  of  33,000  foot-pounds  per  minute. 

It  is  to  be  observed  that  in  every  case  the  unit  is  of  the  same  denomi- 
nation as  the  thing  or  quantity  measured.  The  unit  of  length  must  be  a 
length  ;  the  unit  of  value  must  be  a  definite  quantity  of  some  valuable 
commodity.  The  numbers,  to  determine  which  is  one  of  the  objects  of 
physical  research,  are  to  be  considered  as  abstract  numbers,  representing 
how  many  times  the  unit  is  taken. 

6ia.  Systems  of  units.— The  units  of  mass,  length,  and  time  are  said 
to  be  fundamental  units,  as  all  other  units,  such  as  those  of  area,  velocity, 
acceleration,  power,  &c.,  are  referred  to  them.  These  latter  units  are  there- 
fore called  derived  units.  The  magnitudes  of  the  fundamental  units  are, 
however,  arbitrary.  A  large  class  of  writers  use  the  centimetre,  gramme, 
and  second,  and  this  system  is  usually  called  the  C.G.S.  system  ;  others 
use  the  foot,  pound,  and  second.  It  thus  becomes  important  to  have  a 
systematic  method  of  reducing  measurements  from  one  system  of  units  to 
another. 

Let  L,  M,  T  represent  respectively  the  magnitude  or  dimensions  of  the 
centimetre,  the  gramme,  and  the  second,  and  L',  M',  T'  represent  the 
dimensions  of  the  foot,  the  pound,  and  the  minute.  Then,  if  a  wire  is  found 
to  be  /  cm.  or  /'  ft.  in  length,  its  length  may  be  represented  either  by  /L  or 
/'I/,  and  hence 

/L-/'L',  or /=£-/'. 

The  ratio  -'  is  the  length  of  a  foot  in  centimetres,  and  has  been  found 
L. 


48  On  Matter,  Force,  and  Motion.  [61a- 

by  direct  comparison  to  be  30-4797.     Hence  any  measurement,  I'  in  feet,  is 
converted  into  centimetres  by  multiplying  /'  by  this  number. 

In  a  similar  manner,  if  m  and  m'  represent  the  number  of  units  of  mass 
in  a  piece  of  matter  in  the  two  systems, 

M'    , 
m  =  ^  m', 
M 

where  the  unit  ratio  is  the  number  of  grammes  in  a  pound,  or  453'59. 
For  converting  a  volume  vf  into  the  equivalent  V, 


For  Density,  ?J  = 


m     M  =m'     M' 
T3  '  P"/73  '  L73' 


Here  the  ratio  ^  is  said  to  be  a  measure  of  the  magnitude  or  dimensions 

of  the  unit  of  density,  in  terms  of  the  dimensions  of  the  fundamental  units 
of  mass  and  length.  If  a  substance  is  said  to  have  a  unit  density,  then  if  M 
is  the  gramme  and  L3  the  cubic  centimetre,  the  density  of  the  substance 
would  be  that  of  water.  If,  however,  M  were  the  kilogramme  and  L3  the 
cubic  centimetre,  the  density  would  be  a  thousand  times  that  of  water. 
If,  again,  L3  represents  a  cubic  decimetre,  and  M  the  kilogramme,  the 
density  would  again  be  that  of  water.  It  appears,  then,  that  the  magnitude 
of  the  unit  of  density  is  directly  proportional  to  the  magnitude  of  the  unit 
of  mass,  and  inversely  as  the  magnitude  of  the  unit  of  volume  or  the  cube  of 
the  unit  of  length.  As  the  unit  density  is  the  density  of  a  unit  mass  to  the 

unit  volume,  it  is  clear  that    -^   measures   the   dimensions  of  the  unit   of 
density.     Similar  explanations  apply  in  the  succeeding  cases. 
For  Velocity,  v  = 


v  „> 

L      T'' 

TheratioT      second      i 
T'     minute     60 

If  the  units  of  time  were  the  same,  the  unit  factor  T7  =  i,  and  the  velo- 
city in  centimetres  would  be 

~g*i 

where  v'  is  the  velocity  in  feet  per  second. 


~61a]  Systems  of  Units.  49 

For  Momentum,  mv  =  _ 

^.ML^wV'     M'L' 

AT/  T /  T 
or  w.7/  =  ^L    *•     x      ^,/. 


X2 


^?r  Acceleration,  a  =  ^  =  _£ 
/     /8 


where  a'  is  the  acceleration  in  feet  per  minute. 
For  Force,?  =  ma  = 


F-M/    L' 
M      L 

In  the  C.G.S.  system  the  unit  is  called  the  Dyne. 
For  Work,  W  =  F/  =  ^ 

ml*     ML2     m'l'*     WL'* 


In  the  C.G.S.  system  the  unit  of  work  is  called  the  Erg. 
RateofWork,  or  Power,  P  =  ^/=w/_2 


M'L'3 


If  work  is  expressed  in  foot-pounds  or  kilogramme-metres,  the  unit  of 
force  being  the  weight  of  a  pound  or  kilogramme,  then  to  convert  a  certain 
number  of  foot-pounds  into  kilogramme-metres  we  have 

wl. 


Work  (kgr.-m.)  =  (^  .  tj  work,  foot-pounds, 


the  unit  factor  being  thus  0-1383. 


50  On  Matter,  Force,  and  Motion.  [61a- 

Similarly,  to  convert  foot-pounds  per  minute  into  kilogr.  -metres  per  second, 

p     /W'L'   T\p/ 
\W    L  T'J 

where  the  conversion  factor  becomes  0*00230. 

The  units  commonly  used  for  measuring  the  power  of  engines  are  the 
horse-power,  which  is  33,000  times  as  great  as  the  unit  in  which  P'  of  the 
last  equation  was  measured,  and  the  force  de  cheval,  which  is  75  times  as 
great  as  the  unit  in  which  P  was  measured.  Hence,  if  P'  is  to  be  in  horse- 
power, and  P  in.  force  de  cheval,  the  equation  will  become 


=  0-00230 

=  1-0139?', 

and  hence  one  British  horse-power  =  1-0139  force  de  cheval. 

These  examples  will  be  sufficient  to  indicate  the  method  of  converting 
measurements  from  one  system  of  units  to  any  other,  and  the  treatment  of 
other  derived  units  may  be  deferred  until  they  are  needed. 
)?  62.  Energy.  —  The  fact  that  any  agent  is  capable  of  doing  work  is  usually 
expressed  by  saying  that  it  possesses  Energy,  and  the  quantity  of  energy  it 
possesses  is  measured  by  the  amount  of  work  it  can  do.  For  example,  in 
the  case  of  the  inclined  plane  above  referred  to,  the  working  power  or  energy 
of  the  force  P  is  P  x  RS  ;  and  if  this  force  acts  under  the  conditions  last 
supposed,  by  the  time  its  own  energy  is  exhausted  (in  consequence  of  its 
point  of  application  having  arrived  at  S,  the  limit  of  the  range  through  which 
it  is  supposed  able  to  act),  it  has  conferred  upon  the  weight  W  a  quantity  of 
energy  equal  to  that  which  has  been  expended  ;  for,  in  the  first  place,  W 
has  been  raised  through  a  vertical  height  equal  to  ST,  and  could  by  falling 
again  through  the  same  height  do  an  amount  of  work  represented  by  W  x  ST  ; 
and  in  the  second  place  W  can  do  work  by  virtue  of  the  velocity  that  has 
been  imparted  to  it,  and  can  continue  moving  in  opposition  to  any  given 
resistance  R  through  a  distance  s,  such  that 


The  energy  possessed  by  the  mass  M  in  consequence  of  having  been  raised 
from  the  ground  is  commonly  distinguished  as  energy  of  position  or  potential 
energy  y  and  is  measured  by  the  product  of  the  force  tending  to  cause  motion 
into  the  distance  through  which  the  point  of  application  of  the  force  is 
capable  of  being  displaced  in  the  direction  in  which  the  force  acts.  The 
energy  possessed  by  a  body  in  consequence  of  its  velocity  is  commonly  dis- 
tinguished as  energy  of  motion,  or  kinetic  energy  :  it  is  measured  by  half  the 
product  of  the  moving  mass  into  the  square  of  its  velocity. 

63.  Varieties  of  Energy.  —  It  will  be  seen,  on  considering  the  definition 
of  work  given  above,  that  a  force  is  said  to  do  work  when  it  produces  any 
change  in  the  condition  of  bodies  ;  for  the  only  changes  which,  according  to 
the  definition  of  force  given  previously  (26),  a  force  is  capable  of  producing, 
are  changes  in  the  state  of  rest  or  motion  of  bodies  and  changes  of  their 
place,  in  opposition  to  resistances  tending  to  prevent  motion  or  to  produce 


-64]  Transformation  of  Energy.  e ! 

motion  in  an  opposite  direction.  There  are,  however,  many  other  kinds  of 
physical  changes  which  can  be  produced  under  appropriate  conditions,  and 
the  recent  progress  of  investigation  has  shown  that  the  conditions  under 
which  changes  of  all  kinds  ogcur  are  so  far  analogous  to  those  required  for 
the  production  of  work  by  mechanical  forces  that  the  term  work  has  come 
to  be  used  in  a  more  extended  sense  than  formerly,  and  is  now  often  used  to 
signify  the  production  of  any  sort  of  physical  change. 

Thus  work  is  said  to  be  done  when  a  body  at  a  low  temperature  is  raised 
to  a  higher  temperature,  just  as  much  as  when  a  weight  is  raised  from  a 
lower  to  a  higher  level ;  or,  again,  work  is  done  when  an  electrical,  magnetic, 
or  chemical  change  is  produced.  This  extension  of  the  meaning  of  the 
term  work  involves  a  similar  extension  of  the  meaning  of  energy,  which  in 
this  wider  sense  may  be  defined  as  the  capacity  for  producing  physical 
change. 

As  examples  of  energy  in  this  more  general  sense;  the  following  may  be 
mentioned  : — (a)  the  energy  possessed  by  gunpowder  in  virtue  of  the  mutual 
chemical  affinities  of  its  constituents,  whereby  it  is  capable  of  doing  work  by 
generating  heat  or  by  acting  on  a  cannon-ball  so  as  to  change  its  state  of 
rest  into  one  of  rapid  motion  ;  (6)  the  energy  of  a  charged  Leyden  jar,  which, 
according  to  the  way  in  which  the  jar  is  discharged,  can  give  rise  to  changes 
of  temperature,  to  changes  of  chemical  composition,  to  mechanical  changes, 
or  to  changes  of  magnetic  or  electrical  condition  ;  (c]  the  energy  of  a  red-hot 
ball,  which,  amongst  other  effects  it  is  capable  of  producing,  can  raise  the 
temperature  and  increase  the  volume  of  bodies  colder  than  itself,  or  can 
change  ice  into  water  or  water  into  steam  ;  the  energy  of  the  stretched 
string  of  a  bow  :  here  work  has  been  consumed  in  stretching  the  string  ; 
when  it  is  released  the  work  reappears  in  the  velocity  imparted  to  the 
arrow. 

XT  64.  Transformation  of  Energy. — It  has  been  found  by  experiment 
that  when  one  kind  of  energy  disappears  or  is  expended,  energy  of  some 
other  kind  is  produced,  and  that,  under  proper  conditions,  the  disappearance 
of  any  one  of  the  known  kinds  of  energy  can  be  made  to  give  rise  to  a  greater 
or  less  amount  of  any  other  kind.  One  of  the  simplest  illustrations  that  can 
be  given  of  this  transformation  of  energy  is  afforded  by  the  oscillations  of  a 
pendulum.  When  the  pendulum  is  at  rest  in  its  lowest  position  it  dees  not 
possess  any  energy,  for  it  has  no  power  of  setting  either  itself  or  other  bodies 
in  motion,  or  of  producing  in  them  any  kind  of  change.  In  order  to  set  the 
pendulum  oscillating,  work  must  be  done  upon  it,  and  it  thereafter  possesses 
an  amount  of  energy  corresponding  to  the  work  that  has  been  expended. 
When  it  has  reached  either  end  of  its  path,  the  pendulum  is  for  an  instant  at 
rest';  but  it  possesses  energy  by  virtue  of  its  position,  and  can  do  an  amount  of 
work  while  falling  to  its  lowest  position,  which  is  represented  by  the  product 
of  its  weight  into  the  vertical  height  through  which  its  centre  of  gravity  de- 
scends. When  at  the  middle  of  its  path  the  pendulum  is  passing  through  its 
position  of  equilibrium,  and  has  no  power  of  doing  work  by  falling  lower ;  but 
it  now  possesses  energy  by  virtue  of  the  velocity  which  it  has  gained,  and 
this  energy  is  able  to  carry  it  up  on  the  second  side  of  its  lowest  position  to 
a  height  equal  to  that  from  which  it  has  descended  on  the  first  side.  By 
the  time  it  reaches  this  position  the  pendulum  has  lost  all  its  velocity,  but  it 

E  2 


52  On  Matter,  Force,  and  Motion.  [64- 

has  regained  the  power  of  falling  :  this,  in  its  turn,  is  lost  as  the  pendulum 
returns  again  to  its  lowest  position,  but  at  the  same  time  it  regains  its  pre- 
vious velocity.  Thus,  during  every  quarter  of  an  oscillation  the  energy  of 
the  pendulum  changes  from  potential  energy  of  position  into  actual  energy 
or  energy  of  motion,  or  vice  versa. 

A  more  complex  case  of  the  transformation  of  energy  is  afforded  by  a 
thermo-electric  pile,  the  terminals  of  which  are  connected  by  a  conducting 
wire :  the  application  of  energy  in  the  form  of  heat  to  one  face  of  the  pile 
gives  rise  to  an  electric  current  in  the  wire,  which,  in  its  turn,  reproduces 
heat,  or  by  proper  arrangements  can  be  made  to  produce  chemical,  magnetic, 
or  mechanical  effects,  such  as  those  described  below  in  the  chapters  on 
Electricity. 

It  has  also  been  found  that  the  transformations  of  energy  always  take 
place  according  to  fixed  proportions.  For  instance,  when  coal  or  any  other 
combustible  is  burned,  its  chemical  energy,  or  power  of  combining  with 
oxygen,  vanishes,  and  heat  or  thermal  energy  is  produced,  and  the  quantity 
of  heat  produced  by  the  combustion  of  a  given  amount  of  coal  is  fixed  and 
invariable.  If  the  combustion  take  place  under  the  boiler  of  a  steam-engine, 
mechanical  work  can  be  obtained  by  the  expenditure  of  part  of  the  heat  pro- 
duced, and  here  again  the  quantitative  relation  between  the  heat  expended 
and  the  work  gained  in  place  of  it  is  perfectly  constant. 

65.  Conservation  of  Energy. — Another  result  of  great  importance,  which 
has  been  arrived  at  by  experiment,  is  that  the  total  amount  of  energy  possessed 
by  any  system  of  bodies  is  unaltered  by  any  transformations  arising  from  the 
action  of  one  part  of  the  system  upon  another,  and  can  only  be  increased  or 
diminished  by  effects  produced  on  the  system  by  external  agents.  In  this 
statement  it  is  of  course  understood  that  in  reckoning  the  sum  of  the  energy 
of  various  kinds  which  the  system  may  possess,  those  amounts  of  the 
different  forms  of  energy  which  are  mutually  convertible  into  each  other  are 
taken  as  being  numerically  equal ;  or,  what  comes  virtually  to  the  same 
thing,  the  total  energy  of  the  system  is  supposed  to  be  reduced — either  ac- 
tually, or  by  calculation  from  the  known  ratio  of  transformation  of  the  various 
forms  of  energy — to  energy  of  some  one  kind  ;  then  the  statement  is  equivalent 
to  this  :  that  the  total  energy  of  any  one  form  to  which  the  energy  of  a  given 
system  of  bodies  is  reducible  is  unalterable  so  long  as  the  system  is  not  acted 
on  from  without.  Practically  it  is  always  possible,  in  one  way  or  another,  to 
convert  the  whole  of  the  energy  possessed  by  any  body  or  system  of  bodies 
into  heat,  but  it  cannot  be  all  converted  without  loss  into  any  other  form  of 
energy ;  hence  the  principle  stated  at  the  beginning  of  this  article  can  be 
enunciated  in  the  closest  conformity  with  the  direct  results  of  experiment  by 
saying  that,  so  long  as  any  system  of  bodies  is  not  acted  on  from  without 
the  total  quantity  of  heat  that  can  be  obtained  from  it  is  unalterable  by  any 
changes  which  may  go  on  within  the  system  itself.  For  instance,  a  quantity 
of  air  compressed  into  the  reservoir  of  an  air-gun  possesses  energy  which  is 
represented  partly  by  the  heat  which  gives  to  it  its  actual  temperature  above 
the  absolute  zero  (460),  and  partly  by  the  work  which  the  air  can  do  in  expand- 
ing. This  latter  portion  can  be  converted  into  heat  in  various  ways,  as,  for 
example,  by  allowing  the  air  to  escape  through  a  system  of  capillary  tubes 
so  fine  that  the  air  issues  from  them  without  any  sensible  velocity;  if,  how- 


-65]  Conservation  of  Energy.  53 

ever,  the  expanding  air  be  employed  to  propel  a  bullet  from  the  gun,  it 
produces  considerably  less  heat  than  in  the  case  previously  supposed,  the 
deficiency  being  represented  for  a  time  by  the  energy  of  the  moving  bullet, 
but  reappearing  in  the  form  of  heat  in  the  friction  of  the  bullet  against  the 
air,  and,  when  the  motion  of  the  bullet  is  destroyed,  by  striking  against  an 
inelastic  obstacle  at  the  same  level  as  the  gun.  But  whatever  the  mode  and 
however  numerous  the  intermediate  steps  by  which  the  energy  of  the  com- 
pressed air  is  converted  into  heat,  the  total  quantity  of  heat  finally  obtainable 
from  it  is  the  same. 


54  Gravitation  and  Molecular  Attraction.  [66- 


BOOK    II. 

GRAVITATION   AND    MOLECULAR   ATTRACTION. 


CHAPTER    I. 
GRAVITY.      CENTRE   OF   GRAVITY.      THE   BALANCE. 

66.  Universal  Attraction :  its  Laws. —  Universal  attraction  is  a  force 
in  virtue  of  which  the  material  particles  of  all  bodies  tend  incessantly  to 
approach  each  other ;  it  is  a  mutual  action,  however,  which  all  bodies,  at 
rest  or  in  motion,  exert  upon  one  another,  no  matter  how  great  or  how  small 
the  space  between  them  may  be,  or  whether  this  space  be  occupied  or  un- 
occupied by  other  matter. 

A  vague  hypothesis  of  the  tendency  of  the  matter  of  the  earth  and  stars 
to  a  common  centre  was  adopted  even  by  Democritus  and  Epicurus.  Kepler 
assumed  the  existence  of  a  mutual  attraction  between  the  sun,  the  earth,  and 
the  other  planets.  Bacon,  Galileo,  and  Hooke  also  recognised  the  existence 
of  universal  attraction.  But  Newton  was  the  first  who  established  the  law, 
and  the  universality  of  gravitation. 

Since  Newton's  time  the  attraction  of  matter  by  matter  was  experiment- 
ally established  by  Cavendish.  This  eminent  English  physicist  succeeded, 
by  means  of  a  delicate  torsion  balance  (89),  in  rendering  visible  the  attraction 
between  a  large  leaden  and  a  small  copper  ball. 

The  attraction  between  any  two  bodies  is  the  resultant  of  the  attractions 
of  each  molecule  of  the  one  upon  every  molecule  of  the  other  according  to 
the  law  of  Newton,  which  may  be  thus  expressed  :  the  attraction  between 
two  material  particles  is  directly  proportional  to  the  product  of  their  masses 
and  inversely  proportional  to  the  square  of  their  distances  asunder.  To 
illustrate  this,  we  may  take  the  case  of  two  spheres,  which,  owing  to  their 
symmetery,  attract  each  other  just  as  if  their  masses  were  concentrated  in 
their  centres.  If  without  other  alteration  the  mass  of  one  sphere  were 
doubled,  tripled,  £c.,  the  attraction  between  them  would  be  doubled,  tripled, 
£c.  If,  however,  the  mass  of  one  sphere  being  doubled,  that  of  the  other 
were  increased  three  times,  the  distance  between  their  centres  remaining  the 
same,  the  attraction  would  be  increased  six  times.  Lastly,  if,  without  alter- 
ing their  masses,  the  distance  between  their  centres  were  increased  from  i 
to  2,  3,  4  ....  units,  the  attraction  would  be  diminished  to  the  4th,  Qth, 


~67]  Universal  Attraction  :  its  Laws.  5  r 

i6th,  ....  part  of  its  former  intensity.     In  short,  if  we  define  the  unit  of 
attraction  as  that  which  would  exist  between  two   units   of  mass   whose 
distance  asunder  was  the  unit  of  length,  the  attraction  of  two  molecule 
having  the  masses  m  and  m',  at  the  distance  r,  would  be  expressed  bv 
mm'  * 

67.  Terrestrial  gravitation.- The  tendency  of  any  body  to  fall  towards 
the  earth  is  due  to  the  mutual  attraction  of  that  body  and  the  earth  or  to 
terrestrial  gravitation,  and  is,  in  fact,  merely  a  particular  case  of  universal 
attraction. 

At  any  point  of  the  earth's  surface,  the  direction  of  gravity— that  is  the 
line  which  a  falling  body  describes— is  called  the  vertical  line.  The  vertical 
lines  drawn  at  different  points  of  the  earth's  surface  converge  very  nearly  to 
the  earth's  centre.  For  points  situated  on  the  same  meridian  the  angle  con- 
tained between  the  vertical  lines  equals  the  difference  between  the  latitudes 
of  those  points. 

The  directions  of  the  earth's  attraction  upon  neighbouring  bodies,  or  upon 
different  molecules  of  one  and  the  same  body,  must,  therefore,  be  considered 
as  parallel,  for  the  two  vertical  lines  form  the  sides  of  a  triangle  whose  vertex 
is  near  the  earth's  centre,  about  4,000  miles  distant,  and  whose  base  is  the 
small  distance  between  the  molecules  under  consideration. 

A  plane  or  line  is  said  to  be  horizontal  when  it  is  perpendicular  to  the 
vertical  line. 

The  vertical  line  at  any  point  of  the  globe  is  generally  determined  by  the 
plumb-line  (fig.  39),  which  consists  of  a  weight  attached  to  the  end  of  a  string. 
It  is  evident  that  the  weight  cannot  be  in  equilibrium  un- 
less the  direction  of  the  earth's  attraction  upon  it  passes 
through  the  point  of  support,  and  therefore  coincides  with 
that  of  the  string. 

The  horizontal  plane  is  also  determined  with  great 
ease,  since  it  coincides,  as  will  be  afterwards  shown,  with 
the  level  surface  of  every  liquid  when  in  a  state  of  equili- 
brium. 

When  the  mean  figure  of  the  earth  has  been  approxi- 
mately determined,  it  becomes  possible  to  compare  the 
direction  of  the  plumb-line  at  any  place  with  that  of  the 
normal  to  the  mean  figure  at  that  place.  When  any  differ- 
ence in  these  directions  can  be  detected,  it  constitutes  a 
deviation  of  the  plumb-line,  and  is  due  to  the  attraction  of  ~ 
some  great  mass  of  matter  in  the  neighbourhood,  such  as 
a  mountain.  Thus,  in  the  case  of  the  mountain  of  Schehallien,  in  Perthshire, 
it  was  found  by  Dr.  Maskelyne  that  the  angle  between  the  directions  of  two 
plumb-lines,  one  at  a  station  to  the  north,  and  the  other  to  the  south,  of  the 
mountain,  was  greater  by  ii"-6  than  the  angle  between  the  normals  of  the 
mean  surface  of  the  earth  at  those  points  ;  in  other  words,  each  plumb-line 
was  deflected  by  about  6"  towards  the  mountain.  By  calculating  the  volume 
and  mass  of  the  mountain,  it  was  inferred  from  this  observation  that  the 
mean  density  of  the  mountain  was  to  that  of  the  earth  in  the  ratio  of  5  :  9, 
and  that  the  mean  density  of  the  earth  is  about  five  times  that  of  water — a 


56  Gravitation  and  Molecular  Attraction.  [67- 

result  agreeing  pretty  closely  with  that  deduced  from  Cavendish's  experiment 
referred  to  in  the  last  article. 

68.  Centre  of  gravity,  its  experimental  determination. — Into  what- 
ever position  a  body  may  be  turned  with  respect  to  the  earth,  there  is  a 
certain  point,  invariably  situated  with  respect  to  the  body,  through  which 
the  resultant  of  the  attracting  forces  between  the  earth  and  its  several  mole- 
cules always  passes.  This  point  is  called  the  centre  of  gravity  :  it  may  be 
within  or  without  the  body,  according  to  the  form  of  the  latter  ;  its  existence, 
however,  is  easily  established  by  the  following  considerations  :  Let  m  m'  m" 
m'".  .  .  .  (fig.  40)  be  molecules  of  any  body.  The  earth's  attraction  upon 
these  molecules  will  constitute  a  system  of  parallel  forces,  having  a  common 
vertical  direction,  whose  resultant  will  be  found  by  seeking  first  the  resultant 
of  the  forces  which  act  on  any  two  molecules,  m  and  m',  then  that  of  this 
resultant,  and  a  third  force  acting  on  ;#",  and  so  on  until  we  arrive  at  the 
final  resultant,  W,  representing  the  weight  of  the  body,  and  applied  at  a 
certain  point,  G.  If  the  body  be  now  turned  into  the  position  shown  in 
fig.  41,  the  molecules  ;;z,  m\  m".  .  .  will  continue  to  be  acted  on  by  the 


same  forces  as  before,  the  resultant  of  the  forces  on  m  and  mf  will  pass 
through  the  same  point  o  in  the  line  mm' ,  the  following  resultant  will  again 
pass  through  the  same  point  o'  in  om"^  and  so  on  up  to  the  final  resultant 
P,  which  will  still  pass  through  the  same  point  G,  which  is  the  centre  of 
gravity. 

To  find  the  centre  of  gravity  of  a  body  is  a  purely  geometrical  problem  ; 
in  many  cases,  however,  it  can  be  at  once  determined.  For  instance,  the 
centre  of  gravity  of  a  right  line  of  uniform  density  is  the  point  which  bisects 
its  length ;  in  the  circle  and  sphere  it  coincides  with  the  geometrical  centre ; 
in  cylindrical  bars  it  is  the  middle  point  of  the  axis.  The  centre  of  gravity 
of  a  plane  triangle  is  in  the  line  which  joins  any  vertex  with  the  middle  of 
the  opposite  side,  and  at  a  distance  from  the  vertex  equal  to  two-thirds  of 
this  line  :  in  a  cone  or  pyramid  it  is  in  the  line  which  joins  the  vertex  with 
the  centre  of  gravity  of  the  base,  and  at  a  distance  from  the  vertex  equal  to 
three-fourths  of  this  line.  These  rules,  it  must  be  remembered,  presuppose 
that  the  several  bodies  are  of  uniform  density. 

In  order  to  determine  experimentally  the  centre  of  gravity  of  a  body,  it 
is  suspended  by  a  string  in  two  different  positions,  as  shown  in  figs.  42  and 
43  ;  the  point  where  the  directions  AB  and  CD  of  the  string  in  the  two  ex- 


-70] 


Centre  of  Gravity. 


Fig.  42. 


Fig.  43- 


57 

periments  intersect  each  other  is  the  centre  of  gravity  required.  For  the 
resultant  of  the  earth's  attraction  being  a  vertical  force  applied  at  the  centre 
of  gravity,  the  body  can  only  be  in  equilibrium  when  the  point  lies  vertically 
under  the  point  of  suspension  ;  that  is,  in  the  prolongation  of  the  suspended 
string.  But  the  centre  of  gravity, 
being  in  AB  as  well  as  in  CD,  must 
coincide  with  the  point  of  intersec- 
tion of  these  two  lines. 

The  centre  of  gravity  of  a  thin 
piece  of  cardboard  of  irregular 
shape,  for  instance,  may  be  found 
by  balancing  it  in  two  positions  on 
a  knife-edge  ;  the  centre  of  gravity 
will  then  lie  in  the  intersection  of 
the  two  lines. 

69.  Equilibrium       of      heavy 
bodies. — Since  the  action  of  gravity 
upon    a   body  reduces    itself  to   a 
single  vertical  force  applied  at  the 
centre  of  gravity  and  directed  to- 
wards   the    earth's    centre,   equili- 
brium will   be   established   only  when   this   resultant  is  balanced  by  the 
resultant  of  other  forces  and  resistances  acting  on  the  body  at  the  fixed  point 
through  which  it  passes. 

When  only  one  point  of  the  body  is  fixed,  it  will  be  in  equilibrium  if  the 
vertical  line  through  its  centre  of  gravity  passes  through  the  fixed  point.  If 
more  than  one  point  is  supported,  the  body  will  be  in  equilibrium  if  a  vertical 
line  through  the  centre  of  gravity  passes  through  a  point  within  the  polygon 
formed  by  joining  the  points  of  support. 

The  Leaning  Tower  of  Pisa  continues  to  stand  because  the  vertical  line 
drawn  through  its  centre  of  gravity  passes  within  its  base. 

It  is  easier  to  stand  on  our  feet  than  on  stilts,  because  in  the  latter  case 
the  smallest  motion  is  sufficient  to  cause  the  vertical  line  through  the  centre 
of  gravity  of  our  bodies  to  pass  outside  the  supporting  base,  which  is  here 
reduced  to  a  mere  line  joining  the  feet  of  the  stilts.  Again,  it  is  impossible 
to  stand  on  one  leg  if  we  keep  one  side  of  the  foot  and  head  close  to  a  vertical 
wall,  because  the  latter  prevents  us  from  throwing  the  body's  centre  of  gravity 
vertically  above  the  supporting  base. 

70.  Different  states  of  equilibrium. — Although  a  body  supported  by  a 
fixed  point  is  in  equilibrium  whenever  its  centre  of  gravity  is  in  the  vertical 
line  through  that  point,  the  fact  that  the  centre  of  gravity  tends  incessantly 
to  occupy  the  lowest  possible  position  leads  us  to  distinguish  between  three 
states  of  equilibrium — stable,  unstable,  neutral. 

A  body  is  said  to  be  in  stable  equilibrium  if  it  tends  to  return  to  its  first 
position  after  the  equilibrium  has  been  slightly  disturbed.  Every  body  is  m 
this  state  when  its  position  is  such  that  the  slightest  alteration  of  the  same 
-elevates  its  centre  of  gravity  ;  for  the  centre  of  gravity  will  descend  again 
when  permitted,  and  after  a  few  oscillations  the  body  will  return  to  its 
original  position. 


Gravitation  and  Molecular  Attraction. 


[70- 


The  pendulum  of  a  clock  continually  oscillates  about  its  position  of  stable 
equilibrium,  and  an  egg  on  a  level  table  is  in  this  state  when  its  long  axis 
is  horizontal.  We  have  another  illustration  in  the  toy  represented  in  the 
adjoining  fig.  45.  A  small  figure  cut  in  ivory  is  made  to  stand  on  one  foot 
at  the  top  of  a  pedestal  by  being  loaded  with  two  leaden  balls,  a,  b,  placed 
sufficiently  low  to  throw  the  centre  of  gravity,  g,  of  the  whole  compound 
body  below  the  foot  of  the  figure.  After  being  disturbed,  the  little  figure 
oscillates  like  a  pendulum,  having  its  point  of  suspen- 
sion at  the  toe,  and  its  centre  of  gravity  at  a  lower 
point,  g. 

A  body  is  said  to  be  in  unstable  equilibrium  when, 
after  the  slightest  disturbance,  it  tends  to  depart  still 
more  from  its  original  position.  A  body  is  in  this  state 
when  its  centre  of  gravity  is  vertically  above  the  point 
of  support,  or  higher  than  it  would  be  in  any  adjacent 


Fig.  44- 


Fig.  45- 


position  of  the  body.  An  egg  standing  on  its  end,  or  a  stick  balanced  upright 
on  the  finger,  is  in  this  state. 

Lastly,  if  in  any  adjacent  position  a  body  still  remains  in  equilibrium,  its 
state  of  equilibrium  is  said  to  be  neutral.  In  this  case  an  alteration  in  the 
position  of  the  body  neither  raises  nor  lowers  its  centre  of  gravity.  A  perfect 
sphere  resting  on  a  horizontal  plane  is  in  this  state. 

Fig.  44  represents  three  cones,  A,  B,  C,  placed  respectively  in  stable, 
unstable,  and  neutral  equilibrium  upon  a  horizontal  plane.  The  letter  g  in 
each  shows  the  position  of  the  centre  of  gravity. 

71.  The  Balance. — The  balance  is  an  instrument  for  determining  the 
relative  weights  or  masses  of  bodies.  There  are  many  varieties. 

The  ordinary  balance  (fig.  46)  consists  of  a  lever  of  the  first  kind,  called 
the  beam,  AB,  with  its  fulcrum  in  the  middle  ;  at  the  extremities  of  the  beam 
are  suspended  two  scale-pans,  C  and  D,  one  intended  to  receive  the  object 
to  be  weighed,  and  the  other  the  counterpoise.  The  fulcrum  consists  of  a 
steel  prism,  n,  commonly  called  a  knife-edge,  which  passes  through  the  beam, 
and  rests  with  its  sharp  edge,  or  axis  of  suspension,  upon  two  supports  ;  these 
are  formed  of  agate,  in  order  to  diminish  the  friction.  A  needle  or  pointer 
is  fixed  to  the  beam,  and  oscillates  with  it  in  front  of  the  graduated  arc,  a  : 
when  the  beam  is  perfectly  horizontal  the  needle  points  to  the  zero  of  the 
graduated  arc. 

Since  by  (40)  two  equal  forces  in  a  lever  of  the  first  kind  cannot  be  in 
equilibrium  unless  their  leverages  are  equal,  the  length  of  the  arms  «A  and 
;zB  ought  to  remain  equal  during  the  process  of  weighing.  To  secure  this 


-72] 


T/ie  Balance. 


59 


the  scales  are  suspended  from  hooks,  whose  curved  parts  have  sharp  edges 
and  rest  on  similar  edges  at  the  ends  of  the  beam.  In  this  manner  the 
scales  are  in  effect  supported  on  mere  points,  which  remain  unmoved  durin- 
the  oscillations  of  the  beam.  This  mode  of  suspension  is  represented  in 

fig.  46. 

72.  Conditions  to  be  satisfied  by  a  balance.— A  good  balance  ought 
to  satisfy  the  following  conditions  : 

i.  The  two  arms  of  the  beam  ought  to  be  precisely  equal,  otherwise, 
according  to  the  principle  of  the  lever,  unequal  weights  will  be  required  to 
produce  equilibrium.  To  test  whether  the  arms  of  the  beam  are  equal, 
weights  are  placed  in  the  two  scales,  until  the  beam  becomes  horizontal  • 
the  contents  of  the  scales  being  then  interchanged,  the  beam  will  remain 
horizontal  if  its  arms  are  equal,  but  if  not,  it  will  descend  on  the  side  of  the 
longer  arm. 


Fig.  46. 

ii.  The  balance  ought  to  be  in  equilibrium  when  the  scales  are  empty,  for 
.  otherwise  unequal  weights  must  be  placed  in  the  scales  in  order  to  produce 
equilibrium.  It  must  be  borne  in  mind,  however,  that  the  arms  are  not 
necessarily  equal,  even  if  the  beam  remains  horizontal  when  the  scales  are 
empty  ;  for  this  result  might  also  be  produced  by  giving  to  the  longer  arm 
the  lighter  scale. 

iii.  The  beam  being  horizontal,  its  centre  of  gravity  ought  to  be  in  the 
same  "vertical  line  with  the  edge  of  the  fulcrum,  and  a  little  below  the  latter, 
for  otherwise  the  beam  would  not  be  in  stable  equilibrium  (70;. 

The  effect  of  changing  the  position  of  the  centre  of  gravity  may  be  shown 
by  means  of  a  beam  (fig.  47),  whose  fulcrum  being  the  nut  of  a  screw,  a,  can 
be  raised  or  lowered  by  turning  the  screw-head,  b. 


<5o 


Gravitation  and  Molecular  A  ttraction. 


[72- 


When  the  fulcrum  is  at  the  top  of  the  groove  r,  in  which  it  slides,  the 
centre  of  gravity  of  the  beam  is  below  its  edge,  and  the  latter  oscillates 


Fig.  47- 

freely  about  a  position  of  stable  equilibrium.  By  gradually  lowering  the 
fulcrum  its  edge  may  be  made  to  pass  through  the  centre  of  gravity  of  the 
beam  when  the  latter  is  in  neutral  equilibrium  ;  that  is  to  say,  it  no  longer 
•oscillates,  but  remains  in  equilibrium  in  all  positions.  When  the  fulcrum 
is  lowered  still  more,  the  centre  of  gravity  passes  above  its  edge,  the 
beam  is  in  a  state  of  unstable  equilibrium,  and  is  overturned  by  the  least 
•displacement. 

73.  Delicacy  of  the  balance. — A  balance  is  said  to  be  delicate  when  a 
very  small  difference  between  the  weights  in  the  scales  causes  a  perceptible 
deflection  of  the  pointer. 

Let  A  and  B  (figs.  48  and  49)  be  the  points  from  which  the  scale-pans 
.are  suspended,  and  C  the  axis  of  suspension  of  the  beam.  A,  B,  and  C  are 
assumed  to  be  in  the  same  straight  line,  according  to  the  usual  arrangement. 
Suppose  weights  P  and  Q  to  be  in  the  pans,  suspended  from  A  and  B  re- 
spectively, and  let  G  be  the  centre  of  gravity  of  the  beam  ;  then  the  beam 


* 


Fig.  48. 


Fig.  49. 


will  come  to  rest  in  the  position  shown  in  the  figure,  where  the  line  DCN  is 
vertical,  and  ECG  is  the  direction  of  the  pointer.  According  to  the  above 
statement,  the  greater  the  angle  ECD  for  a  given  difference  between  P  and 
Q,  the  greater  is  the  delicacy  of  the  balance.  Draw  GN  at  right  angles 
toCG. 

Let  W  be  the  weight  of  the  beam,  then  from  the  properties  of  the  lever  (40) 
it  follows  that  measuring  moments  with  respect  to  C,  the  moment  of  P  equals 
the  sum  of  the  moments  of  Q  and  W,  a  condition  which  at  once  leads  to  the 
relation 

(P-Q)AC=WxGN 

Now  it  is  clear  that  for  a  given  value  of  CG  the  angle  GCN  (that  is  ECD, 
which  measures  the  delicacy)  is  greater  as  GN  is  greater ;  and  from  the 
formula  it  is  clear  that  for  a  given  value  of  P  —  Q  we  shall  have  GN  greater 


-74] 


Delicacy  of  the  Balance. 


61 


as  AC  is  greater,  and  as  W  is  less.  Again,  for  a  given  value  of  GN  the 
angle  GCN  is  greater  as  GC  is  less.  Hence  the  means  of  rendering  a 
balance  delicate  are — 

i.   To  make  the  arms  of  the  balance  long. 

\\.  To  make  the  weight  of  the  beam  as  small  as  is  consistent  with  its 
rigidity. 

iii.  To  bring  the  centre  of  gravity  of  the  beam  a  very  little  below  the  point 
of  support. 

Moreover,  since  friction  will  always  oppose  the  action  of  the  force  that 
tends  to  preponderate,  the  balance  will  be  rendered  more  delicate  by  diminish- 
ing friction.  To  secure  this  advantage  the  edges  from  which  the  beam  and 
scales  are  suspended  are  made  as  sharp  and  as  hard  as  possible,  and  the 
supports  on  which  they  rest  are  very  smooth  and  hard.  This  is  effected  by 
the  use  of  agate  knife-edges.  And,  further,  the  pointer  is  made  long,  since 
its  elongation  renders  a  given  deflection  more  perceptible  by  increasing  the 
arc  which  its  end  describes. 

The  sensitiveness  of  a  balance  is  expressed  by  the  ratio  of  the  smallest 
weight,  which  will  produce  a  measurable  deflection  of  the  pointer,  to  the 
load. 

74.  Physical  and  cbemical  balances. — Fig.  50  represents  one  of  the 
accurate  balances  ordinarily  used  for  chemical  analysis.  Its  sensitiveness  is 


Fig.  5°- 


such  that  when  charged  with  a  kilogramme  (1,000  grms.)  in  each  scale  an 
excess  of  a  tenth  of  a  milligramme  (T^  of  a  g™1-)  in  either  scale  prc 
a  very  perceptible  deflection  of  the  index. 

In  order  to  protect  the  balance  from  air-currents,  dust,  and  moisture, 
it  is  always,  even  when  weighing,  surrounded  by  a  glass  case,  whose  front 


62  Gravitation  and  Molecular  A  ttr action.  [74- 

slides  up  and  down,  to  enable  the  operator  to  introduce  the  objects  to  be 
weighed.  Where  extreme  accuracy  is  desired  the  case  is  constructed  so 
that  the  space  may  be  exhausted,  and  the  weighing  made  in  vacua. 

In  order  to  preserve  the  edge  of  the  fulcrum  as  much  as  possible,  the 
whole  beam,  BB,  with  its  fulcrum  K,  can  be  raised  from  the  support  on 
which  the  latter  rests  by  simply  turning  the  button  O  outside  the  case. 

The  horizontally  of  the  beam  is  determined  by  means  of  a  long  index, 
which  points  downwards  to  a  graduated  arc  near  the  foot  of  the  supporting 
pillar.  Lastly,  the  button  C  serves  to  alter  the  sensitiveness  of  the  balance  ; 
by  turning  it,  the  centre  of  gravity  of  the  beam  can  be  made  to  approach 
or  recede  from  the  fulcrum  (69). 

75.  method  of  double  weighing. — Even  if  a  balance  be  not  perfectly 
accurate,  the  true  weight  of  a  body  may  still  be  determined  by  its  means.  To 
do  so,  the  body  to  be  weighed  is  placed  in  one  scale,  and  shot  or  sand  poured 
into  the  other  until  equilibrium  is  produced ;  the  body  is  then  replaced 
by  known  weights  until  equilibrium  is  re-established.  The  sum  of  these 
weights  will  necessarily  be  equal  to  the  weight  of  the  body,  for,  acting  under 
precisely  the  same  circumstances,  both  have  produced  precisely  the  same 
effect. 

The  exact  weight  of  a  body  may  also  be  determined  by  placing  it  suc- 
cessively in  the  two  pans  of  a  balance,  and  then  deducing  its  true  weight. 

For  having  placed  in  one  pan  the  body  to  be  weighed,  whose  true  weight 
is  x,  and  in  the  other  the  weight  p^  required  to  balance  it,  let  a  and  b  be 
the  arms  of  levers  corresponding  to  x  and  p.  Then  from  the  principle  of 
the  lever  (40)  we  have  ax=^pb.  Similarly,  if  pl  is  the  weight  when  the  body 
is  placed  in  the  other  pan,  then  bx=a,pv  Hence  abx^^abpp^  from  which 
x=,Jppv  This  method  was  invented  by  Pere  Amiot,  but  is  ordinarily 
known  as  Borders  Method. 

Jolly  made  use  of  the  balance  to  determine  the  constant  of  gravity.  He 
counterbalanced  one  and  the  same  mass,  in  one  case  by  placing  weights  in 
a  scale  pan  on  the  same  level ;  and  in  another  case  by  placing  weights  in  a 
scale  pan  at  a  distance  of  21  metres  below,  and  connected  with  the  upper 
one  by  a  wire.  There  was  an  increase  in  weight  in  the  lower  one,  and  the 
increase  corresponded  to  that  calculated  from  the  formula  in  (82). 

A  large  lead  sphere  was  then  placed  immediately  below  the  mass  in  the 
lower  pan,  and  produced  a  measurable  attraction.  From  the  attraction  thus 
produced  by  the  known  mass  of  the  lead  it  was  possible  to  deduce  the  mass 
and  the  mean  density  of  the  Earth  ;  the  number  obtained  was  5-69.  Similar 
experiments  have  been  made  by  Prof.  Poynting  and  have  led  to  the  same 
number. 


-76] 


Laws  of  Falling  Bodies. 


CHAPTER   II. 

LAWS   OF   FALLING   BODIES.      INTENSITY  OF  TERRESTRIAL  GRAVITY. 
THE    PENDULUM. 

76.  laws   of  falling:   bodies.— Since    a   body 

falls  to  the  ground  in  consequence  of  the  earth's 

attraction  on  each  of  its  molecules,  it  follows  that, 

everything  else  being  the  same,  all  bodies,  great 

and  small,  light  and  heavy,  ought  to  fall  with  equal 

rapidity,  and  a  lump  of  sand  without  cohesion  should, 

during  its  fall,  retain  its  original  form  as  perfectly 

as  if  it  were  compact  stone.     The  fact  that  a  stone 

falls  more  rapidly  than  a  feather  is  due  solely  to  the 

unequal  resistances  opposed  by  the  air  to  the  descent 

of  these  bodies  \  in  a  vacttum  all  bodies  fall  with 

equal  rapidity.   To  demonstrate  this  by  experiment 

a  glass  tube  about  two  yards  long  (fig.  51)  may  be 

taken,  having  one  of  its  ends  completely  closed, 

and  a  brass  cock  fixed  to  the  other.     After  having 

introduced  bodies  of  different  weights  and  densities 

(pieces  of  lead,  paper,  feather,  &c.)  into  the  tube, 

the  air  is  withdrawn  from  it  by  an  air-pump,  and 

the  cock  closed.     If  the  tube  be  now  suddenly  re- 
versed, all  the  bodies  will  fall  equally  quickly.     On 

introducing  a  little  air  and  again  inverting  the  tube, 

the  lighter  bodies  become  slightly  retarded,  and 

this  retardation  increases  with  the  quantity  of  air 
introduced. 

The  resistance  opposed  by  the  air  to  falling 
bodies  is  especially  remarkable  in  the  case  of 
liquids.  The  Staubbach  in  Switzerland  is  a  good 
illustration ;  an  immense  mass  of  water  is  seen  fall- 
ing over  a  high  precipice,  but  before  reaching  the 
bottom  it  is  shattered  by  the  air  into  the  finest 
mist.  In  a  vacuum,  however,  liquids  fall  like 
solids  without  separation  of  their  molecules.  The 
water-hammer  illustrates  this  :  the  instrument  con- 
sists of  a  thick  glass  tube  about  a  foot  long,  half- 
filled  with  water,  the  air  having  been  expelled  by 
ebullition  previous  to  closing  one  extremity  with  the 
blow-pipe.  When  such  a  tube  is  suddenly  inverted, 
the  water  falls  in  one  undivided  mass  against  the  Fig.  51. 


Gravitation  and  Molecular  Attraction. 


[76- 


other  extremity  of  the  tube,  and  produces  a  sharp  dry  sound,  resembling- 

that  which  accompanies  the  shock  of  two  solid  bodies. 

From  Newton's  law  (66)  it 
follows  that  when  a  body  falls 
to  the  earth  the  force  of  attrac- 
tion which  causes  it  to  do 
so  increases  as  the  body  ap- 
proaches the  earth.  Unless  the 
height  from  which  the  body 
falls,  however,  be  very  great, 
this  increase  will  be  altogether 
inappreciable,  and  the  force  in 
question  may  be  considered  as 
constant  and  continuous.  If 
the  resistance  of  the  air  were 
removed,  therefore,  the  motion 
of  all  bodies  falling  to  the 
earth  would  be  uniformly  ac- 
celerated, and  would  obey  the 
laws  already  explained  (49). 

77-  Atwood's  machine. — 
Several  instruments  have  been 
invented  for  illustrating  and 
experimentally  verifying  the 
laws  of  falling  bodies.  Galileo, 
who  discovered  these  laws  in 
the  early  part  of  the  seven- 
teenth century,  illustrated 
them  by  means  of  bodies 
falling  down  inclined  planes. 
The  great  object  of  all  such 
instruments  is  to  diminish  the 
rapidity  of  the  fall  of  bodies 
without  altering  the  character 
of  their  motion,  for  by  this 
means  their  motion  may  not 
only  be  better  observed,  but 
it  will  be  less  modified  by  the 
resistance  of  the  air  (48). 

The  most  convenient  instru- 
ment of  this  kind  is  that  in- 
vented by  Atwood  at  the  end  of 
the  last  century,  and  represented 
in  fig.  52.  It  consists  of  a  stout 
pillar  of  wood,  about  2.\  yards 
high,  at  the  top  of  which  is  a  brass 
pulley,  whose  axle  rests  and 


Fig.  52. 


turns  upon  four  other  wheels,  called  friction  wheels,  inasmuch  as  they  serve 
to  diminish  friction.     Two  equal  weights,  M  and  M',  are  attached  to  the  ex- 


-77]  Ativood's  Machine.  65 

tremities  of  a  fine  silk  thread,  which  passes  round  the  pulley  ;  a  timepiece, 
H,  fixed  to  the  pillar,  is  regulated  by  a  seconds  pendulum,  P,  in  the  usual 
way  ;  that  is  to  say,  the  oscillations  of  the  pendulum  are  communicated  to  a 
ratchet,  whose  two  teeth,  as  seen  in  the  figure,  fit  into  those  of  the  ratchet 
wheel.  The  axle  of  this  wheel  gives  motion  to  the  seconds  hand  of  the  dial, 
and  also  to  an  eccentric  behind  the  dial,  as  shown  at  E  by  a  separate  figure! 
This  eccentric  plays  against  the  extremity  of  a  lever  D,  which  it  pushes 
until  the  latter  no  longer  supports  the  small  plate  i ;  and  thus  the  weight  M, 
which  at  first  rested  on  this  plate,  is  suddenly  exposed  to  the  free  action  of 
gravity.  The  eccentric  is  so  constructed  that  the  little  plate  i  falls  precisely 
when  the  hand  of  the  dial  points  to  zero. 

The  weights  M  and  M',  being  equal,  hold  each  other  in  equilibrium  ; 
the  weight  M,  however,  is  made  to  descend  slowly  by  putting  a  small  bar  or 
overweight  m  upon  it  ;  and  to  measure  the  spaces  which  it  describes,  the  rod 
or  scale  Q  is  divided  into  feet  and  inches,  commencing  from  the  plate  /. 
To  complete  the  instrument  there  are  a  number  of  plates,  A,  A',  C,  C',  and 
a  number  of  rings,  B,  B',  which  may  be  fixed  by  screws  at  any  part  of  the 
scale.  The  plates  arrest  the  descending  weight  M,  the  rings  only  arrest  the 
bar  or  overweight  ;;z,  which  was  the  cause  of  motion,  so  that  after  passing 
through  them,  the  weight  M,  in  consequence  of  its  inertia,  will  move  on 
uniformly  with  the  velocity  it  had  acquired  on  reaching  the  ring.  The 
several  parts  of  the  apparatus  being  described,  a  few  words  will  suffice  to 
explain  the  method  of  experimenting. 

Let  the  hand  of  the  dial  be  placed  behind  the  zero  point,  the  lever  D 
adjusted  to  support  the  plate  z,  on  which  the  weight  M  with  its  overweight 
m  rests,  and  the  pendulum  put  in  motion.  As  soon  as  the  hand  of  the  dial 
points  to  zero  the  plate  /  will  fall,  the  weights  M  and  m  will  descend,  and  by 
a  little  attention  and  a  few  trials  it  will  be  easy  to  place  a  plate  A  so  that  M 
may  reach  it  exactly  as  the  dial  indicates  the  expiration  of  one  second.  To 
make  a  second  experiment  let  the  weights  M  and  ;«,  the  plate  z,  and  the 
lever  D  be  placed  as  at  first  ;  remove  the  plate  A,  and  in  its  place  put  a  ring, 
B,  so  as  to  arrest  the  overweight  m  just  when  the  weight  M  would  have 
reached  A  ;  on  putting  the  pendulum  in  motion  again  it  will  be  easy,  after  a 
few  trials,  to  put  a  plate,  C,  so  that  the  weight  M  may  fall  upon  it  precisely 
when  the  hands  of  the  dial  point  to  two  seconds.  Since  the  overweight  m 
in  this  experiment  was  arrested  by  the  ring  B  at  the  expiration  of  one  second, 
the  space  BC  was  described  by  M  in  one  second  purely  in  virtue  of  its  own 
inertia,  and  consequently  by  (24)  BC  will  indicate  the  velocity  of  the  falling 
mass  at  the  expiration  of  one  second. 

Proceeding  in  the  same  manner  as  before,  let  a  third  experiment  be  made 
in  order  to  ascertain  the  point  W  at  which  the  weights  M  and  m  arrive  after 
the  lapse  of  two  seconds,  and  putting  a  ring  at  B',  ascertain  by  a  fourth 
experiment  the  point  C'  at  which  M  arrives  alone,  three  seconds  after  the 
descent  commenced  ;  B'C'  will  then  express  the  velocity  acquired  after  a 
descent  of  two  seconds.  In  a  similar  manner,  by  a  fifth  and  sixth  experiment, 
we  may  determine  the  space  OB"  described  in  three  seconds,  and  the  velo- 
city BX/C"  acquired  during  those  three  seconds,  and  so  on  ;  we  shall  find 
that  B'C'  is  twice,  and  B^C"  three  times  as  great  as  BC— in  other  words, 
that  the  velocities  BC,  B'C',  B"C"  increase  in  the  same  proportion  as  the 

F 


66  Gravitation  and  Molecular  A  ttraction.  [77- 

times  (i,  2,  3,  ...  seconds)  employed  in  their  acquirement.  By  the  defi- 
nition (49),  therefore,  the  motion  is  uniformly  accelerated.  The  same  ex- 
periments will  also  serve  to  verify  and  illustrate  the  four  laws  of  uniformly 
accelerated  motion  as  enunciated  in  (49).  For  example,  the  spaces  OB, 
OB',  OB",  ....  described  from  a  state  of  rest  in  1,2,  3,  ....  seconds, 
will  be  found  to  be  proportional  to  the  numbers  I,  4,  9  .  .  .  ;  that  is  to  say, 
to  the  squares  of  those  numbers  of  seconds,  as  stated  in  the  third  law. 

Lastly,  if  the  overweight  m  be  changed,  the  acceleration  or  velocity  BC 
acquired  per  second  will  also  be  changed,  and  we  may  easily  verify  the 
assertion  in  (27),  that  force  is  proportional  to  the  product  of  the  mass  moved 
into  the  acceleration  produced  in  a  given  time.  For  instance,  assuming  the 
pulley  to  be  so  light  that  its  inertia  can  be  neglected  if  m  weighed  half  an 
ounce,  and  M  and  M'  each  15!  ounces,  the  acceleration  BC  would  be  found 
to  be  six  inches  ;  whilst  if  m  weighed  one  ounce,  and  M  and  M'  each  63^ 
ounces,  the  acceleration  BC  would  be  found  to  be  three  inches. 

Now  in  these  cases  the  forces  producing  motion,  that  is  the  overweights, 
are  in  the  ratio  of  i  :  2  ;  while  the  products  of  the  masses  and  the  accelera- 
tions are  in  the  ratio  of  (£  +  1 5f  +  1 5f)  x  6  to  (i  +  63^  +  63^)  x  3  ;  that  is,  they 
are  also  in  the  ratio  i  :  2.  Now  the  same  result  is  obtained  in  whatever 
way  the  magnitudes  of  /«,  M,  and  M'  are  varied,  and  consequently  in  all 
cases  the  ratio  of  the  forces  producing  motion  equals  the  ratio  of  the  mo- 
menta generated. 

78.  Morin's  apparatus. — The  principle  of  this  apparatus,  the  original 
idea  of  which  is  due  to  General  Poncelet,  is  to  make  the  falling  body  trace 
its  own  path.  Fig.  53  gives  a  view  of  the  whole  apparatus,  and  fig.  54 
gives  the  details.  The  apparatus  consists  of  a  wooden  framework,  about 
7  feet  high,  which  holds  in  a  vertical  position  a  very  light  wooden  cylinder, 
M,  which  can  turn  freely  about  its  axis.  This  cylinder  is  coated  with 
paper  divided  into  squares  by  equidistant  horizontal  and  vertical  lines.  The 
latter  measure  the  path  traversed  by  the  body  falling  along  the  cylinder, 
while  the  horizontal  lines  are  intended  to  divide  the  duration  of  the  fall  into 
equal  parts. 

The  falling  body  is  a  mass  of  iron,  P,  provided  with  a  pencil  which  is 
pressed  against  the  paper  by  a  small  spring.  The  iron  is  guided  in  its  fall 
by  two  light  iron  wires  which  pass  through  guide-holes  on  the  two  sides. 
The  top  of  this  mass  is  provided  with  a  tipper  which  catches  against  the  end 
of  a  bent  lever,  AC.  This  being  pulled  by  the  string  K  attached  at  A,  the 
weight  falls.  If  the  cylinder"  M  were  fixed,  the  pencil  would  trace  a  straight 
line  on  it  ;  but  if  the  cylinder  moves  uniformly,  the  pencil  traces  the  line 
mn,  which  serves  to  deduce  the  law  of  the  fall. 

The  cylinder  is  rotated  by  means  of  a  weight,  Q,  suspended  to  a  cord 
which  passes  round  the  axle  G.  At  the  end  of  this  is  a  toothed  wheel,  c, 
which  turns  two  endless  screws,  a  and  b,  one  of  which  turns  the  cylinder, 
and  the  other  two  vanes,  x  and  x1  (fig.  54).  At  the  other  end  is  a  ratchet 
wheel,  in  which  fits  the  end  of  a  lever,  B  ;  by  pulling  at  a  cord  fixed  to  the 
other  end  of  B,  the  wheel  is  liberated,  the  weight  Q  descends,  and  the  whole 
system  begins  to  turn.  The  motion  is  at  first  accelerated,  but  as  the  air 
offers  a  resistance  to  the  vanes  (48),  which  increases  as  the  rotation  becomes 
more  rapid,  the  resistance  finally  equals  the  acceleration  which  gravity  tends 


-78] 


Morin's  Apparatus. 


67 


to  impart.     From  this  time  the  motion  becomes  uniform.     This  is  the  c 
when  the  we.ght  Q  has  traversed  about  three-quarters  of  its  course     at  this 

K'  -  **  P-n't  nen 


If,  by  means  of  this  curve,  we  examine  the  double  motion  of  the  pencil 
on  the  small  squares  which  divide  the  paper,  we  see  that,  for  displacements 


Fig.  54- 


Fig.  53. 

i,  2,  3  ....  in  a  horizontal  direction,  the  displacements  are  I,  4,  9  .... 
in  a  vertical  direction.  This  shows  that  the  paths  traversed  in  the  direction 
of  the  fall  are  directly  as  the  squares  of  the  lines  in  the  direction  of  the 
rotation,  which  verifies  the  second  law  of  falling  bodies. 

From  the  relation  which  exists  between  the  two  dimensions  of  the  curve 
inn,  it  is  concluded  that  this  curve  is  a  parabola. 

F  2 


68 


Gravitation  and  Molecular  A  ttraction. 


[79- 


79.  The  length  of  tlie  compound  pendulum. — The  formula  deduced  in 
article  ($5)  and  the  conclusions  which  follow  therefrom,  refer  to  the  case  of  the 
simple  or  mathematical  pendulum  ;  that  is,  to  a  single  heavy  point  suspended 
by  a  thread  without  weight.  Such  a  pendulum  has  only  an  imaginary 
existence,  and  any  pendulum  which  does  not  realise  these  conditions  is 
called  a  compound  or  physical  pendulum.  The  laws  for  the  time  of  vibra- 
tion of  a  compound  pendulum  are  the  same  as  those  which  regulate  the 
motion  of  the  simple  pendulum,  though  it  will  be  necessary  to  define  ac- 
curately what  is  meant  by  the  length  of  such  a  pendulum.  A  compound 
pendulum  being  formed  of  a  heavy  rod  terminated  by  a  greater  or  less  mass, 
it  follows  that  the  several  material  points  of  the  whole  system  will 
strive  to  perform  their  oscillations  in  different  times,  their  distances 
from  the  axis  of  suspension  being  different,  and  the  more  distant 
points  requiring  a  longer  time  to  complete  an  oscillation.  From 
this,  and  from  the  fact  that  being  points  of  the  same  body  they 
must  all  oscillate  together,  it  follows  that  the  motion  of  the  points 
near  the  axis  of  suspension  will  be  retarded,  whilst  that  of  the  more 
distant  points  will  be  accelerated,  and  between  the  two  extremities 
there  will  necessarily  be  a  series  of  points  whose  motion  will  be 
neither  accelerated  nor  retarded,  but  which  will  oscillate  precisely 
as  if  they  were  perfectly  free  and  unconnected  with  the  other  points 
of  the  system.  These  points,  being  equidistant  from  the  axis  of. 
suspension,  constitute  a  parallel  axis  known  as  the  axis  of  oscil- 
lation ;  and  it  is  to  the  distance  between  these  two  axes  that  the 
term  length  of  the  compound  pendulum  is  applied  :  we  may  say, 
therefore,  that  the  length  of  a  compound  pendulum  is  that  of  the 
simple  pendulum  which  would  describe  its  oscillations  in  the  same 
time. 

Huyghens,  the  celebrated  Dutch  physicist,  discovered  that  the 
axes  of  suspension  and  oscillation  are  mutually  convertible  ;  that 
is  to  say,  the  time  of  oscillation  will  remain  unaltered  when  the 
pendulum  is  suspended  from  its  axis  of  oscillation.  This  enables  us 
to  determine  experimentally  the  length  of  the  compound  pendulum. 
For  this  purpose  the  reversible  pendulum  devised  by  Bohnenberger 
and  Kater  may  be  used.  One  form  of  this  (fig.  55)  is  a  rod  with 
the  knife-edges  a  and  b  turned  towards  each  other.  W  and  V  are 
lens-shaped  masses  the  relative  positions  of  which  may  be  varied. 
By  a  series  of  trials  a  position  can  be  found  such  that  the  number 
of  oscillations  of  the  pendulum  in  a  given  time  is  the  same  whether 
it  oscillates  about  the  axis  a  or  the  axis  b.  This  being  so,  the  dis- 
tance ab  represents  the  length  /  of  a  simple  pendulum  which  has 


Fig.  55- 


the  same  time  of  oscillation.     From  the  value  of  /,  thus  obtained, 


it  is  easy  to  determine  the  length  of  the  seconds  pendulum. 
The  length  of  the  seconds  pendulum — that  is  to  say,  of  the  pendulum 
which  makes  one  oscillation  in  a  second — varies,  of  course,  with  the 
force  of  gravity.  The  following  table  gives  its  value  at  the  sea-level  at 
various  places  as  determined  by  observation.  The.  accelerative  effect  of 
gravity  at  these  places,  according  to  formula  (55),  is  obtained  in  feet  and 


-80J 


Verification  of  the  Laws  of  the  Pendulum. 


69 


metres,  by  multiplying  the  length  of  the  seconds  pendulum,  reduced  to  feet 
.and  metres  respectively,  by  the  square  of  3*14159  or  9-87. 


Latitude 

Length  of  Pen- 

Acceleration  of  Gravity  in 

Feet 

Metres 

Hammerfest  . 
Aberdeen 
Konigsberg   . 
Manchester  . 
Dublin  . 
Berlin    . 
Greenwich     . 
Paris      . 

70°.  40'  N 

57.9 

54  42 
53-29 
53-21 
52.30 
51  .29 
48  .50 

39-I948 
39-1550 
39-1507 
39-I466 
39-I46I 
39-I439 
39-I398 
39-I285 

32-2364 
32-2066 
32-2002 
32-1968 
32*1968 
32-1945 
32-I9I2 
32-l8l9 

9-8258 
9-8164 
9-8142 
9-8I34 
9-8I32 
9-8124 
9-8II5 
9-8039 

Rome     . 
New  York     . 
Washington  . 
Madras 
Ascension 
St.  Thomas   . 
Cape  of  Good  Hope 

41  .54 
40.43 
38.54 
13-4 
7-56 
0.25 
33  -55  S. 

39'II45 

39-1012 
39-0968 
39-0268 
39-0242 
39-0207 
39-0780 

32  1712 
32-1594 
32-1558 
32-0992 
32-0939 
32-0957 
32-I404 

9^053 
9-8019 
9-8006 
9-7836 

97817 
97826 
97962 

Consequently,  $g  or  the  space  described  in  the  first  second  of  its  motion 
by  a  body  falling  in  vacuo  from  a  state  of  rest  (49)  is 

16*0478  feet  or  4*891  metres  at  St.  Thomas, 
16-0956  „  „  4-905  „  at  London,  and 
16-1182  „  „  4*913  „  at  Hammerfest. 

In  all  calculations  which  are  merely  used  for  the  sake  of  illustration  we 
may  take  32  feet,  or  9-8  metres,  as  the  accelerative  effect  due  to  gravity. 

From  observations  of  this  kind,  after  applying  the  necessary  corrections, 
and  taking  into  account  the  effect  of  rotation  (82),  the  form  of  the  earth  can 
be  deduced. 

80.  Verification  of  the  laws  of  the  pendulum. — In  order  to  verify  the 
laws  of  the  simple  pendulum  (55)  we  are  compelled  to  employ  a  compound 
one,  whose  construction  differs  as  little  as  possible  from  that  of  the  former. 
For  this  purpose  a  small  sphere  of  a  very  dense  substance,  such  as  lead  or 
platinum,  is  suspended  from  a  fixed  point  by'means  of  a  very  fine  metal  wire. 
A  pendulum  thus  formed  oscillates  almost  like  a  simple  pendulum,  whose 
length  is  equal  to  the  distance  of  the  centre  of  the  sphere  from  the  point  of 
suspension. 

In  order  to  verify  the  isochronism  of  small  oscillations,  it  is  merely  necessary 
to  count  the  number  of  oscillations  made  in  equal  times,  as  the  amplitudes  of 
these  oscillations  diminish  from  3  degrees  to  a  fraction  of  a  degree ;  this 
number  is  found  to  be  constant. 

That  the  time  of  vibration  is  proportional  to  the  square  root  of  the  length 
is  verified  by  causing  pendulums,  whose  lengths  are  as  the  numbers  I,  4, 
9,  ....  to  oscillate  simultaneously.  The  corresponding  numbers  of  oscil- 
lations in  a  given  time  are  then  found  to  be  proportional  to  the  fractions  I, 


Gravitation  and  Molecular  Attraction. 


[80- 

^,  f,  &c.,  ....  which  shows  that  the  times  of  oscillation  increase  as  the 
numbers   i,  2,  3,  ....  &c. 

By  taking  several  pendulums  of  exactly  equal  length,  B,  C,  D  (fig.  56), 
but  with  spheres  of  different  substances — lead, 
copper,  ivory — it  is  found  that,  neglecting  the 
resistance  of  the  air,  these  pendulums  oscillate 
in  equal  times,  thereby  showing  that  the  acce- 
lerative  effect  of  gravity  on  all  bodies  is  the 
same  at  the  same  place. 

By  means  of  an  arrangement  resembling  the 
above,  Newton  verified  the  fact  that  the  masses 
of  bodies  are  determined  by  the  balance  ;  which, 
it  will  be  remarked,  lies  at  the  foundation  of 
the  measure  of  force  (28).  For  it  will  be  seen 
on  comparing  (54)  and  (55)  with  (49)  that  the 
law  of  the  time  of  a  small  oscillation  is  obtained 
on  the  supposition  that  the  force  of  gravity  on 
all  bodies  is  represented  by  M^-,  in  which  M  is 
determined  by  the  balance.  In  order  to  verify 
this,  he  had  made  two  round  equal  wooden 
boxes  ;  he  filled  one  with  wood,  and  as  nearly 
as  possible  in  the  centre  of  oscillation  of  the 
other  he  placed  an  equal  weight  of  gold.  He 
then  suspended  the  boxes  by  threads  eleven 
feet  long,  so  that  they  formed  pendulums  exactly 
equal  so  far  as  weight,  figure,  and  resistance  of 
the  air  were  concerned.  Their  oscillations  were 
performed  in  exactly  the  same  time.  The  same 
results  were  obtained  when  other  substances 
were  used,  such  as  silver,  lead,  glass,  sand,  salt,  wood,  water,  corn.  Now  all 
these  bodies  had  equal  weights,  and  if  the  inference,  that  therefore  they  had 
equal  masses,  had  been  erroneous,  by  so  much  as  the  one-thousandth  part 
of  the  whole,  the  experiment  would  have  detected  it. 

8 1.  Application  of  the  pendulum  to  Clocks.— The  regulation  of  the 
motion  of  clocks  is  effected  by  means  of  pendulums,  that  of  watches  by 
balance-springs.  Pendulums  were  first  applied  to  this  purpose  by  Huyghens. 
in  1658,  and  in  the  same  year  Hooke  applied  a  spiral  spring  to  the  balance 
of  a  watch.  The  manner  of  employing  the  pendulum  is  shown  in  fig.  57. 
The  pendulum  rod  passing  between  the  prongs  of  a  fork  a  communicates  its 
motion  to  a  rod  b,  which  oscillates  on  a  horizontal  axis  o.  To  this  axis  is  . 
fixed  a  piece  ;«»,  called  an  escapement  or  crutch,  terminated  by  two  projec- 
tions or  pallets,  which  work  alternately  with  the  teeth  of  the  escapement 
wheel  R.  This  wheel  being  acted  on  by  the  weight  tends  to  move  con- 
tinuously, let  us  say,  in  the  direction  indicated  by  the  arrow-head.  Now,  if 
the  pendulum  is  at  rest,  the  wheel  is  held  at  rest  by  the  pallet  m,  and  with  it 
the  whole  of  the  clockwork  and  the  weight.  If,  however,  the  pendulum 
moves  and  takes  the  position  shown  by  the  dotted  line,  m  is  raised,  the 
wheel  escapes  from  the  confinement  in  which  it  was  held  by  the  pallet,  the 
weight  descends,  and  causes  the  wheel  to  turn  until  its  motion  is  arrested  by 


Fig.  56. 


-82] 


Causes  which  Modify  Terrestrial  Gravitation. 


the  other  pallet  n ;  which,  in  consequence  of  the  motion  of  the  pendulum, 
will  be  brought  into  contact  with  another  tooth  of  the  escapement  wheel.  In 
this  manner  the  descent  of  the  weight  is  alternately  permitted  and  arrested 
—or,  in  a  word,  regulated— \sy  the  pendulum.  By 
means  of  a  proper  train  of  wheelwork  the  motion  of 
the  escapement  is  communicated  to  the  hands  of  the 
clock  ;  and  consequently  their  motion,  also,  is  regu- 
lated by  the  pendulum. 

The  pendulum  has  also  been  used  for  measuring 
great  velocities.  A  large  wooden  box  filled  with  sand 
and  weighing  from  3  to  5  tons  is  coated  with  iron ; 
against  this  arrangement,  which  is  known  as  a  ballistic 
pendulum,  a  shot  is  fired,  and  the  deflection  thereby 
produced  is  observed.  From  the  laws  of  the  impact 
of  inelastic  bodies,  and  from  those  of  the  pendulum, 
the  velocity  of  the  ball  may  be  calculated  from  the 
amount  of  this  deflection. 

The  gun  may  also  be  fastened  to  a  pendulum  ar- 
rangement ;  and,  when  fired,  the  reaction  causes  an 
angular  velocity,  from  which  the  pressure  of  the  enclosed 
gases  can  be  deduced,  and  therefrom  the  initial  velocity 
of  the  shot. 

82.  Causes  which  modify  the  intensity  of 
terrestrial  gravitation. — The  intensity  of  the  force 
of  gravity — that  is,  the  value  of  g — is  not  the  same  in 
all  parts  of  the  earth.  It  is  modified  by  several  causes, 
of  which  the  form  of  the  earth  and  its  rotation  are  the 
most  important. 

i.  The  attraction  which  the  earth  exerts  upon  a 
body  at  its  surface  is  the  sum  of  the  partial  attractions 
which  each  part  of  the  earth  exerts  upon  that  body, 
and  the  resultant  of  all  these  attractions  may  be  considered  to  act  from  a 
single  point — the  centre.  Hence,  if  the  earth  were  a  perfect  sphere,  a  given 
body  would  be  equally  attracted  at  any  part  of  the  earth's  surface.  The 
attraction  would,  however,  vary  with  the  height  above  the  surface.  For  small 
alterations  of  level  the  differences  would  be  inappreciable  ;  but  for  greater 
heights  and  in  accurate  measurements  observations  of  the  value  of  g  must 
be  reduced  to  the  sea-level.  The  attraction  of  gravitation  being  inversely 
as  the  square  of  the  distance  from  the  centre  (66)  we  shall  have 

g\     gt  =  _L  :  I where  g  is  the  value  of  the  acceleration  of  gravity  at 

the  sea-level,  g,  its  value  at  any  height  h,  and  R  is  the  radius  of  the  earth. 
From  this,  seeing  that  h  is  very  small  compared  with  R,  and  that  therefore 
its  square  may  be  neglected,  we  get  by  simple  algebraical  transformation 


Fig.  57. 


TT>' 

But  even  at  the  sea-level  the  force  of  gravity  varies  in  different  parts  in 
consequence  of  the  form  of  the  earth.     The  earth  is  not  a  true  sphere,  but 


Gravitation  and  Molecular  A  ttraction. 


[82- 


an  ellipsoid,  the  major  axis  of  which  is  12,754,796  metres,  and  the  minor 
12,712,160  metres.  The  distance,  therefore,  at  the  centre  being  greater  at 
the  Equator  than  at  the  Poles,  and  as  the  attraction  on  a  body  is  inversely 
as  the  square  of  these  distances,  calculation  shows  that  the  attraction  due  to 
this  cause  is  ^  greater  at  the  Poles  than  at  the  Equator.  This  is  what 
would  be  true  if,  other  things  being  the  same,  the  earth  were  at  rest. 

ii.  In  consequence  of  the  earth's  rotation,  the  force  of  gravity  is  further 
modified.  If  we  imagine  a  body  relatively  at  rest  on  the  Equator,  it  really 
shares  the  earth's  rotation,  and  describes,  in  the  course  of  one  day,  a  circle 
whose  centre  and  radius  are  the  centre  and  radius  of  the  earth.  Now,  since 
a  body  in  motion  tends  by  reason  of  its  inertia  to  move  in  a  straight  line,  it 
follows  that  to  make  it  move  in  a  circle,  a  force  must  be  employed  at  each 
instant  to  deflect  it  from  the  tangent  (53).  Consequently,  a  certain  portion 
•of  the  earth's  attraction  must  be  employed  in  keeping  the  above  body  on  the 
surface  of  the  earth,  and  only  the  remainder  is  sensible  as  weight  or  accele- 
rating force.  It  appears  from  calculation  that  at  the  Equator  the  afgth  part 
of  the  earth's  attraction  on  any  body  is  thus  employed,  so  that  the  magnitude 
of  g  at  the  Equator  is  less  by  the  2!  etn  Part  °f  what  it  would  be  were  the 
earth  at  rest. 

iii.  As  the  body  goes  nearer  the  Poles  the  force  of  gravity  is  less  and  less 
diminished  by  the  effect  of  centrifugal  force.  For  in  any  given  latitude  it 
will  describe  a  circle  coinciding  with  the  parallel  of  latitude  in  which  it  is 
placed  ;  but  as  the  radii  of  these  circles  diminish, 
so  does  the  centrifugal  force  until  the  Pole,  where 
the  radius  is  null.  Further,  on  the  Equator  the 
centrifugal  force  is  directly  opposed  to  gravitation  ; 
in  any  other  latitude  only  a  component  of  the  whole 
force  is  thus  employed.  This  is  seen  in  fig.  58,  in. 
which  PP'  represents  the  axis  of  rotation  of  the 
earth,  and  EE'  the  Equator.  At  any  given  point 
E  on  the  Equator  the  centrifugal  force  is  directed 
along  CE,  and  acts  wholly  in  diminishing  the 
intensity  of  gravitation  ;  but  on  any  other  point,  a, 
nearer  the  Pole,  the  centrifugal  force  acting  on  a 
right  line  ab  at  right  angles  to  the  axis  PP',  while  gravity  acts  along  aC, 
gravity  is  no  longer  directly  diminished  by  centrifugal  force,  but  only  by  its 
component  a  d,  which  is  less  the  nearer  a  is  to  the  Pole. 

The  combined  effect  of  these  two  causes — the  flattening  of  the  earth  at 
the  Poles,  and  the  centrifugal  force — is  to  make  thq  attraction  of  gravitation 
at  the  Equator  less  by  about  the  y^d  part  of  its  value  at  the  Poles. 


-84]  Cohesion. 


73 


CHAPTER    III. 

MOLECULAR   FORCES. 

83.  Wature  of  molecular  forces. — The  various  phenomena  which  bodies 
present  show  that  their  molecules  are  under  the  influence  of  two  contrary 
forces,  one  of  which  tends  to  bring  them  together,  and  the  other  to  separate 
them  from  each  other.     The  first  force,  which  is  called  molecular  attraction, 
varies  in  one  and  the  same  body  with  the  distance  only.     The  second  force 
is  due  to  the  vis  viva,  or  moving  force,  which  the  molecules*  possess.     It  is 
the  mutual  relation  between  these  forces,  the  preponderance  of  the  one  or  the 
other,  which  determines  the  molecular  state  of  a  body  (4) — whether  it  be 
solid,  liquid,  or  gaseous. 

Molecular  attraction  is  only  exerted  at  infinitely  small  distances.  Its  effect 
is  inappreciable  when  the  distance  between  the  molecules  is  appreciable. 

According  to  the -manner  in  which  it  is  regarded,  molecular  attraction  is 
designated  by  the  terms  cohesion,  affinity,  or  adhesion. 

84.  Cohesion. — Cohesion  is  the  force  which  unites  adjacent  molecules  of 
the  same  nature  ;  for  example,  two  molecules  of  water,  or  two  molecules  of 
iron.     Cohesion  is  strongly  exerted  in  solids,  less   strongly  in  liquids,  and 
scarcely  at  all  in  gases.     Its  strength  decreases  as  the  temperature  increases, 
because  then  the  vis  viva  of  the  molecules  increases.     Hence  it  is  that  when 
solid  bodies  are  heated  they  first  liquefy,  and  are  ultimately  converted  into 
the  gaseous  state,  provided  that  heat  produces  in  them  no  chemical  change. 

Cohesion  varies  not  only  with  the  nature  of  bodies,  but  also  with  the 
arrangement  of  their  molecules  ;  thus,  the  difference  between  tempered  and 
untempered  steel  is  due  to  a  difference  in  the  molecular  arrangement  pro- 
duced by  tempering.  Many  of  the  properties  of  bodies,  such  as  tenacity, 
hardness,  and  ductility,  are  due  to  the  modifications  which  this  force  un- 
dergoes. 

In  large  masses  of  liquids  the  force  of  gravity  overcomes  that  of  cohesion. 
Hence  liquids  acted  upon  by  the  former  force  have  no  special  shape  ;  they 
take  that  of  the  vessel  in  which  they  are  contained.  But  in  smaller  masses 
•cohesion  gets  the  upper  hand,  and  liquids  assume  then  the  spheroidal  form. 
This  is  seen  in  the  drops  of  dew  on  the  leaves  of  plants.  It  is  also  seen  when 
a  liquid  is  placed  on  a  solid  which  it  does  not  moisten  ;  as,  for  example, 
mercury  upon  wood.  The  experiment  may  also  be  made  with  water,  by 
sprinkling  upon  the  surface  of  the  wood  some  light  powder,  such  as  lyco- 
podium  or  lampblack,  and  then  dropping  a  little  water  on  it.  The  following 
•experiment  is  an  illustration  of  the  force  of  cohesion  causing  a  liquid  to  assume 
the  spheroidal  form.  A  saturated  solution  of  zinc  sulphate  is  placed  in  a 


74 


Gravitation  and  Molecular  A  ttraction. 


[84- 


narrow-necked  bottle,  and  a  few  drops  of  bisulphide  of  carbon,  coloured  with 
iodine,  made  to  float  on  the  *  surface.  If  pure  water  be  now  carefully  added, 
so  as  to  rest  on  the  surface  of  the  sulphate  of  zinc  solution,  the  bisulphide 
collects  in  the  form  of  a  flattened  spheroid,  which  presents  the  appearance 
of  blown  coloured  glass,  and  is  larger  than  the  neck  of  the  bottle,  provided 
a  sufficient  quantity  has  been  taken. 

The  force  of  cohesion  of  liquids  may  be  illustrated  and  even  measured  as 
follows.  A  plane,  perfectly  smooth  disc  U  (fig.  59)  is  suspended  horizontally  to 
one  scale-pan  p  of  a  delicate  balance,  and  is  accu- 
rately equipoised.  A  somewhat  wide  vessel  of  liquid 
is  placed  below,  and  the  position  of  the  disc  regulated 
by  means  of  the  sliding  screw  S  until  it  just  touches 
the  liquid.  Weights  are  then  carefully  added  to  the 
other  scale-pan  until  the  disc  is  detached  from  the 
liquid.  In  this  way  it  has  been  found  that  the  weights 
required  to  detach  the  disc  vary  with  the  nature  of 
the  liquid  ;  with  a  disc  of  118  mm.  diameter  the 
numbers  for  water,  alcohol,  and  turpentine  were 
59'4,  31,  and  34  grammes  respectively. 

The  results  were  the  same  whether  the  disc 
was  of  glass,  of  copper,  or  of  other  metals,  and 
they  thus  only  depend  on  the  nature  of  the  liquid. 
It  is  a  measure  of  the  cohesion  of  the  liquid,  for  a 
layer  remains  adhering  to  the  disc  ;  hence  the 
weight  on  the  other  side  does  not  separate  the  disc 
from  the  liquid,  but  separates  the  particles  of  liquid 
from  each  other. 

85.  Affinity. — Chemical  affinity,  or  chemical  at- 
traction, is  the  force  which  is  exerted  between  mole- 
cules not  of  the  same  kind.  Thus,  in  water,  which 
is  composed  of  oxygen  and  hydrogen,  it  is  affinity 
which  unites  these  elements,  but  it  is  cohesion 
which  binds  together  two  molecules  of  water.  In 
compound  bodies  cohesion  and  affinity  operate 
simultaneously,  while  in  simple  bodies  or  elements  cohesion  has  alone  to  be 
considered. 

To  affinity  are  due  all  the  phenomena  of  combustion,  and  of  chemical 
combination  and  decomposition. 

Those  causes  which  tend  to  weaken  cohesion  are  most  favourable  to  affinity; 
for  instance,  the  action  of  affinity  between  substances  is  facilitated  by  their 
division,  and  still  more  by  reducing  them  to  a  liquid  or  gaseous  state.  It  is 
most  powerfully  exerted  by  a  body  in  its  nascent  state — that  is,  the  state  in 
which  the  body  exists  at  the  moment  it  is  disengaged  from  a  compound  ;  the 
body  is  then  free  and  ready  to  obey  the  feeblest  affinity.  An  increase  of 
temperature  modifies  affinity  differently  under  different  circumstances.  In 
some  cases  by  diminishing  cohesion,  and  increasing  the  distance  between 
the  molecules,  heat  promotes  combination.  Sulphur  and  oxygen,  which  at 
the  ordinary  temperature  are  without  action  on  each  other,  combine  to  form 
sulphur  dioxide  when  the  temperature  is  raised  :  in  other  cases  heat  tends. 


Fig.  59- 


—86]  Adhesion.  *? 

to  decompose  compounds  by  imparting  to  their  elements  an  unequal  expan- 
sibility. Thus  it  is  that  many  metallic  oxides— as,  for  example,  those  of  silver 
and  mercury-  are  decomposed,  by  the  action  of  heat,  into  gas  and  metal. 

86.  Adhesion. — The  molecular  attraction  exerted  between  the  surfaces  of 
bodies  in  contact  is  called  adhesion. 

i.  Adhesion  takes  place  between  solids.  If  two  leaden  bullets  are  cut 
with  a  penknife  so  as  to  form  two  equal  and  brightly  polished  surfaces,  and 
the  two  faces  are  pressed  and  turned  against  each  other,  until  they  are  in  the 
closest  contact,  they  adhere  so  strongly  as  to  require  a  force  of  more  than 
100  grammes  to  separate  them.  The  same  experiment  may  be  made  with 
two  equal  pieces  of  glass  which  are  polished  and  made  perfectly  plane. 
When  they  are  pressed  one  against  the  other,  the  adhesion  is  so  powerful 
that  they  cannot  be  separated  without  breaking.  As  the  experiment  succeeds 
in  vacuo,  it  cannot  be  due  to  atmospheric  pressure,  but  must  be  attributed  to 
a  reciprocal  action  between  the  two  surfaces.  The  attraction  also  increases 
as  the  contact  is  prolonged,  and  is  greater  in  proportion  as  the  contact  is 
closer. 

In  the  operation  of  glueing  the  adhesion  is  complete,  for  the  pores  and 
crevices  of  the  fresh  surfaces  being  filled  with  liquid  glue,  so  that  there  is  no 
empty  space  on  drying,  wood  and  glue  form  one  compact  whole.  In  some 
cases  the  adhesion  of  cemented  objects  is  so  powerful  that  the  mass  breaks  more 
readily  at  other  places  than  at  the  cemented  parts.  Both  in  glueing  and 
cementing  the  layer  should  be  thin. 

Soldering  is  due  to  cohesion  ;  the  surface  of  the  metals  must  be  quite 
clean,  which  is  effected  by  removing  the  layer  of  oxide,  with  which  they  are 
usually  coated,  by  acid  or  by  borax.  The  solder  when  it  solidifies  only 
adheres  to  clean  metal  surfaces. 

There  is  no  real  difference  between  adhesion  and  cohesion  ;  thus,  when 
two  freshly  cut  surfaces  of  caoutchouc  are  pressed  together,  they  adhere  with 
considerable  force,  and  ultimately  form  one  compact  solid  mass. 

ii.  Adhesion  also  takes  place  between  solids  and  liquids.  If  we  dip  a  glass 
rod  into  water,  on  withdrawing  it  a  drop  will  be  found  to  collect  at  its  lower 
extremity,  and  remain  suspended  there.  As  the  weight  of  the  drop  tends  to 
detach  it,  there  must  necessarily  be  some  force  superior  to  this  weight  which 
maintains  it  there  :  this  force  is  the  force  of  adhesion. 

The  adhesion  between  liquids  and  solids  is  more  powerful  than  that 
between  solids.  Thus,  if  in  the  above  experiment  a  thin  layer  of  oil  is  inter- 
posed between  the  plates  they  adhere  firmly,  but  when  pulled  asunder  each 
plate  is  moistened  by  the  oil,  thus  showing  that  in  separating  the  plates  the 
cohesion  of  the  plates  is  overcome,  but  not  the  adhesion  of  the  oil  to  the 
metal. 

In  the  above  case  the  solid  is  wetted  by  the  liquid  ;  that  is,  some  remains 
adhering  even  when  the  drop  falls.  But  liquids  adhere  to  solids  even  when 
they  are  not  wetted.  Thus  if  a  smooth  glass  plate  be  placed  on  mercury  an 
appreciable  force  is  required  to  detach  it.  Small  drops  of  mercury,  too, 
adhere  to  the  underside  of  a  glass  or  porcelain  plate. 

iii.   The  force  of  adhesion  operates,  lastly,  between  solids  and  gases. 
If  a  glass  or  metal  plate  be  immersed  in  water,  bubbles  will  be  found  1 
appear  on  the  surface.     As  air  cannot  penetrate  into  the  pores  of  the  plate, 


76  Gravitation  and  Molecular  Attraction.  [86- 

the  bubbles  could  not  arise  from  the  air  which  had  been  expelled.  It  is 
solely  due  to  the  layer  of  air  which  covered  the  plate,  and  moistened  it  like 
a  liquid.  In  many  cases  when  gases  are  separated  in  the  nascent  state 
on  the  surface  of  metals — as  in  electrolysis — the  layer  of  gas  which  covers 
the  plate  has  such  a  density  that  it  can  produce  chemical  actions  more  power- 
ful than  those  which  it  can  bring  about  in  the  free  state. 

The  collection  of  dust  on  walls,  writing  and  drawing  with  chalks  and 
pencils,  depend  on  the  adhesion  of  solids.  Yet  these  are  easily  rubbed  out, 
for  the  adhesion  is  only  to  the  surface  layer.  In  writing  with  ink,  and  in 
water-colour  painting,  the  liquid  penetrates  into  the  pores,  taking  the  solid 
with  it,  which  is  left  behind  as  the  liquid  evaporates,  and  hence  the  adhesion 
of  such  writing  and  painting  is  far  more  complete. 


-88] 


Elasticity  of  Traction. 


77 


CHAPTER   IV. 

PROPERTIES   PECULIAR  TO   SOLIDS. 

87.  Various  special  properties. — After  having  described  the  principal 
properties  common  to  solids,  liquids,  and  gases,  we  shall  discuss  the  properties 
peculiar  to  solids.     They  are  elasticity  of  traction,  elasticity  of  torsion,  elas- 
ticity oj flexure,  tenacity,  ductility,  and  hardness. 

88.  Elasticity  of  traction. — Elasticity,  as  a  general  property  of  matter, 
has  been  already  mentioned  (17),  but  simply  in  reference  to  the  elasticity 
developed  by  pressure  ;  in  solids  it  may  also  be  called  into  play  by  traction, 
by  torsion,  and  by  flexure.     The  definitions  there  given  require  some  exten- 
sion.    In  ordinary  life  we  consider 

those  bodies  as  highly  elastic 
which,  like  caoutchouc,  undergo 
considerable  change  on  the  appli- 
cation of  only  a  small  force.  Yet 
the  force  of  elasticity  is  greatest  in 
many  bodies,  such  as  iron,  which 
do  not  seem  to  be  very  elastic.  For 
by  force  of  elasticity  is  understood 
the  force  with  which  the  displaced 
particles  tend  to  revert  to  their 
original  position,  and  which  force  is 
equivalent  to  that  which  has  brought 
about  the  change.  Considered  from 
this  point  of  view,  gases  have  the 
least  force  of  elasticity ;  that  of 
liquids  is  considerably  greater,  and 
is,  indeed,  greater  than  that  of  many 
solids.  Thus  the  force  of  elasticity 
of  mercury  is  greater  than  that  of 
caoutchouc,  glass,  wood,  and  stone. 
It  is,  however,  less  than  that  of  the 
other  metals,  with  the  exception  of 
lead. 

This  seems  discordant  with  or- 
dinary ideas  about  elasticity  ;  but 
it  must  be  remembered  that  those 
bodies  which,  by  the  exertion  of  a  small  force,  undergo  a  considerable 
change,  generally  have  also  the  property  of  undergoing  this  change  without 
losing  the  property  of  reverting  completely  to  their  original  state.  They 


78  Gravitation  and  Molecular  Attraction.  [88 

have  a  wide  limit  of  elasticity  (17).  Those  bodies  which  require  great  force 
to  effect  a  change  are  also,  for  the  most  part,  those  on  which  the  exertion 
of  a  force  produces  a  permanent  alteration  ;  when  the  force  is  no  longer 
exerted,  they  do  not  completely  revert  to  their  original  state. 

In  order  to  study  the  laws  of  the  elasticity  of  traction,  Savart  used  the 
apparatus  represented  in  fig.  60.  It  consists  of  a  wooden  support  from  which 
are  suspended  the  rods  or  wires  taken  for  experiment.  At  the  lower  ex- 
tremity there  is  a  scale-pan,  and  on  the  wire  two  points,  A  and  B,  are  marked, 
the  distance  between  which  is  measured  by  means  of  the  cathetometer  before 
the  weights  are  added. 

The  cathetometer  consists  of  a  strong  upright  brass  support,  K,  divided 
into  millimetres,  and  which  can  be  adjusted  in  an  exactly  vertical  position 
"by  means  of  levelling  screws  and  the  plumb-line.  A  small  telescope,  exactly 
at  right  angles  to  the  scale,  can  be  moved  up  and  down,  and  is  provided  with 
a  vernier  which  measures  fiftieths  of  a  millimetre.  By  adjusting  the  telescope 
successively  on  the  two  points  A  and  B,  as  represented  in  the  figure,  the 
distance  between  these  points  is  obtained  on  the  graduated  scale.  Placing, 
then,  weights  in  the  pan,  and  measuring  again  the  distance  from  A  to  B,  the 
elongation  is  obtained. 

By  experiments  of  this  kind  it  has  been  ascertained  that  for  elasticity  of 
traction  or  pressure  — 

The  alteration  in  length  within  the  limits  of  elasticity  is  in  proportion  to  the 
length  and  to  the  load  acting  on  the  body,  and  is  inversely  as  the  cross  section. 

It  depends,  moreover,  on  the  specific  elasticity  ;  that  is,  on  a  special 
property  of  the  material  of  the  body.  If  this  coefficient  be  denoted  by  E, 
and  if  the  length,  cross  section,  and  load  are  respectively  designated  by  /,  j, 
and  P,  then  for  the  alteration  in  length,  e,  we  have 


If  in  the  above  expression  the  sectional  area  be  a  square  millimetre,  and 
P  be  one  kilogramme,  then 

e  =  E/,  from  which  E  =  *» 

which  expresses  by  what  fraction  the  length  of  a  bar  a  square  millimetre  in 
section  is  altered  by  a  load  of  a  kilogramme.  This  is  called  the  coefficient  of 
elasticity  ;  it  is  a  very  small  fraction,  and  it  is  therefore  desirable  to  use  its 
reciprocal,  that  is  -  or  /*,  as  the  modulus  of  elasticity  ;  or  the  weight  in 

kilogrammes  which  applied  to  a  bar  would  elongate  it  by  its  own  length, 
assuming  it  to  be  perfectly  elastic.  This  coefficient  is  known  as  Youngs 
modulus.  This  cannot  be  observed,  for  no  body  is  perfectly  elastic,  but*  it 
may  be  calculated  from  any  accurate  observations  by  means  of  the  above 
formula. 

The  following  are  the  best  values  for  some  of  the  principal  substances  :— 

Steel  ....  21,000  Slate.        .        .        .  11,035 

Wrought  Iron    .         .  19,000  Brass.         .         .         .  ^ooo 

Platinum    .         .         .  17,044  Zinc    ....  3^700 

Copper       .         .         .  12,400  Silver.         .         .         .  ?AOO 


88] 


Elasticity  of  Flexure. 


Plate  Glass 
Rock  Salt  . 
Marble 
Lead        -. 
Bone 


79 


7,015 
4,230 
2,609 
i,  800 
1,635 


Wood 
Whalebone 
Gypsum 
Sandstone  . 
Ice 


1,100 
700 
400 

631 
236 


Thus,  to  double  the  length  of  a  wrought-iron  wire  a  square  millimetre  in 
section,  would  (if  these  were  possible)  require  a  weight  of  19,000  kilogrammes ; 
but  a  weight  of  15  kilogrammes  produces  a  permanent  alteration  in  length 
of  TF54th>  and  this  is  the  limit  of  elasticity.  The  weight,  which  when  applied 
to  a  body  of  unit  section,  just  brings  about  an  appreciable  permanent  change, 
is  a  measure  of  the  limit  of  elasticity.  Whalebone  has  only  a  modulus  of 
700,  and  experiences  a  permanent  elongation  by  a 
weight  of  5  kilogrammes  ;  its  limit  is,  therefore,  rela- 
tively greater  than  that  of  iron.  Steel  has  a  high 
modulus,  along  with  a  wide  limit. 

This  longitudinal  stretching  is  accompanied  by  a 
lateral  contraction,  and  the  ratio  of  the  contraction  to 
the  proportional  stretching  is  known  as  Poissorts  coeffi- 
cient. It  was  taken  by  him  to  be  £,  but  later  experi- 
ments have  found  the  ratio  to  be  about  ^. 

Both  calculation  and  experiment  show  that  when 
bodies  are  lengthened  by  traction  their  volume  in- 
creases. 

When  weights  are  placed  on  a  bar,  the  amount  by 
which  it  is  shortened,  or  the  coefficient  of  contraction, 
is  equal  to  the  elongation  which  it  would  experience  if 
the  same  weights  were  suspended  to  it,  and  is  repre- 
sented by  the  above  numbers. 

The  influence  of  temperature  on  the  elasticity  of 
iron,  copper,  and  brass  was  investigated  by  Kohlrausch 
and  Loomis.  They  found  that  the  alteration  in  the 
coefficient  of  elasticity  by  heat  is  the  same  as  that 
which  heat  produces  in  the  coefficient  of  expansion 
and  in  the  refractive  power  ;  it  is  also  much  the  same 
as  the  change  in  the  permanent  magnetism,  and  in  the 
specific  heat,  while  it  is  less  than  the  alteration  in  the 
conductivity  for  electricity. 

As  an  application  may  be  mentioned  Jolly's  spring 
balance.  This  consists  of  a  long  steel  wire  ab,  wound 
in  the  form  of  a  spiral,  which  is  suspended  in  front  of 
an  accurately  graduated  scale.  To  the  lower  end  of 
the  spiral  two  scale  pans,  c  and  d^  are  hung  by  a  thread,  Fjg  6i 

the  lower  one,  d,  dipping  in  a  small  vessel  of  water  on 
an  adjustable  support.  The  instrument  is  graduated  empirically  by  observing 
what  displacement  of  the  mark  m  is  produced  by  putting  a  known  weight  in 
the  scale-pan  d.  Knowing  then  once  for  all  the  constant  of  the  instrument, 
it  is  easy  to  determine  the  weight  of  a  body  by  reading  the  displacement  which 
it  produces  along  the  scale. 


8o 


Gravitation  and  Molecular  Attraction. 


[89- 


Fig.  62. 


89.  Elasticity  of  torsion. — The  laws  of  the  torsion  of  wires  were  deter- 
mined by  Coulomb,  by  means  of  an  apparatus  called  the  torsion  balance 

(fig.  62).  It  consists  essentially  of  a  metal  wire, 
clamped  at  one  end  in  a  support,  A,  and  hold- 
ing at  the  other  a  metal  sphere,  B,  to  which 
is  affixed  an  index,  C.  Immediately  below 
this  there  is  a  graduated  circle,  CD.  If  the 
needle  is  turned  from  its  position  of  equilibrium 
through  a  certain  angle,  which  is  the  angle1 
of  torsion,  the  force  necessary  to  produce  this 
effect  is  the  force  of  torsion.  When,  after  this, 
deflection,  the  sphere  is  left  to  itself,  the  reac- 
tion of  torsion  produces  its  effect,  the  wire  un- 
twists itself,  and  the  sphere  rotates  about  its 
vertical  axis  with  increasing  rapidity  until  it 
reaches  its  position  of  equilibrium.  It  does  not,, 
however,  rest  there  ;  in  virtue  of  its  inertia  it 
passes  this  position,  and  the  wire  undergoes  a 
torsion  in  the  opposite  direction.  The  equili- 
brium being  again  destroyed,  the  wire  again  tends 
to  untwist  itself,  the  same  alterations  are  again 
produced,  and  the  needle  does  not  rest  at  zero 
of  the  scale  until  after  a  certain  number  of  oscil- 
lations about  this  point  have  been  completed. 
By  means  of  this  apparatus  Coulomb  found  that  when  the  amplitude  of 
the  oscillations  is  within  certain  limits,  the  oscillations  are  subject  to  the 
following  laws  : 

I.  The  oscillations  are  very  nearly  isochronous. 

II.  For  the  same  wire,  the  angle  of  torsion  is  proportional  to  the  moment 
of  the  force  of  torsion. 

III.  With  the  same  force  of  torsion,  and  witJi,  wires  of  the  same  diameter^ 
the  angles  of  torsion  are  proportional  to  the  lengths  of  the  wires. 

IV.  The  same  force  of  torsion  being  applied  to  wires  of  the  same  length ,. 
the  angles  of  torsion  are  inversely  proportional  to  the  fourth  powers  of  the 
diameters. 

Wertheim  examined  the  elasticity  of  torsion  in  the  case  of  stout  rods 
by  means  of  a  different  apparatus,  and  found  that  it  is  also  subject  to  these 
laws.  He  further  found  that,  all  dimensions  being  the  same,  different  sub- 
stances undergo  different  degrees  of  torsion  for  the  same  force,  and  each 

substance  has  its  own  coefficient  of  torsion,  which  is  usually  denoted  by  — 

or  by  r.  The  value  of  this  coefficient  is  about  \  that  of  the  modulus  of 
elasticity. 

The  laws  of  torsion  may  be  enunciated  in  the  formula  w  =  - - ;  in 

which  w  is  the  angle  of  torsion,  F  the  moment  of  the  force  of  torsion,  /  the 
length  of  the  wire,  r  its  radius,  and  ^  the  specific  torsion-coefficient. 

As  the  angle  of  torsion  is  inversely  proportional  to  the  fourth  power  of 


-90] 


of  Flexure. 


81 


the  radius,  rods  of  some  t^fess  require  very  great  force  to  produce  even 
small  twists.  With  very^PTll  cf  ameters,  such  as  those  of  a  cocoon  or  glass 
thread,  the  proportionality  between  the  angle  of  torsion  and  the  twisting 
force  holds  even  for  several  complete  turns. 

90.  Elasticity  of  flexure.—  A  solid,  when  cut  into  a  rod  or  thin  plate, 
and  fixed  at  one  end,  after  having  been  more  or  less  bent,  strives  to  return 
to  its  original  position  when  left  to  itself.  This  property  is  known  as  the 
elasticity  of  flexure,  and  is  very  distinct  in  steel,  caoutchouc,  wood,  and  paper. 

If  a  rectangular  bar  A  B  be  clamped  at  one  end  and  loaded  at  the  other 
end  by  a  weight  W  (fig.  63),  a  flexure  will  be  produced  which  may  be  observed 
by  the  '  cathetometer.  The  amount  of  this  flexure  e  is  represented  by  the 
formula 


where  P  is  the  load,  /  the  length  of  the  bar,  b  its  breadth,  h  its  depth  or 
thickness,  all  in  mm.,  and  p  the  modulus  of  elasticity. 
If  the  section  of  the  bar  is  a  circle  of  radius  r,  then 


It  is  clear  that  an  accurate  measurement  of  the  flexure  of  a  bar  furnishes 
a  means  of  determining  its  modulus  of  elasticity. 

The  elasticity  of  flexure  is  applied  in  a  vast  variety  of  instances  —  for 
example,  in  bows,  watch-springs,  carriage-springs  ;  in  spring  balances  it  is 
used  to  determine  weights, 
in  dynamometers   to  de- 
termine the  force  of  agents 
in  prime  movers  ;  and,  as  a 
property  of  wool,  hair,  and 
feathers,  it  is  applied  to 
domestic  uses  in  cushions 
and  mattresses. 

Whatever  be  the  kind 
of  elasticity,  there  is,  as 
has  been  already  said,  a 
limit  to  it—  that  is,  there 
is  a  molecular  displace- 
ment, beyond  which  Fig  6s 

bodies  are  broken,  or  at 

any  rate  do  not  regain  their  primitive  form.  This  limit  is  affected  by 
various  causes.  The  elasticity  of  many  metals  is  increased  by  hardening, 
whether  by  cold,  by  means  of  the  draw-plate,  by  rolling,  or  by  hammering. 
Some  substances,  such  as  steel,  cast  iron,  and  glass,  become  both  harder 
and  more  elastic  by  tempering  (94). 

Elasticity,  on  the  other  hand,  is  diminished  by  annealing,  which  consists 
in  raising  the  body  to  a  temperature  lower  than  that  necessary  for  tempering, 
and  allowing  it  to  cool  slowly.  It  is  by  this  means  that  the  elasticity  of 
springs  may  be  regulated  at  pleasure.  Glass,  when  it  is  heated,  undergoes 


8  2  Gravitation  and  Molecular  A  ttr action.  [90- 

a  true  tempering  in  being  rapidly  cooled,  and  hence,  in  order  to  lessen  the 
fragility  of  glass  objects,  they  are  reheated  in  a  furnace,  and  are  carefully 
allowed  to  cool  slowly,  so  that  the  particles  have  time  to  assume  their  most 
stable  position  (94). 

91.  Tenacity. — Tenacity  is  the  resistance  which  a  body  opposes  to  the 
total  separation  of  its  parts.  According  to  the  manner  in  which  the  external 
force  acts,  we  may  have  various  kinds  of  tenacity  :  tenacity  in  the  ordinary 
sense,  or  resistance  to  traction  ;  relative  tenacity,  or  resistance  to  fracture  ; 
reactive  tenacity,  or  resistance  to  crushing  ;  sheering  tenacity,  or  resistance 
to  displacement  of  particles  in  a  lateral  direction  ;  and  torsional  tenacity,  or 
resistance  to  twisting.  Ordinary  tenacity  is  determined  in  different  bodies 
by  forming  them  into  cylindrical  or  prismatic  wires,  and  ascertaining  the 
weight  necessary  to  break  them. 

Mere  increase  in  length  does  not  influence  the  breaking  weight,  for  the 
weight  acts  in  the  direction  of  the  length,  and  stretches  all  parts  as  if  it  had 
been  directly  applied  to  them. 

Tenacity  is  directly  proportional  to  the  breaking  weight,  and  inversely 
proportional  to  the  area  of  a  transverse  section  of  the  wire. 

Tenacity  diminishes  with  the  duration  of  the  traction.  A  small  force 
continuously  applied  for  a  long  time  will  often  break  a  wire,  which  would  not 
at  once  be  broken  by  a  larger  weight. 

In  many  bodies  such  as  metals,  and  more  especially  in  organic  substances, 
some  time  often  elapses  before  the  full  effect  of  a  change  is  produced  by  a 
force  ;  and  also  before  the  body  reverts  to  its  original  state  after  the  force 
has  ceased  to  act.  This  is  known  as  elastic  after-action. 

Not  only  does  tenacity  vary  with  different  substances,  but  it  also  varies 
with  the  form  of  the  body.  Thus,  with  the  same  sectional  area,  a  cylinder 
has  greater  tenacity  than  a  prism.  The  quantity  of  matter  being  the  same, 
a  hollow  cylinder  has  greater  tenacity  than  a  solid  one  ;  and  the  tenacity  of 
this  hollow  cylinder  is  greatest  when  the  external  radius  is  to  the  internal 
one  in  the  ratio  of  1 1  to  5.  The  shape  has  also  the  same  influence  on  the 
resistance  to  crushing  as  it  has  on  the  resistance  to  traction.  A  hollow 
cylinder  with  the  same  mass,  and  the  same  weight,  offers  a  greater  resistance 
than  a  solid  cylinder.  Thus  it  is  that  the  bones  of  animals,  the  feathers  of 
birds,  the  stems  of  corn  and  other  plants,  offer  greater  resistance  than  if  they 
were  solid,  the  mass  remaining  the  same. 

Tenacity,  like  elasticity,  is  different  in  different  directions  in  bodies.  In 
wood,  for  example,  both  the  tenacity  and  the  elasticity  are  greater  in  the 
direction  of  the  fibres  than  in  a  transverse  direction.  And  this  difference 
obtains  in  general  in  all  bodies,  the  texture  of  which  is  not  the  same  in  all 
directions. 

Wires  by  being  worked  acquire  greater  tenacity  on  the  surface,  and  have 
therefore  a  higher  coefficient,  than  even  somewhat  thicker  rods  of  the  same 
material ;  and  according  to  some  physicists,  solids  have  a  surface  tension 
analogous  to  the  surface  tension  of  liquids  (136).  A  strand  of  wires  is  stronger 
than  a  rod  whose  section  is  equal  to  the  sum  of  the  sections  of  the  wires. 

Wertheim  found  the  following  numbers  representing  the  weight  in  kilo- 
grammes for  the  limit  of  elasticity,  and  for  the  tenacity  of  wires,  imm.  in 
diameter. 


-92] 


Ductility. 


Lead  . 


Tin 


Silver 


Copper 
Platinum 


Iron 


Steel . 


Cast  Steel . 


)  drawn 
I  annealed 
j  drawn 
f  annealed 

drawn 

annealed 
j  drawn 
I  annealed 
|  drawn 
}  annealed 
j  drawn 
(  annealed 
\  drawn 
|  annealed 

drawn 

annealed 


Limit  of  Elasticity. 
Kilogrammes 
.         0-25 
0'20 


0-20 

275 
12-00 

3-00 
26-00 

14-50 
32-5 
5-0 
42-5 
15-0 

55-6 


Tenacity. 
Kilogrammes 
2-07 
I -80 

2-45 

170 

29-00 

16-02 

40-30 

34-10 
23-50 
6rio 
46-88 
70-00 
40-00 
80-00 
6575 


The  table  shows  that  of  all  metals  cast  steel  has  the  greatest  tenacity. 
Yet  it  is  exceeded  by  fibres  of  unspim  silk,  a  thread  of  which  i  square  milli- 
metre in  section  can  carry  a  load  of  500  kilogrammes.  Single  fibres  of  cotton 
can  support  a  weight  of  100  to  300  grammes  ;  that  is,  millions  of  times  their 
own  weight. 

In  this  table  the  bodies  are  supposed  to  be  at  the  ordinary  temperature. 
At  higher  temperatures  the  tenacity  rapidly  decreases.  Seguin  made  some 
experiments  on  this  point  with  iron  and  copper,  and  obtained  the  following 
values  for  the  tenacity,  in  kilogrammes,  of  millimetre  wire  at  different  tem- 
peratures : — 

Iron         .         .  at  10°,  60  ;  at  370°,  54  ;  at  500°,  37  ; 
Copper   .         .       „       21  ;        „         77  ;      „        o. 

92.  Ductility. — Ductility  is  the  property  in  virtue  of  which  a  great  num- 
ber of  bodies  change  their  forms  by  the  action  of  traction  or  pressure. 

With  certain  bodies,  such  as  clay,  wax,  &c.,  the  application  of  a  very 
little  force  is  sufficient  to  produce  a  change  ;  with  others,  such  as  the  resins 
and  glass,  the  aid  of  heat  is  needed,  while  with  the  metals  more  powerful 
agents  must  be  used,  such  as  percussion,  the  draw-plate,  or  the  rolling-mill. 

Malleability  is  that  modification  of  ductility  which  is  exhibited  by  ham- 
mering. The  most  malleable  metal  is  gold,  which  has  been  beaten  into 
leaves  about  the  go^ooo^  °f  an  mc^  thick- 

The  most  ductile  metal  is  platinum.  Wollaston  obtained  a  wire  of  it 
0-00003  °f  an  mch  m  diameter.  This  he  effected  by  covering  with  silver  a 
platinum  wire  o-oi  of  an  inch  in  diameter,  so  as  to  obtain  a  cylinder  0*2  inch 
in  diameter  only,  the  axis  of  which  was  of  platinum.  This  was  then  drawn 
out  in  the  form  of  wire  as  fine  as  possible  ;  the  two  metals  were  equally  ex- 
tended. When  this  wire  was  afterwards  boiled  with  dilute  nitric  acid  the 
silver  was  dissolved,  and  the  platinum  wire  left  intact.  The  wire  was  so  fine 
that  a  mile  of  it  would  have  only  weighed  1-25  of  a  grain. 

G  2 


84  Gravitation  and  Molecular  Attraction.  [93- 

93.  Hardness. — Hardness  is  the  resistance  which  bodies  offer  to  being 
scratched  or  worn  by  others.    It  is  only  a  relative  property,  for  a  body  which 
is  hard  in  reference  to  one  body  may  be  soft  in  reference  to  others.     The  re- 
lative hardness  of  two  bodies  is  ascertained  by  trying  which  of  them  will 
scratch  the  other.     Diamond  is  the  hardest  of  all  bodies,  for  it  scratches  all, 
and  is  not  scratched  by  any.     The  hardness  of  a  body  is  expressed  by  re- 
ferring it  to  a  scale  of  hardness  :  that  usually  adopted  is — 

1.  Talc  5.  Apatite  8.  Topaz 

2.  Rock  salt  6.  Felspar  9.  Corundum 

3.  Calcspar  7.  Quartz  10.  Diamond 

4.  Fluorspar 

Thus,  the  hardness  of  a  bddy  which  would  scratch  felspar,  but  would  be 
scratched  by  quartz,  would  be  expressed  by  the  number  6-5. 

The  pure  metals  are  softer  than  their  alloys.  Hence  it  is  that,  for  jewel- 
lery and  coinage,  gold  and  silver  are  alloyed  with  copper  to  increase  their 
hardness. 

The  hardness  of  a  body  has  no  relation  to  its  resistance  to  compression. 
Glass  and  diamond  are  much  harder  than  wood,  but  the  latter  offers  far 
greater  resistance  to  the  blow  of  a  hammer.  Hard  bodies  are  often  used 
for  polishing  powders  ;  for  example,  emery,  pumice,  and  tripoli.  Diamond, 
being  the  hardest  of  all  bodies,  can  only  be  ground  by  means  of  its  own 
powder. 

A  body  which  moves  with  great  velocity  can  cut  into  bodies  which  are 
harder  than  itself.  Thus  a  disc  of  wrought  iron  rotating  with  a  velocity 
of  1 1  metres  in  a  second  was  cut  by  a  steel  graver  ;  while  when  it  rotated 
with  a  velocity  of  20  metres,  the  edge  of  the  disc  could  cut  the  graver,  and 
with  a  velocity  of  50  to  100  metres  it  could  even  cut  into  agate  and  quartz. 

94.  Temper. — By  sudden  cooling  after  they  have  been  raised  to  a  high 
temperature,  many  bodies,  more  especially  steel,  become  hard  and  brittle. 
By  reheating  and  cooling  slowly,  which  is  called  annealing,  hard  and  brittle 
steel  may  be  converted  into  a  soft  flexible  material,  and  in  general  by  varying 
the  limits  of  temperature  within  which  the  change  takes  place,  almost  any 
degree  of  elasticity  and  flexibility  may  be  given  to  it.     This  operation  is 
called  tempering.      All  cutting   instruments  are   made  of  tempered  steel. 
There  are,  however,  some  few  bodies  upon  which  tempering  produces  quite 
a  contrary  effect.     An  alloy  of  one  part  of  tin  and  four  parts  of  copper,  called 
tamtam  metal,  is  ductile  and  malleable  when  rapidly  cooled,  but  hard  and 
brittle  as  glass  when  cooled  slowly. 


~97]  Compressibility  of  Liquids. 


BOOK  III. 

ON     LIQUIDS. 


CHAPTER  I. 

HYDROSTATICS. 

95.  Province  of  Hydrostatics.— The  science  of  hydrostatics  treats  of  the 
conditions  of  the  equilibrium  of  liquids,  and  of  the  pressures  they  exert, 
whether  within  their  own  mass  or  on  the  sides  of  the  vessels  in  which  they 
are  contained. 

96.  General  characters  of  liquids.— It  has  been  already  seen  (4)  that 
liquids  are  bodies  whose  molecules  are  displaced  by  the   slightest  force. 
Their  fluidity,  however,  is  not  perfect ;  their  particles  always  adhere  slightly 
to  each  other,  and  when  a  thread  of  liquid  moves,  it  attempts  to  drag  the 
adjacent  stationary  particles  with  it,  and  conversely  is  held  back  by  them. 
This  property  is  called  viscosity •,  and  bodies  which  possess  this  property  in  a 
high  degree  are  said  to  be  viscous. 

Gases  also  possess  fluidity,  but  in  a  higher  degree  than  liquids.  The 
distinction  between  the  two  forms  of  matter  is  that  liquids  are  almost  incom- 
pressible and  are  comparatively  inexpansible,  while  gases  are  eminently 
compressible  and  expand  spontaneously. 

The  fluidity  of  liquids  is  seen  in  the  readiness  with  which  they  take  all 
sorts  of  shapes.  Their  compressibility  is  established  by  the  following  expe- 
riment. 

97.  Compressibility  of  liquids. — From  the  experiment  of  the  Florentine 
Academicians  (13),  liquids  were  for  a  long  time  regarded  as  being  completely 
incompressible.     Since  then  researches  have  been  made  on  this  subject  by 
various  physicists,  which  have  shown  that  liquids  are  really  compressible. 

The  apparatus  used  for  measuring  the  compressibility  of  liquids  has  been 
named  the  piezometer  (irtcfa,  I  compress  ;  /zeYpoi/,  measure).  That  shown  in 
%.  64  consists  of  a  strong  glass  cylinder,  with  very  thick  sides,  and  an 
internal  diameter  of  about  3^  inches.  The  base  of  the  cylinder  is  firmly 
cemented  into  a  wooden  foot,  and  on  its  upper  part  is  fitted  a  metal  cylin- 
der closed  by  a  cap  which  can  be  unscrewed.  In  this  cap  there  is  a  funnel, 
R,  for  introducing  water  into  the  cylinder,  and  a  small  barrel  hermetically 
closed  by  a  piston,  which  is  moved  by  a  screw,  P. 


86 


On  Liquids. 


[97- 


In  the  inside  of  the  apparatus  there  is  a  glass  vessel,  A,  containing  the 
liquid  to  be  compressed.  The  upper  part  of  this  vessel  terminates  in  a 
capillary  tube,  which  dips  under  mercury,  O.  This  tube  has  been  previously 
divided  into  parts  of  equal  capacity,  and  it  has  been  determined  how  many 
of  these  parts  the  vessel  A  contains.  The  latter  is  ascertained  by  finding  the 
weight,  P,  of  the  mercury  which  the  reservoir, 
A,  contains,  and  the  weight,  p,  of  the  mercury 
contained  in  a  certain  number  of  divisions,  ?z, 
of  the  capillary  tube.  If  N  be  the  number  of 
divisions  of  the  small  tube  contained  in  the 

whole  reservoir,  we  have  —  =  - ,  from  which  the 

value  of  N  is  obtained.  There  is  further  a 
manometer.  This  is  a  glass  tube,  B,  containing 
air  closed  at  one  end,  and  the  other  end  of 
which  dips  under  mercury.  When  there  is  no 
pressure  on  the  water  in  the  cylinder,  the  tube 
B  is  completely  full  of  air  ;  but  when  the  water 
within  the  cylinder  is  compressed  by  means  of 
the  screw  P,  the  pressure  is  transmitted  to  the 
mercury,  which  rises  in  the  tube,  compressing 
the  air  which  it  contains.  A  graduated  scale 
fixed  on  the  side  of  the  tube  shows  the  reduction 
of  volume,  and  this  reduction  of  volume  indicates 
the  pressure  exerted  on  the  liquid  in  the  cylin- 
der, as  will  be  seen  in  speaking  of  the  mano- 
meter (184). 

In  making  the  experiment,  the  vessel  A  is 
filled  with  the  liquid  to  be  compressed,  and  the 
end  dipped  under  the  mercury.  By  means  of 
the  funnel  R  the  cylinder  is  entirely  filled  with 
water.  The  screw  P  being  then  turned  the 
piston  moves  downwards,  and  the  pressure  exerted  upon  the  water  is  trans- 
mitted to  the  mercury  and  the  air  ;  in  consequence  of  which  the  mercury 
rises  in  the  tube  B,  and  also  in  the  capillary  tube.  The  ascent  of  mercury 
in  the  capillary  tube  shows  that  the  liquid  in  the  vessel  A  has  diminished  in 
volume,  and  gives  the  amount  of  its  compression,  for  the  capacity  of  the 
whole  vessel  A  in  terms  of  the  graduated  divisions  on  the  capillary  tube  has 
been  previously  determined. 

In  his  first  experimeuts^Oersted  assumed  that  the  capacity  of  the  vessel 
A  remained  the  same,  its  sides  being  compressed  both  internally  and  ex- 
ternally by  the  liquid.  But  this  capacity  diminishes  in  consequence  of  the 
external  and  internal  pressures.  Colladon  and  Sturm  made  some  experiments 
allowing  for  this  change  of  capacity,  and  found  that  for  a  pressure  equal  to 
that  of  the  atmosphere,  mercury  experiences  a  compression  of  0*000003  part 
of  its  original  volume,  water  a  compression  of  0*00005,  and  ether  a  compression 
of  0-000133  Part  °f  its  original  bulk.  The  compressibility  of  sea  water  is  only 
about  0-000044  :  it  is  not  materially  denser  even  at  great  depths  ;  thus  at 
the  depth  of  a  mile  its  density  would  only  be  about  T|oth  the  greater.  The 


Fig.  64. 


-98] 


Equality  of  Pressures.     Pascal's  Law. 


compressibility  is  greater  the  higher  the  temperature  ;  thus  that  of  ether  at 
14°  is  one-fourth  greater  than  its  compressibility  at  o°. 

It  appears  from  recent  researches  that  the  compressibility  of  water 
diminishes  with  increase  of  temperature  up  to  a  certain  limit,  beyond  which 
it  increases  again.  This  limit  seems  to  be  about  63°  C. 

As  the  pressure  increases,  the  average  compressibility  for  each  atmo- 
sphere diminishes. 

Whatever  be  the  pressure  to  which  a  liquid  has  been  subjected,  experi- 
ment shows  that  as  soon  as  the  pressure  is  removed  the  liquid  regains 
its  original  volume,  from  which  it  is  concluded  that  liquids  are  perfectly 
elastic. 

98.  Equality  of  pressures.  Pascal's  law. — By  considering  liquids  as 
perfectly  fluid,  and  assuming  them  to  be  uninfluenced  by  the  action  of  gravity, 
the  following  law  has  been  established.  It  is  often  called  Pascal's  taw,  for 
it  was  first  enunciated  by  him. 

Pressure  exerted  anywhere  upon  a  mass  of  liquid  is  transmitted  undi- 
minished  in  all  directions,  and  acts  with  the  same  force  on  all  equal  surfaces, 
and  in  a  direction  at  right  angles  to  those  surfaces. 

To  get  a  clearer  idea  of  the  truth  of  this  principle,  let  us  conceive  a  vessel 
of  any  given  form  in  the  sides  of  which  are  placed  various  cylindrical  aper- 
tures, all  of  the  same  size,  and   closed  by  movable 
pistons.     Let  us,  further,  imagine  this  vessel  to  be 
filled  with  liquid  and  unaffected  by  the  action  of 
gravity ;  the  pistons  will,  obviously,  have  no  ten- 
dency to  move.     If  now  upon  the  piston  A  (fig. 
65),  which  has  a  surface  a,  a  weight  of  P  pounds 
be   placed,   it   will  be  pressed  inwards,  and    the 
pressure  will  be  transmitted  to  the  internal  faces 
of  each  of  the  pistons  B,  C,  D,  and  E,  which  will 
each  be  forced  outwards  by   a  pressure  P,  their 
surfaces   being  equal  to  that  of  the  first  piston. 
Since  each  of  the  pistons  undergoes  a  pressure  P, 
equal  to  that  on  A,  let  us  suppose  two  of  the  pis- 
tons united  so  "as  to  constitute  a  surface  20,  it  will  have  to  support  a  pres 
sure  2  P.     Similarly,  if  the  piston  were  equal  to  30,  it  would  experience  a 
pressure  of  3?  ;  and  if  its  area 
were  100  or  1,000  times  that  of 
•a,  it  would  sustain  a  pressure  of 
loo  or  1,000  times  P.     In  other 
words,  the  pressure  on  any  part 
•of  the     internal   walls     of    the 
vessel  would  be  proportional  to 
the  surface. 

The  principle  of  the  equality 
of  pressure  is  assumed  as  a 
consequence  of  the  constitution 
of  fluids.  By  the  following  ex- 
periment it  can  be  shown  that  pressure  is  transmitted  in  all  directions, 
although  it  cannot  be  shown  that  it  is  equally  transmitted.  A  cylir 


Fig.  65. 


Fig.  66. 


88 


On  Liquids. 


[98- 


provided  with  a  piston  is  fitted  into  a  hollow  sphere  (fig.  66),  in  which 
small  cylindrical  jets  are  placed  perpendicular  to  the  sides.  The  sphere 
and  the  cylinder  being  both  filled  with  water,  when  the  piston  is  moved 
the  liquid  spouts  forth  from  all  the  orifices,  and  not  merely  from  that  which 
is  opposite  to  the  piston. 

The  reason  why  a  satisfactory  quantitative  experimental  demonstration 
of  the  principle  of  the  equality  of  pressure  cannot  be  given  is,  that  the 
influence  of  the  weight  of  the  liquid  and  of  the  friction  of  the  pistons  cannot 
be  eliminated. 

Yet  an  approximate  verification  may  be  effected  by  the  experiment 
represented  in  fig.  67.  Two  cylinders  of  different  diameters  are  joined  by  a 
tube  and  filled  with  water.  On  the  surface  of  the  liquid  are  two  pistons  P 
and  p,  which  hermetically  close  the  cylinders,  but  move  without  friction. 

Let  the  area  of  the  large  piston  be, 
for  instance,  thirty  times  that  of  the 
smaller  one.  That  being  assumed,  let 
a  weight,  say  of  two  pounds,  be  placed 
upon  the  small  piston  ;  this  pressure 
will  be  transmitted  to  the  water  and 
to  the  large  piston,  and  as  this  pres- 
sure amounts  to  two  pounds  on  each 
portion  of  its  surface  eqtial  to  that  of 
the  small  piston,  the  large  piston  must 
be  exposed  to  an  upward  pressure 
thirty  times  as  much,  or  of  sixty  pounds.  If  now  this  weight  be  placed 
upon  the  large  piston,  both  will  remain  in  equilibrium  ;  but  if  the  weight  is 
greater  or  less,  this  is  no  longer  the  case.  If  S  and  s  are  the  areas  of  the 
large  and  small  piston  respectively,  and  P  and  p  the  corresponding  loads, 

then?  =  5;  whence  P  =^§' 
p     s  s 

It  is  important  to  observe  that  in  speaking  of  the  transmission  of  pres- 
sures to  the  sides  of  the  containing  vessel,  these  pressures  must  always  be 
supposed  to  be  perpendicular  to  the  sides  ;  for  any  oblique  pressure  may  be 
decomposed  into  two  others,  one  at  right  angles  to  the  side,  and  the  other 
acting  parallel  with  the  side  ;  but  as  the  latter  has  no  action  on  the  side,  the 
perpendicular  pressure  is  the  only  one  to  be  considered. 


Fig.  67. 


PRESSURE  PRODUCED   IN   LIQUIDS   BY  GRAVITY. 

99.  Vertical  downward  pressure :  its  laws.— Any  given  liquid  being 
in  a  state  of  rest  in  a  vessel,  if  we  suppose  it  to  be  divided  into  horizontal 
layers  of  the  same  density,  it  is  evident  that  each  layer  supports  the  weight 
of  those  above  it.  Gravity,  therefore,  produces  internal  pressures  in  the 
mass  of  a  liquid  which  vary  at  different  points.  These  pressures  are 
submitted  to  the  following  general  laws  : — 

I.  The  pressure  in  each  layer  is  proportional  to  the  depth. 

I 1 .  With  different  liquids  and  the  same  depth,  the  pressure  is  proportional 
to  the  density  of  the  liquid. 

III.  The  pressure  is  the  same  at  all  points  of  the  same  horizontal  layer. 


-101]     Pressure  is  Independent  of  the  Shape  of  the  Vessel.         89 

The  first  two  laws  are  self-evident  ;  the  third  necessarily  follows  from 

the  first  and  from  Pascal's  principle. 

Meyer  has  found,  by  direct  experiments,  that  pressures  are  transmitted 

through  liquids  contained  in  tubes,  with  the  same  velocity  as  that  with  whicl 

sound  travels  in  the  same  circumstances. 

loo.  Vertical  upward  pressure.-The  pressure  which  the  upper  layers 

of  a  liquid  exert  on  the  lower  layers  causes  them  to  exert  an  equal  reaction 

man  upward  direction,  a  necessary  consequence  of  the  principle  of  trans- 
mission of  pressure  in  all  directions.     This  upward  pressure  is  termed  the 

buoyancy  of  liquids  ;  it  is  very  sensible  when  the  hand  is  plunged  into  a 

liquid,  more  especially  one  of  great  density,  like  mercury. 

The  following  experiment  (fig.  68)  serves  to  exhibit  the  upward  pressure 

of  liquids.     A  large  open  glass  tube  A,  one  end  of  which  is  ground,  is  fitted 

with  a  ground-glass  disc  O,  or  still  better  with  a 

thin  card  or  piece  of  mica,  the  weight  of  which  may 

be  neglected.     To  the  disc  is  fitted  a  string  C,  by 

which  it  can  be  held  against  the  bottom  of  the  tube. 

The  whole  is  then  immersed  in  water,  and  now  the 

disc  does  not  fall,  although  no  longer  held  by  the 

string  ;  it  is  consequently  kept  in  its  position  by  the 

upward  pressure  of  the  water.     If  water  be  now 

slowly  poured  into  the  tube,  the  disc  will  only  sink 

when  the  height  of  the  water  inside  the  tube  is 

equal  to  the  height  outside.     It  follows  thence  that     A 

the  upward  pressure  on  the  disc  is  equal  to  the    ' 

pressure  of  a  column  of  water,  the  base  of  which  is 

the  internal  section  of  the  tube  A,  and  the  height 

the  distance  from  the  disc  to  the  upper  surface  of  the  liquid.     Hence  the 

upward  pressure  of  liquids  at  any  point  is  governed  by  the  same  laws  as  the 

downward  pressure.  +  . 

101.  Pressure  is  independent  of  the  shape  of  the  vessel.— The 
pressure  exerted  by  a  liquid,  in  virtue  of  its  weight,  on  any  portion  of  the 
liquid,  or  on  the  sides  of  the  vessel  in  which  it  is  contained,  depends  on  the 
depth  and  density  of  the  liquid,  but  is  independent  of  the  shape  of  the  vessel 
and  of  the  quantity  of  the  liquid. 

This  principle,  which  follows  from  the  law  of  the  equality  of  pressure, 
may  be  experimentally  demonstrated  by  many  forms  of  apparatus.  The 
following  is  the  one  most  frequently  used,  and  is  due  to  Haldat.  It  consists 
of  a  bent  tube,  ABC  (fig.  69),  at  one  end  of  which,  A,  is  fitted  a  stop-cock,  in 
which  can  be  screwed  two  vessels,  M  and  P,  of  the  same  height,  but  different 
in  shape  and  capacity,  the  first  being  conical,  and  the  other  nearly  cylindri- 
cal. Mercury  is  poured  into  the  tube  ABC,  until  its  level  nearly  reaches  A. 
The  vessel  M  is  then  screwed  on  and  filled  with  water.  The  pressure  of 
the  water  acting  on  the  mercury  causes  it  to  rise  in  the  tube  C,  and  its 
height  may  be  marked  by  means  of  a  little  collar,  «,  which  slides  up  and 
down  the  tube.  The  level  of  the  water  in  M  is  also  marked  by  means  of  the 
movable  rod  o.  When  this  is  done,  M  is  emptied  by  means  of  the  stop-cock, 
unscrewed,  and  replaced  by  P.  When  water  is  now  poured  in  this,  the 
mercury,  which  had  resumed  its  original  level  in  the  tube  ABC,  again  rises 


Fig.  68. 


On  Liquids. 


[101- 


in  C  ;  and  when  the  water  in  P  has  the  same  height  as  it  had  in  M,  which 
is  indicated  by  the  rod  0,  the  mercury  will  have  risen  to  the  height  it  had 


Fig.  69. 

before,  which  is  marked  by  the  collar  a.  Hence  the  pressure  on  the  mercury 
in  both  cases  is  the  same.  This  pressure  is  therefore  independent  of  the 
shape  of  the  vessels,  and,  consequently,  also  of  the  quantity  of  liquid.  The 
base  of  the  vessel  is  obviously  the  same  in  both  cases  ;  it  is  the  surface  of 
the  mercury  in  the  interior  of  the  tube  A. 

Another  mode  of  demonstrating  this  principle  is  by  means  of  an  apparatus 
devised  by  Masson.  In  this  (fig.  70)  the  pressure  of  the  water  contained  in 
the  vessel  M  is  not  exerted  upon  the  column  of  mercury,  as  in  that  of  Haldat, 
but  on  a  small  disc  or  stop  a,  which  closes  a  tubulure  c,  on  which  is  screwed 
the  vessel  M.  The  disc  is  not  fixed  to  the  tubulure,  but  is  sustained  by  a 
thread  attached  to  the  end  of  a  scale-beam.  At  the  other  end  is  a  pan,  in 
which  weights  can  be  placed  until  they  counterbalance  the  pressure  exerted 
by  the  water  on  the  stop.  The  vessel  M  being  emptied  is  unscrewed, 
and  replaced  by  the  narrow  tube  P.  This  being  filled  to  the  same  height 
as  the  large  vessel,  which  is  observed  by  means  of  the  mark  0,  it  will  be 
observed  that  to  keep  the  disc  in  its  place  just  the  same  weight  must 
be  placed  in  the  pan  as  before,  which  leads,  therefore,  to  the  same  con- 
clusion as  does  Haldat's  experiment.  The  same  result  is  obtained  if,  instead 
of  the  vertical  tube  P,  the  oblique  tube  Q  be  screwed  to  the  tubulure.  . 

From  a  consideration  of  these  principles  it  will  be  readily  seen  that  a 
very  small  quantity  of  water  can  produce  considerable  pressures.  Let  us 
imagine  any  vessel — a  cask,  for  example — filled  with  water,  and  with  a  long 
narrow  tube  tightly  fitted  into  the  side.  If  water  is  poured  into  the  tube, 
there  will  be  a  pressure  on  the  bottom  of  the  cask  equal  to  the  weight  of  a 
column  ot  water  whose  base  is  the  bottom  itself,  and  whose  height  is  equal 


~102]  Pressure  on  the  Sides  of  Vessels.  9I 

to  that  of  the  water  in  the  tube.     The  pressure  may  be  made  as  great  as 
please  ;  by  means  of  a  narrow  thread  of  water  forty  feet  high,  Pascal  sue 
ceeded  in  bursting  a  very  solidly  constructed  cask 

The  toy  known  as  the  hydrostatic  bellows  depends  on  the  same  principle 
and  we  shall  see  a  most  important  application  of  it  in  the  hydraulic  press 

From  the  principle  just  laid  down,  the  pressures  produced  at  the  bottom 
of  the  sea  may  be  calculated.     It  will  be  presently  demonstrated  that  t 
pressure  of  the  atmosphere  is  equal  to  that  of  a  column  of  sea  water  about 


Fig.  70. 

thirty-three  feet  high.  At  sea  the  lead  has  frequently  descended  to  a  depth 
of  thirteen  thousand  feet  ;  at  the  bottom  of  some  seas,  therefore,  there  must 
be  a  pressure  of  four  hundred  atmospheres. 

102.  Pressure  on  the  sides  of  vessels. — Since  the  pressure  caused  by 
gravity  in  the  mass  of  a  liquid  is  transmitted  in  every  direction,  according  to 
the  general  law  of  the  transmission  of  fluid  pressure,  it  follows  that  at  every 
point  of  the  side  of  any  vessel  a  pressure  is  exerted,  at  right  angles  to  the 
side,  which  we  will  suppose  to  be  plane.  The  resultant  of  all  these  pressures 
is  the  total  pressure  on  the  sides.  But  since  these  pressures  increase  in 
proportion  to  the  depth,  and  also  in  proportion  to  the  horizontal  extent  of 
their  side,  their  resultant  can  only  be  obtained  by  calculation,  which  shows 
that  the  total  pressure  on  any  given  portion  of  the  side  is  equal  to  the 
weight  of  a  cohtirrn  of  liquid  which  has  this  portion  of  the  side  for  its  base, 
and  whose  height  is  the  vertical  distance  from  the  centre  of  gravity  of  the 
portion  to  the  szirface  of  the  liquid.  If  the  side  of  a  vessel  is  a  curved  surface 
the  same  rule  gives  the  pressure  on  the  surface,  but  the  total  pressure  is 
no  longer  the  resultant  of  the  fluid  pressures. 

The  point  in  the  side  supposed  plane,  at  which  the  resultant  of  all  the 
pressure  is  applied,  is  called  the  centre  of  pressure,  and  is  always  below  the 
centre  of  gravity  of  the  side.  For  if  the  pressures  exerted  at  different  parts 


92 


On  Liquids. 


[102 


of  the  plane  side  were  equal,  the  point  of  application  of  their  resultant,  the 
centre  of  pressure,  would  obviously  coincide  with  the  centre  of  gravity  of  the 
side.  But  since  the  pressure  increases  with  the  depth,  the  centre  of  pressure 
is  necessarily  below  the  centre  of  gravity.  This  point  is  determined  by  cal- 
culation, which  leads  to  the  following  results  : — 

i.  With  a  rectangular  side  whose  upper  edge  is  level  with  the  water,  the 
centre  of  pressure  is  at  two-thirds  of  the  line  which  joins  the  middle  of  the 
horizontal  sides  measured  from  the  top. 

ii.  With  a  triangular  side  whose  base  is  horizontal,  and  coincident  with 
the  level  of  the  water,  the  centre  of  pressure  is  at  the  middle  of  the  line  which 
joins  the  vertex  of  the  triangle  with  the  middle  of  the  base. 

iii.  With  a  triangular  side  whose  vertex  is  level  with  the  water,  the  centre 
of  pressure  is  in  the  line  joining  the  vertex  and  the  middle  of  the  base,  and 
at  three-fourths  of  the  distance  of  the  latter  from  the  vertex. 

103.  Hydrostatic  paradox. — We  have  already  seen  that  the  pressure  on 
the  bottom  of  a  vessel  depends  neither  on  the  form  of  the  vessel  nor  on  the 
quantity  of  the  liquid,  but  simply  on  the  height  of  the  liquid  above  the 
bottom.  But  the  pressure  thus  exerted  must  not  be  confounded  with  the 
pressure  which  the  vessel  itself  exerts  on  the  body  which  supports  it.  The 
latter  is  always  equal  to  the  combined  weight  of  the  liquid  and  the  vessel  in 
which  it  is  contained,  while  the  former  may  be  either  smaller  or  greater  than 
this  weight,  according  to  the  form  of  the  vessel. 
This  fact  is  often  termed  the  hydrostatic  paradox, 
because  at  first  sight  it  appears  paradoxical. 

CD  (fig.  71)  is  a  vessel  composed  of  two  cylin- 
drical parts  of  unequal  diameters,  and  filled  with 
water  to  a.  From  what  has  been  said  before,  the 
bottom  of  the  vessel  CD  supports  the  same  pressure 
as  if  its  diameter  were  everywhere  the  same  as  that 
of  its  lower  part  ;  and  it  would  at  first  sight  seem 
that  the  scale  MN  of  the  balance,  in  which  the 
vessel  CD  is  placed,  ought  to  show  the  same 
weight  as  if  there  had  been  placed  in  it  a  cylin- 
drical vessel  having  the  same  height  of  water,  and 
having  the  diameter  of  the  part  D.  But  the 
pressure  exerted  on  the  bottom  of  the  vessel  is  not 
all  transmitted  to  the  scale  MN  ;  for  the  upward  pressure  upon  the  surface  no 
of  the  vessel  is  precisely  equal  to  the  weight  of  the  extra  quantity  of  water 
which  a  cylindrical  vessel  would  contain,  and  balances  an  equal  portion  of 
the  downward  pressure  on  m.  Consequently  the  pressure  on  the  plate  MN  is 
simply  equal  to  the  weight  of  the  vessel  CD  and  of  the  water  which  it  contains. 


Fig.  71. 


CONDITIONS    OF  THE   EQUILIBRIUM    OF   LIQUIDS. 

104.  Equilibrium  of  a  liquid  in  a  single  vessel. — In  order  that  a  liquid 
may  remain  at  rest  in  a  vessel  of  any  given  form,  it  must  satisfy  the  two 
following  conditions  : — 

I.  Its  surface  must  be  everywhere  perpendicular  to  the  resultant  of  the 
forces  which  act  on  the  molecules  of  the  liquid. 


-105]          Equilibrium  of  a  Liquid  in  a  Single  Vessel  93 

1 1 .  Every  molecule  of  the  mass  of  the  liquid  must  be  subject  in  every  direc- 
tion to  equal  and  contrary  pressures. 

The  second  condition  is  self-evident ;  for  if,  in  two  opposite  directions, 
the  pressures  exerted  on  any  given  molecule  were  not  equal  and  contrary' 
the  molecule  would  be  moved  in  the  direction  of  the  greater  pressure,  and 
there  would  be  no  equilibrium.  Thus  the  second  condition  follows  from  the 
principle  of  the  equality  of  pressures,  and  from  the  reaction  which  all  pres- 
sure causes  on  the  mass  of  liquids. 

To  prove  the  first  condition,  let  us  suppose  that  mp  is  the  resultant  of  all 
the  forces  acting  upon  any  molecule  m  on  the 
surface  (fig.  72),  and  that  this  surface  is  inclined 
in  reference  to  the  force  mp.  The  latter  can 
consequently  be  decomposed  into  two  forces, 
mq  and  mf\  the  one  perpendicular  to  the  sur- 
face of  the  liquid,  and  the  other  to  the  direction 
mp.  Now  the  first  force,  mq,  would  be  destroyed 
by  the  resistance  of  the  liquid,  while  the  second 
would  move  the  molecule  in  the  direction  mf,  which  shows  that  the  equili- 
brium is  impossible. 

If  gravity  be  the  force  acting  on  the  liquid,  the  direction  mp  is  vertical ; 
hence,  if  the  liquid  is  contained  in  a  basin  or  vessel  of  small  extent,  the  sur- 
face ought  to  be  plane  and  horizontal  (67),  because  then  the  direction  of 
gravity  is  the  same  in  every  point.  But  the  case  is  different  with  liquid  sur- 
faces of  greater  extent,  like  the  ocean.  The  surface  will  be  perpendicular 
to  the  direction  of  gravity :  but  as 
this  changes  from  one  point  to  another, 
and  always  tends  towards  a  point  near 
the  centre  of  the  earth,  it  follows  that 
the  direction  of  the  surface  of  the  ocean 
will  change  also,  and  assume  a  nearly 
spherical  form. 

105.  Equilibrium  of  the  same 
liquid  in  several  communicating- 
vessels. — When  several  vessels  of 
any  given  form  communicate  with 
each  other,  there  will  be  equili- 
brium when  the  liquid  in  each  vessel 
satisfies  the  two  preceding  conditions 
(104),  and  further,  when  the  surfaces  of 
the  liquids  in  all  the  vessels  are  in  the 
same  horizontal  plane. 

In  the  vessels  ABCD  (fig.  73),  which  communicate  with  each  other,  let 
us  consider  any  transverse  section  of  the  tube  mn  ',  the  liquid  can  only 
remain  in  equilibrium  as  long  as  the  pressures  which  this   section  supports 
from  m  in  the  direction  of  «,  and  from  n  in  the  direction  of  m,  are  equal  and 
opposite.     Now  it  has  been  already  proved  that  these  pressures  are  i 
lively  equal  to  the  weight  of  a  column  of  water,  whose  base  is  the  supposed 
section,  and  whose  height  is  the  distance  from  the  centre  of  gravity  of ^  th 
section  to  the  surface  of  the  liquid.     If  we  conceive,  then,  a  horizontal  plane, 


Fig.  73- 


94 


On  Liquids. 


[105- 


»/»,  drawn  through  the  centre  of  gravity  of  this  section,  it  will  be  seen  that 
there  will  only  be  equilibrium  as  long  as  the  height  of  the  liquid  above  this 
plane  is  the  same  in  each  vessel,  which  demonstrates  the  principle  enunciated. 
106.  Equilibrium  of  superposed  liquids. — In  order  that  there  should 
be  equilibrium  when  several  heterogeneous  liquids  are  superposed  in  the 
same  vessel,  each  of  them  must  satisfy  the  conditions  necessary  for  a  single 
liquid  (104)  ;  and  further,  there  will  be  stable  equilibrium  only  when  the 
liquids  are  arranged  in  the  order  of  their  decreasing  densities  from  the 
bottom  upwards. 

The  last  condition  is  experimentally  demonstrated  by  means  of  the  phial 
of  four  elements.  This  consists  of  a  long  narrow  bottle  containing  mercury, 
water  saturated  with  carbonate  of  potass,  alcohol  coloured  red,  and  petroleum. 
When  the  phial  is  shaken  the  liquids  mix,  but  when  it  is  allowed  to  rest  they 
separate  ;  the  mercury  sinks  to  the  bottom,  then  comes  the  water,  then  the 
alcohol,  and  then  the  petroleum.  This  is  the  order  of  the  decreasing  densi- 
ties of  the  bodies.  The  water  is  saturated  with  carbonate  of  potass  to  prevent 
its  mixing  with  the  alcohol. 

This  separation  of  the  liquids  is  due  to  the  same  cause  as  that  which 
enables  solid  bodies  to  float  on  the  surface  of  a  liquid  of  greater  density  than 
their  own.  It  is  also  on  this  account  that  fresh  water,  at  the  mouths  of 
rivers,  floats  for  a  long  time  on  the  denser  salt  water  of  the  sea  ;  and  it  is 
for  the  same  reason  that  cream,  which  is  lighter  than  milk,  rises  to  the  surface. 

107.  Equilibrium  of  two  different 
liquids  in  communicating-  vessels. — 
When  two  liquids  of  different  densities, 
which  do  not  mix,  are  contained  in  two 
communicating  vessels,  they  will  be  in 
equilibrium  when,  in  addition  to  the  pre- 
ceding principles,  they  are  subject  to  the 
following  :  that  the  heights  above  the  hori- 
zontal surface  of  contact  of  two  columns  of 
liquid  in  equilibrium  are  in  the  inverse  ratio 
of  their  densities. 

.  To  show  this  experimentally,  mercury  is 
poured  into  a  bent  glass  tube,  mn,  fixed 
against  an  upright  wooden  support  (fig.  74), 
and  then  water  is  poured  into  one  of  the 
legs,  AB.  The  column  of  water,  AB,  press- 
ing on  the  mercury  at  B,  lowers  its  level  in 
the  leg  AB,  and  raises  it  in  the  other  by  a 
when  equilibrium  is  established,  we  imagine 
a  horizontal  plane,  BC,  to  pass  through  B,  the  column  of  water  in  AB  will 
balance  the  column  of  mercury  CD.  If  the  heights  of  these  two  columns  are 
then  measured  by  means  of  the  scales,  it  will  be  found  that  the  height  of  the 
column  of  water  is  about  13^  times  that  of  the  height  of  the  column  of  mercury. 
We  shall  presently  see  that  the  density  of  mercury  is  about  13^  times  that  of 
water,  from  which  it  follows  that  the  heights  are  inversely  as  the  densities. 

It  maybe  added  that  the  equilibrium  cannot  exist  unless  there  is  a  sufficient 
quantity  of  the  heavier  liquid  for  part  of  it  to  remain  in  both  legs  of  the  tube. 


Fig.  74- 


quantity   CD  ;   so  that   if, 


-108] 


Hydraulic  Press. 


95 


The  preceding  principle  may  be  deduced  by  a  very  simple  calculation. 
Let  d  and  d'  be  the  densities  of  water  and  mercury,  and  h  and  h'  their  re- 
spective heights,  and  let  g  be  the  force  of  gravity.  The  pressure  on  B  will 
be  proportional  to  the  density  of  the  liquid,  to  its  height,  and  to  the  force  of 
gravity  ;  on  the  whole,  therefore,  to  the  product  dhg.  Similarly  the  pres- 
sure at  C  will  be  proportional  to  d'h'g.  But  in  order  to  produce  equilibrium, 
dhg  must  be  equal  to  tfh'g,  or  dh  =  d'h'.  This  is  nothing  more  than  an 
algebraical  expression  of  the  above  principle  ;  for  since  the  two  products 
must  always  be  equal,  d'  must  be  as  many  times  greater  than  d  as  h'  is  less 
than  h. 

In  this  manner  the  density  of  a  liquid  may  be  determined.  Suppose  one 
of  the  branches  contained  water  and  the  other  oil,  and  their  heights  were, 
respectively,  15  inches  for  the  oil  and  14  inches  for  the  water.  The  density 
of  water  being  taken  as  unity,  and  that  of  oil  being  called  x,  we  shall  have 


1 5  x  .r  =  14  x  i  ;  whence  #•«_!- 0-933. 


' 


APPLICATIONS   OF  THE   PRECEDING  HYDROSTATIC  PRINCIPLES. 

1 08.  Hydraulic  press, — The  law  of  the  equality  of  pressure  has  received 
a  most  important  application  in  the  hydraulic  press,  a  machine  by  which 


. 


Fig.  75. 


enormous  pressures  may  be  produced.     Its  principle  is  due  to  Pascal,  but  it 
was  first  constructed  by  Bramah  in  179"- 


On  Liquids. 


[108- 


It  consists  of  a  cylinder,  B,  with  very  strong  thick  sides  (fig.  75),  in 
which  there  is  a  cast-iron  ram,  P,  working  water-tight  in  the  collar  of  the 
cylinder.  On  the  ram  P  there  is  a  cast-iron  plate  on  which  the  substance 
to  be  pressed  is  placed.  Four  .strong  columns  serve  to  support  and  fix  a 
second  plate  Q. 

By  means  of  a  leaden  pipe  K,  the  cylinder  B,  which  is  filled  with  water, 
communicates  with  a  small  force-pump  A,  which  works  by  means  of  a  lever 
M.  When  the  piston  of  this  pump^  ascends,  a  vacuum  is  produced,  and  the 
water  rises  in  the  tube  a,  at  the  end  of  which  there  is  a  rose,  to  prevent  the 
entrance  of  foreign  matters.  When  the  piston  p  descends,  it  drives  the  water 
into  the  cylinder  by  the  tube  K. 

Fig.  76  represents  a  section,  on  a  larger  scale,  of  the  system  of  valves 
necessary  in  working  the  apparatus.  The  valve  o,  below  the  piston  p,  opens 

when  the  piston  rises, 
and  closes  when  it 
descends.  The  valve 
o,  during  this  descent, 
is  opened  by  the 
pressure  of  the  water 
which  passes  by  the 
pipe  K.  The  valve  i 
is  a  safety '-valve,  held 
by  a  weight  which 
acts  on  it  by  means  of 
a  lever.  By  weight- 
ing the  latter  to  a 
greater  or  less  extent 
the  pressure  can  be 
regulated,  for  as  soon  as  there  is  an  upward  pressure  greater  than  that  of  the 
weight  upon  it,  it  opens  and  water  escapes.  A  screw  r  serves  to  relieve  the 
pressure,  for  when  it  is  opened  it  affords  a  passage  for  the  efflux  of  the  water 
in  the  cylinder  B. 

A  most  important  part  is  the  leather  collar,  «,  the  invention  of  which  by 
Bramah  removed  the  difficulties  which  had  been  experienced  in  making  the 
large  ram  work  water-tight  when  submitted  to 
great  pressures.  It  consists  of  a  circular  piece  of 
stout  leather  (fig.  77),  saturated  with  oil  so  as  to 
be  impervious  to  water,  in  the  centre  of  which  a 
circular  hole  is  cut.  This  piece  is  bent  so  that 
a  section  of  it  represents  a  reversed  U3  and  is 
fitted  into  a  grove  n  made  in  the  neck  of  the 
cylinder.  This  collar  being  concave  downwards 

in  proportion  as  the  pressure  increases,  it  fits  the  more  tightly  against  the 
ram  P  on  one  side  and  the  neck  of  the  cylinder  on  the  other,  and  quite  pre- 
vents any  escape  of  water. 

The  pressure  which  can  be  obtained  by  this  press  depends  on  the  relation 
of  the  piston  P  to  that  of  the  piston  p.  If  the  former  has  a  transverse  section 
fifty  or  a  hundred  times  as  large  as  the  latter,  the  upward  pressure  on  the 
large  piston  will  be  fifty  or  a  hundred  times  that  exerted  upon  the  small  one. 


Fig.  76. 


109] 


The  Water-level. 


97 


By  means  of  the  lever  M  an  additional  advantage  is  obtained.  If  the 
distance  from  the  fulcrum  to  the  point  where  the  power  is  applied  is  five  times 
the  distance  from  the  fulcrum  to  the  piston  /,  the  pressure  on  p  will  be  five 
times  the  power.  Thus,  if  a  man  acts  on  M  with  a  force  of  sixty  pounds,  the 
force  transmitted  by  the  piston/  will  be  300  pounds,  and  the  force  which  tends 
to  raise  the  piston  P  will  be  30,000  pounds,  supposing  the  section  of  P  is  a 
hundred  times  that  of/. 

The  hydraulic  press  is  used  in  all  cases  in  which  great  pressures  are  re- 
quired. It  is  used  in  pressing  cloth  and  paper,  in  extracting  the  juice  of  beet- 
root, in  compressing  hay  and  cotton,  in  expressing  oil  from  seeds,  and  in 
bending  iron  plates  ;  it  also  serves  to  test  the  strength  of  cannon,  of  steam 
boilers,  and  of  chain  cables.  The  parts  composing  the  tubular  bridge  which 
spans  the  Menai  Straits  were  raised  by  means  of  an  hydraulic  press.  The 
cylinder  of  this  machine,  the  largest  which  has  ever  been  constructed,  was 
nine  feet  long,  and  twenty-two  inches  in  internal  diameter  ;  it  was  capable 
of  raising  a  weight  of  two  thousand  tons. 

The  principle  of  the  hydraulic  press  is  advantageously  employed  in  cases 
in  which  great  power  is  only  required  at  intervals,  such  as  in  opening  dock 
gates,  in  lifts  in  hotels,  warehouses,  and  the  like.  In  these  cases  an  accu- 
mulator is  used.  The  piston  P  is  loaded  with  very  great  weights,  and  water 
is  forced  into  the  cylinder  B  by  powerful  pumps.  From  the  bottom  of  this 
cylinder  a  tube  conducts  water  to  any  place  where  the  power  is  to  be  applied, 
and  the  flow  of  even  small  quantities  of  water  can  perform  a  great  amount 
of  work. 

Suppose,  for  instance,  that  the  area  of  the  piston  P  is  four  square  feet,  and 
that  it  has  a  load  of  100  tons ;  this  represents  a  pressure  of  over  370  pounds 
on  the  square  inch,  or  more  han  25  atmospheres.  When  the  large  piston 
sinks  through  the  —th  of  an  inch  about  a  pint  of  water  will  flow  out,  and  this 
represents  a  work  of  about  1,100  foot-pounds. 

109.  The  Water-level. — The  water-level  is  an  application  of  the  con- 
ditions of  equilibrium  in  communicating  vessels.  It  consists  of  a  metal  tube 


Fig.  78- 

bent  at  both  ends,  in  which  are  fitted  glass  tubes  D  and  E  (fig.  78)-     lt ' 
placed  on  a  tripod,  and  water  poured  in  until  it  rises  in  both  legs.     Wh( 
liquid  is  at  rest,  the  level  of  the  water  in  both  tubes  is  the  same  ;  tl 
they  are  both  in  the  same  horizontal  plane. 


On  Liquids. 


[109- 


This  instrument  is  used  in  levelling,  or  ascertaining  how  much  one  point 
is  higher  than  another.  If,  for  example,  it  is  desired  to  find  the  difference 
between  the  heights  of  B  and  A,  a  levelling-staff\*  fixed  on  the  latter  place. 
This  staff  consists  of  a  rule  formed  of  two  sliding  pieces  of  wood,  and  sup- 
porting a  piece  of  tin  plate  M,  in  the  centre  of  which  there  is  a  mark.  This 
staff  being  held  vertically  at  A,  an  observer  looks  at  it  through  the  level 
along  the  surfaces  D  and  E,  and  directs  the  holder  to  raise  or  lower  the  slide 
until  the  mark  is  in  the  prolongation  of  the  line  DE.  The  height  AM  is 
then  measured,  and  subtracting  it  from  the  height  of  the  level,  the  height  of 
the  point  A  above  B  is  obtained. 

no.  Tlie  Spirit-level.  The  spirit-level  is  both  more  delicate  and  more 
accurate  than  the  water-level.  It  consists  of  a  glass  tube  AB  (fig.  79),  very 

slightly  curved  ;  that   is, 

Fig.  79- 


the  tube,  instead  of  being 
a  true  cylinder  as  it  seems 
to  be,  is  in  fact  slightly 
curved  in  such  a  manner 
that  its  axis  is  an  arc  of 
a  circle  of  very  large 
radius.  It  is  filled  with 
spirit  with  the  exception 
of  a  bubble  of  air,  which 
tends  to  occupy  the  high- 
est part.  The  tube  is 
placed  in  a  brass  case 

CD  (fig.  80),  which  is  so  arranged  that  when  it  is  in  a  perfectly  horizontal 
position  the  bubble  of  air  is  exactly  between  the  two  points  marked  in  the 
case. 

To  take  levels  with  this  apparatus,  it  is  fixed  on  a  telescope,  which  can. 
be  placed  in  a  horizontal  position. 

ill.  Artesian  wells. — All  natural  collections  of  water  exemplify  the 
tendency  of  water  to  find  its  level.  Thus,  a  group  of  lakes,  such  as  the 
great  lakes  of  North  America,  may  be  regarded  as  a  number  of  vessels  in 
communication,  and  consequently  the  waters  tend  to  maintain  the  same 
level  in  all.  This,  too,  is  the  case  with  the  source  of  a  river  and  the  sea, 
and,  as  the  latter  is  on  the  lower  level,  the  river  continually  flows  down  to- 
the  sea  along  its  bed,  which  is,  in  fact,  the  means  of  communication  between 
the  two. 

Perhaps  the  most  striking  instance  of  this  class  of  natural  phenomena  is 
that  of  artesian  wells.  These  wells  derive  their  name  from  the  province 
of  Artois,  where  it  has  long  been  customary  to  dig  them,  and  whence  their 
use  in  other  parts  of  France  and  Europe  was  derived.  It  seems,  however, 
that  at  a  very  remote  period  wells  of  the  same  kind  were  dug  in  China  and 
Egypt. 

To  understand  the  theory  of  these  wells  it  must  be  premised  that  the 
strata  composing  the  earth's  crust  are  of  two  kinds  :  the  one  permeable  to 
water,  such  as  sand,  gravel,  &c.  ;  the  other  impermeable,  such  as  clay.  Let 
us  suppose,  then,  a  geographical  basin  of  greater  or  less  extent,  in  which  the 
two  impermeable  layers  AB,  CD  (fig.  81),  enclose  between  them  a  permeable: 


-112]  Pressure  Supported  by  a  Body  Immersed  in  a  Liquid.  99 
layer  KK.  The  rain-water  falling  on  that  part  of  this  layer  which  comes  to  the 
surface,  and  which  is  called  the  outcrop,  will  filter  through  it,  and  following 
the  natural  fall  of  the  ground  will  collect  in  the  hollow  of  the  basin,  whence 
it  cannot  escape  owing  to  the  impermeable  strata  above  and  below  it.  If 
now,  a  vertical  hole,  I,  be  sunk  down  to  the  water-bearing  stratum,  the  water 
striving  to  regain  its  level  will  spout  out  to  a  height  which  depends  on  the 
difference  between  the  levels  of  the  outcrop  and  of  the  point  at  which  the 
perforation  is  made. 

The  waters  which  feed  artesian  wells  often  come  from  a  distance  of 
sixty  or  seventy  miles.     The  depth  varies  in  different  places.     The  well  at 


Fig.  81. 

Crenelle  is  1,800  feet  deep  ;  it  gives  656  gallons  of  water  in  a  minute,  and 
is  one  of  the  deepest  and  most  abundant  which  has  been  made.  The 
temperature  of  the  water  is  27°  C.  It  follows  from  the  law  of  the  in- 
crease of  temperature  with  the  increasing  depth  below  the  surface  of  the 
ground,  that,  if  this  well  were  210  feet  deeper,  the  water  would  have  all 
the  year  round  a  temperature  of  32°  C.;  that  is,  the  ordinary  temperature  of 
baths. 

BODIES   IMMERSED   IN   LIQUIDS. 

112.  Pressure  supported  by  a  body  immersed  in  a  liquid. — When  a 
solid  is  immersed  in  a  liquid,  every  portion  of  its  surface  is  submitted  to  a 
perpendicular  pressure  which  increases  with  the  depth.  If  we  imagine  all 
these  pressures  decomposed  into  horizontal  and  vertical  pressures,  the  first 
set  are  in  equilibrium.  The  vertical  pressures  are  obviously  unequal,  and 
will  tend  to  move  the  body  upwards. 

Let  us  imagine  a  cube  immersed  in  a  mass  of  water  (fig.  82),  and  that 
four  of  its  edges  are  vertical.  The  pressures  upon  the  four  vertical  faces  being 
clearly  in  equilibrium,  we  need  only  consider  the  pressures  exerted  on  the 
horizontal  faces  A  and  B.  The  first  is  pressed  downwards  by  a  column  of 
water  whose  base  is  the  face  A,  and  whose  height  is  AD  ;  the  lower  face  B 
is  pressed  upwards  by  the  weight  of  a  column  of  water  whose  base  is  the 
face  itself,  and  whose  height  is  BD  (100).  The  cube,  therefore,  is  urged 

H  2 


IOO  On  Liquids.  [112- 

upwards  by  a  force  equal  to  the  difference  between  these  two  pressures, 
which  latter  is  manifestly  equal  to  the  weight  of  a  column  of  water  having 
the  same  base  and  the  same  height  as  this  cube.  Consequently  this  upward 
pressure  is  equal  to  the  weight  of  the  volume  of  water  displaced  by  the  im- 
mersed body. 

We  shall  readily  see  from  the  following  reasoning  that  every  body 
immersed  in  a  liquid  is  pressed  upwards  by  a  force  equal  to  the  weight  of 
the  displaced  liquid.  In  a  liquid  at  rest  let  us  sup- 
pose a  portion  of  it  of  any  jgiven  shape,  regular 
or  irregular,  to  become  solidified,  without  either 
increase  or  decrease  of  volume.  The  liquid  thus 
solidified  will  remain  at  rest,  and  therefore  must 
be  acted  upon  by  a  force  equal  to  its  weight,  and 
acting  vertically  upwards  through  its  centre  of 
gravity  ;  for  otherwise  motion  would  ensue.  If  in 
the  place  of  the  solidified  water  we  imagine  a  solid 
of  another  substance  of  exactly  the  same  volume 
and  shape,  it  will  necessarily  receive  the  same 
pressures  from  the  surrounding  liquid  as  the  solidi- 
fied portion  did  ;  hence,  like  the  latter,  it  will  sustain 
the  pressure  of  a  force  acting  vertically  upwards 
Fis-  82-  through  the  centre  of  gravity  of  the  displaced  liquid, 

and  equal  to  the  weight  of  the  displaced  liquid.  If,  as  almost  invariably 
happens,  the  liquid  is  of  uniform  density,  the  centre  of  gravity  of  the  displaced 
liquid  means  the  centre  of  gravity  of  the  immersed  part  of  the  body  supposed  to 
be  of  uniform  density.  This  distinction  is  sometimes  of  importance  :  for  ex- 
ample, if  a  sphere  is  composed  of  a  hemisphere  of  iron  and  another  of  wood, 
its  centre  of  gravity  would  not  coincide  with  its  geometrical  centre  ;  but  if  it 
were  placed  under  water,  the  centre  of  gravity  of  the  displaced  water  would 
be  at  the  geometrical  centre — that  is,  would  have  the  same  position  as  the 
centre  of  gravity  of  the  sphere  if  of  uniform  density. 

113.  Principle  of  Archimedes. — The  preceding  principles  prove  that 
every  body  immersed  in  a  liquid  is  submitted  to  the  action  of  two  forces  : 
gravity  which  tends  to  lower  it,  and  the  buoyancy  of  the  liquid  which  tends 
to  raise  it  with  a  force  equal  to  the  weight  of  the  liquid  displaced.  The 
weight  of  the  body  is  either  totally  or  partially  overcome  by  this  buoyancy, 
from  which  it  is  concluded  that  a  body  immersed  in  a  liquid  loses  apart  of 
its  weight  equal  to  the  weight  of  the  displaced  liquid. 

This  principle,  which  is  the  basis  of  the  theory  of  immersed  and  floating 
bodies,  is  called  the  principle  of  Archimedes,  after  the  discoverer.  It  may 
be  shown  experimentally  by  means  of  the  hydrostatic  balance  (fig.  83).  This 
is  an  ordinary  balance,  each  pan  of  which  is  provided  with  a  hook  ;  the 
beam  can  be  raised  by  means  of  a  toothed  rack,  which  is  worked  by  a  little 
pinion  C.  A  catch,  D,  holds  the  rack  when  it  has  been  raised.  The  beam 
being  raised,  a  hollow  brass  cylinder,  A,  is  suspended  from  one  of  the  pans, 
and  below  this  a  solid  cylinder,  B,  whose  volume  is  exactly  equal  to  the 
capacity  of  the  first  cylinder  ;  lastly,  an  equipoise  is  placed  in  the  other  pan. 
If  now  the  hollow  cylinder  A  be  filled  with  water  the  equilibrium  is  disturbed  ; 
but  if  at  the  same  time  the  beam  is  lowered  so  that  the  solid  cylinder  B  be- 


-115] 


Equilibrium  of  Floating  Bodies. 


101 


comes  immersed  in  a  vessel  of  water  placed  beneath  it,'  the  equilibrium  will 
be  restored.  By  being  immersed  in  water  the  cylinder  B  loses  a  portion  of 
its  weight  equal  to  that  of  the  water  in  the  cylinder  A.  Now  as  the  capacity 
of  the  cylinder  A  is  exactly  equal  to  the  volume  of  the  cylinder  B  the  prin- 
ciple which  has  been  before  laid  down  is  proved. 


Fig-  83. 

1 14.  Determination    of    the   volume    of  a   body. — The   principle   of 
Archimedes  furnishes  a  method  for  obtaining  the  volume  of  a  body  of  any 
shape,  provided  it  is  not  soluble  in  water.     The  body  is  suspended  by  a  fine 
thread  to  the  hydrostatic  balance,  and  is  weighed  first  in  the  air,  and  then  in 
distilled  water  at  4°  C.     The  loss  of  weight  is  the  weight  of  the  displaced 
water,  from  which  the  volume  of  the  displaced  water  is  readily  calculated. 
But  this  volume  is  manifestly  that  of  the  body  itself.     Suppose,  for  example, 
155  grammes  is  the  loss  of  weight.     This  is  consequently  the  weight  of  the 
displaced  water.     Now  it  is  known  that  a  gramme  is  the  weight  of  a  cubic 
centimetre  of  water  at  4°  ;  consequently,  the  volume  of  the  body  immersed 
is  155  cubic  centimetres.. 

115.  Equilibrium  of  floating:  bodies. — A  body  whejjpJJeating  is   acted 
on   by   two   forces,   namely,   its  weight,  which  ac^wtfeally  downwards 
through  its  centre  of  gravity,  and  the  resultant  of  the  fluid  pressures,  which 


IO2 


On  Liquids. 


[115- 


(112)  acts  vertically  upwards  through  the  centre  of  gravity  of  the  fluid 
displaced  ;  but  if  the  body  is  at  rest  these  two  forces  must  be  equal  and 
act  in  opposite  directions  ;  whence  follow  the  conditions  of  equilibrium, 
namely, — 

i.  The  floating  body  must  displace  a  'volume  of  liquid  whose  'weight  equals 
that  of  the  body. 

ii.  The  centre  of  gravity  of  the  floating  body  must  be  in  the  same  vertical 
line  with  that  of  the  fluid  displaced. 

Thus  in  fig.  84,  if  C  is  the  centre  of  gravity  of  the  body,  and  G  that  of 
the  displaced  fluid,  the  line  GC  must  be  vertical,  since  when  it  is  so  the 
weight  of  the  body  and  the  fluid  pressure  will  act  in  opposite  directions 
along  the  same  line,  and  will  be  in  equilibrium  if  equal.  It  is  convenient, 
with  reference  to  the  subject  of  the  present  article,  to  speak  of  the  line  CG 
produced  as  the  axis  of  the  body. 

Next  let  it  be  inquired  whether  the  equilibrium  be  stable  or  unstable. 
Suppose  the  body  to  be  turned  through  a  small  angle  (fig:  85),  so  that  the 

axis  takes  a  position 
inclined  to  the  vertical. 
The  centre  of  gravity 
of  the  displaced  fluid 
will  no  longer  be  G, 
but  some  other  point, 
G'.  And  since  the  fluid 
pressure  acts  vertically 
upwards  through  G', 
its  direction  will  cut 
the  axis  in  some  point 
MY  which  will  gene- 
rally have  different  positions  according  as  the  inclination  of  the  axis  to  the 
vertical  is  greater  or  smaller.  If  the  angle  is  indefinitely  small,  M'  will  have 
a  definite  position  M,  which  always  admits  of  determination,  and  is  called 
the  metacentre. 

If  we  suppose  M  to  be  above  C,  an  inspection  of  fig.  86  will  show  that 
when  the  body  has  received  an  indefinitely  small  displacement,  the  weight  of 
the  body  W,  and  the  resultant  of  the  fluid  pressures  R,  tend  to  bring  the 
body  back  to  its  original  position  ;  that  is,  in  this  case,  the  equilibrium  is 
stable  (70).  If,  on  the  contrary,  M  is  below  C,  the  forces  tend  to  cause  the 
axis  to  deviate  farther  from  the  vertical,  and  the  equilibrium  is  unstable. 
Hence  the  rule — 

iii.  The  equilibrium  of  a  floating  body  is  stable  or  unstable  according  as 
the  metacentre  is  above  or  below  the  centre  of  gravity. 

The  determination  of  the  metacentre  can  rarely  be  effected  except  by 
means  of  a  somewhat  difficult  mathematical  process.  When,  however,  the 
form  of  the  immersed  part  of  a  body  is  spherical  it  can  be  readily  determined  ; 
for  since  the  fluid  pressure  at  each  point  converges  to  the  centre,  and  con- 
tinues to  do  so  when  the  body  is  slightly  displaced,  their  resultant  must  in 
all  cases  pass  through  the  centre,  which  is  therefore  the  metacentre.  To 
illustrate  this  :  let  a  spherical  body  float  on  the  surface  of  a  liquid  (fig.  87)  ; 
then,  its  centre  of  gravity  and  the  metacentre  both  coinciding  with  the 


Fig.  84. 


Fig.  85. 


Fig.  86. 


Fig.  87. 


-117]  Swimming-bladder  of  Fishes.  103 

geometrical  centre  C,  its  equilibrium  is  neutral  (70).  Now  suppose  a  small 
heavy  body  to  be  fastened  at  P,  the  summit  of  the  vertical  diameter.  The 
centre  of  gravity  will  now  be  at  some  point  G  above  C.  Consequently,  the 
equilibrium  is  unstable,  and  the  sphere,  left  to  itself,  will  instantly  turn  over 
and  will  rest  when  P  is  the  lower  end  of  a  vertical  diameter. 

On  investigating  the  position  of  the  metacentre 
of  a  cylinder,  it  is  found  that  when  the  ratio  of 
the  radius  to  the  height  is  greater  than  a  certain 
quantity,  the  position  of  stable  equilibrium  is  that 
In  which  the  axis  is  vertical ;  but  if  it  be  less  than 
that  quantity,  the  equilibrium  is  stable  when  the 
axis  is  horizontal.  For  this  reason  the  stump  of  a 
tree  floats  lengthwise,  but  a  thin  disc  of  wood  floats 
flat  on  the  water.  Hence,  also,  if  it  is  required  to 
make  a  cylinder  of  moderate  length  float  with 
its  axis  vertical,  it  is  necessary  to  load  it  at  the 
lower  end.  By  so  doing  its  centre  of  gravity  is  brought  below  the  meta- 
centre. 

The  determination  of  the  metacentre  and  of  the  centre  of  gravity  is  of 
great  importance  in  the  stowage  of  vessels,  for  on  their  relative  positions 
the  stability  depends. 

1 1 6.  Cartesian  diver.— The  different  effects  of  suspension,  immersion, 
and  floating  are  reproduced  by  means  of  a  well- 
known  hydrostatic  toy,  the  Cartesian  diver  (fig.  88). 

It  consists  of  a  glass  cylinder  nearly  full  of  water, 
on  the  top  of  which  a  brass  cap,  provided  with  a 
piston,  is  hermetically  fitted.  In  the  liquid  there  is 
a  little  porcelain  figure  attached  to  a  hollow  glass 
ball  #,  which  contains  air  and  water,  and  floats  on 
the  surface.  In  the  lower  part  of  this  ball  there  is 
a  little  hole  by  which  water  can  enter  or  escape, 
according  as  the  air  in  the  interior  is  more  or  less 
compressed.  The  quantity  of  water  in  the  globe 
is  such  that  very  little  more  is  required  to  make  it 
sink.  If  the  piston  is  slightly  lowered  the  air  is 
compressed,  and  this  pressure  is  transmitted  to  the 
water  of  the  vessel  and  the  air  in  the  bulb.  The 
consequence  is  that  a  small  quantity  of  water  pene- 
trates into  the  bulb,  which  therefore  becomes 
heavier  and  sinks.  If  the  pressure  is  relieved,  the 
air  in  the  bulb  expands,  expels  the  excess  of  water 
which  had  entered  it,  and  the  apparatus,  being 
now  lighter,  rises  to  the  surface.  The  experiment 
may  also  be  simplified  by  replacing  the  brass  cap 
and  piston  by  a  cover  of  sheet  india-rubber,  which 
is  tightly  tied  over  the  mouth  ;  when  this  is  pressed  Fig.  88. 

by  the  hand  the  same  effects  are  produced. 

117.  Swlmminff-bladder  of  fisnes.— Most  fishes  have  an  air-bladder 
below  the  spine,  which  is  called  the  swimming-bladder.     The  fish  can  com- 


IO4  On  Liquids.  [117- 

press  or  dilate  this  at  pleasure  by  means  of  a  muscular  effort,  and  produce 
the  same  effects  as  those  just  described — that  is,  it  can  either  rise  or  sink  in 
water. 

1 1 8.  Swimming. — The  human  body  is  lighter,  on  the  whole,  than  an 
equal  volume  of  water  :  it  consequently  floats  on  the  surface,  and  still  better 
in  sea-water,  which  is  heavier  than  fresh  water.  The  difficulty  in  swimming 
consists  not  so  much  in  floating,  as  in  keeping  the  head  above  water,  so  as 
to  breathe  freely.  In  man  the  head  is  heavier  than  the  lower  parts,  and 
consequently  tends  to  sink,  and  hence  swimming  is  an  art  which  requires  to 
be  learned.  With  quadrupeds,  on  the  contrary,  the  head  being  less  heavy 
than  the  posterior  parts  of  the  body,  remains  above  water  without  any  effort, 
and  these  animals  therefore  swim  naturally. 


SPECIFIC   GRAVITY — HYDROMETERS. 

119.  Determination  of  specific  gravities. — It   has  been    already  ex- 
plained (24)  that  the  specific  gravity  of  a  body,  whether  solid  or  liquid,  is  the 
number  which  expresses  the  relation  of  the  weight  of  a  given  volume  of  this 
body  to  the  weight  of  the  same  volume  of  distilled  water  at  a  temperature 
of  4°.     In  order,  therefore,  to  calculate  the  specific  gravity  of  a  body,  it  is 
sufficient  to  determine  its  weight  and  that  of  an  equal  volume  of  water,  and 
then  to  divide  the  first  weight  by  the  second  :  the  quotient  is  the  specific 
gravity  of  the  body. 

Three  methods  are  commonly  used  in  determining  the  specific  gravities 
of  solids  and  liquids.  These  are — ist,  the  method  of  the  hydrostatic  balance  ; 
2nd,  that  of  the  hydrometer  ;  and  3rd,  the  specific  gravity  flask.  All  three, 
however,  depend  on  the  same  principle — that  of  first  ascertaining  the  weight 
of  a  body,  and  then  that  of  an  equal  volume  of  water.  We  shall  first  apply 
these  methods  to  determining  the  specific  "gravity  of  solids,  and  then  to  the 
specific  gravity  of  liquids. 

120.  Specific  gravity  of  solids. — i.  Hydrostatic  balance. — To  obtain  the 
specific  gravity  of  a  solid  by  the  hydrostatic  balance  (fig.   83),  it  is  first 
weighed  in  the  air,  and  is  then  suspended  to  the  hook  of  the  balance  and 
weighed  in  water  (fig.  89).     The  loss  of  weight  which  it  experiences  is, 
according  to  Archimedes'  principle,  the  weight  of  a  volume  of  water  equal 
to  its  own  volume  ;  consequently,  dividing  the  weight  in  air  by  the  loss  of 
weight  in  water,  the  quotient  is  the  specific  gravity  required.     If  P  is  the 

weight  of  the  body  in  air,  P'  its  weight  in  water,  and  D  its  specific  gravity, 

•p 
P  -  P'  being  the  weight  of  the  displaced  water,  we  have  D 


P-P' 

It  may  be  observed  that  though  the  weighing  is  performed  in  air,  yet, 
strictly  speaking,  the  quantity  required  is  the  weight  of  the  body  in  vacua  ; 
and  when  great  accuracy  is  required,  it  is  necessary  to  apply  to  the  observed 
weights  a  correction  for  the  weights  of  the  unequal  volumes  of  air  displaced 
by  the  substance,  and  the  weights  in  the  other  scale-pan.  The  water  in 
which  bodies  are  weighed  is  supposed  to  be  distilled  water  at  the  standard 
temperature. 

ii.  Nicholsons  hydrometer. — The  apparatus  consists  of  a  hollow  metal 


-121]  Specific  Gravity  Bottle.     Pyknometer.  105 

cylinder  B  (fig.  90),  to  which  is  fixed  a  cone  C,  loaded  with  lead.  The 
object  of  the  latter  is  to  bring  the  centre  of  gravity  below  the  metacentre, 
so  that  the  cylinder  may  float  with  its  axis  vertical.  At  the  top  is  a  stem 
terminated  by  a  pan,  in  which  is  placed  the  substance  whose  specific  gravity 
is  to  be  determined.  On  the  stem  a  standard  point,  o,  is  marked. 

The  apparatus  stands  partly  out  of  the  water,  and  the  first  step  is  to 
ascertain  the  weight  which 
must  be  placed  in  the  pan  in 
order  to  make  the  hydrometer 
sink  to  the  standard  point  o. 
Let  this  weight  be  125  grains, 
and  let  sulphur  be  the  sub- 
stance whose  specific  gravity 
is  to  be  determined.  The 
weights  are  then  removed 
from  the  pan,  and  replaced 
by  a  piece  of  sulphur  which 
weighs  less  than  125  grains, 
and  weights  added  till  the  hy- 
drometer is  again  depressed 
to  the  standard  o.  If,  for 
instance,  it  has  been  neces- 
sary to  add  55  grains,  the 
weight  of  the  sulphur  is  evi- 
dently the  difference  between 
125  and  55  grains  ;  that  is,  70 
grains.  Having  thus  deter- 
mined the  weight  of  the  sulphur  in  air,  it  is  now  only  necessary  to 
ascertain  the  weight  of  an  equal  volume  of  water.  To  do  this,  the  piece  of 
sulphur  is  placed  in  the  lower  pan  C  at  m,  as  represented  in  the  figure.  The 
whole  weight  is  not  changed,  nevertheless  the  hydrometer  no  longer  sinks  to 
the  standard  ;  the  sulphur,  by  immersion,  has  lost  a  part  of  its  weight  equal 
to  that  of  the  water  displaced.  Weights  are  added  to  the  upper  pan  until 
the  hydrometer  sinks  again  to  the  standard.  This  weight,  34-4  grains,  for 
example,  represents  the  weight  of  the  volume  of  water  displaced  ;  that  is,  of 
the  volume  of  water  equal  to  the  volume  of  the  sulphur.  It  is  only  necessary, 
therefore,  to  divide  70  grains,  the  weight  in  air,  by  34-4  .grains,  and  the 
quotient  2*03  is  the  specific  gravity. 

If  the  body  in  question  is  lighter  than  water  it  tends  to  rise  to  the  surface, 
and  will  not  remain  on  the  lower  pan  C.  To  obviate  this,  a  small  movable 
cage  of  fine  wire  is  adjusted  so  as  to  prevent  the  ascent  of  the  body.  The 
experiment  is  in  other  respects  the  same. 

121.  Specific  gravity  bottle.  Pyknometer. — When  the  specific  gravity 
of  a  substance  in  a  state  of  powder  is  required,  it  can  be  found  most  conve- 
niently by  means  of  tti&  pyknometer,  or  specific  gravity  bottle.  This  instru- 
ment is  a  bottle,  in  the  neck  of  which  is  fitted  a  thermometer  A,  an  enlarge- 
ment on  the  stem  being  carefully  ground  for  this  purpose  (fig.  91).  In  the 
side  is  a  narrow  capillary  stem  widened  at  the  top  and  provided  with  a 
stopper,  as  shown  in  the  figure.  On  this  tube  is  a  mark  m,  and  the  thermo- 


Fig.  89. 


io6 


On  Liquids. 


[121- 


meter  stopper  having  been  inserted,  the  bottle  is  filled  with  water  exactly  to 
this  mark  at  each  weighing.  The  bottle  may  conveniently  have  dimensions 
such  that  when  the  thermometer  stopper  is  inserted  and  the  liquid  filled  to 
the  mark  m,  it  represents  a  definite  volume.  This  is  done  by  filling  the 
bottle  when  wholly  under  water,  and  putting  in  the  stopper  while  it  is  im- 
mersed. The  bottle  and  the  tube  are  then  completely  filled,  and  the  quantity 
of  water  in  excess  is  removed  by  blotting-paper.  To  find  the  specific  gravity 
proceed  as  follows  :  Having  weighed  the  powder,  place  it  in  one  of  the 

scale-pans,  and  with  it  the  bottle  filled  exactly 
to  m,  and  carefully  dried.  Then  balance  it  by 
placing  small  shot,  or  sand,  in  the  other  pan. 
Next,  remove  the  bottle  and  pour  the  powder 
into  it,  and,  as  before,  fill  it  up  with  water  to 
the  mark  a.  On  replacing  the  bottle  in  the 
scale-pan  it  will  no  longer  balance  the  shot, 
since  the  powder  has  displaced  a  volume  of 
water  equal  to  its  own  volume.  Place  weights 
in  the  scale-pan  along  with  the  bottle  until 
they  balance  the  shot.  These  weights  give 
the  weight  of  the  water  displaced.  Then  the 
weight  of  the  powder,  and  the  weight  of  an 
equal  bulk  of  water  being  known,  its  specific 
gravity  is  determined  as  before.  The  thermo- 
meter gives  the  temperature  at  which  the 
determination  is  made,  and  thus  renders  it  easy 
to  make  a  correction  (124). 

It  is  important  in  this  determination  to  re- 
move the  layer  of  air  which  adheres  to  the 
powder,  and  unduly  increases  the  quantity  of 
water  expelled.  This  is  effected  by  placing  the 
bottle  under  the  receiver  of  an  air-pump  and 
exhausting.  The  same  result  is  obtained  by 
boiling  the  water  in  which  the  powder  is 
placed. 

122.  Bodies  soluble  in  water.—  If  the  body, 
whose  specific  gravity  is  to  be  determined  by 
any  of  these  methods,  is  soluble  in  water,  the 
determination  is  made  in  some  liquid  in  which 
it  is  not  soluble,  such  as  oil  of  turpentine  or  naphtha,  the  specific  gravity  of 
which  is  known.  The  specific  gravity  is  obtained  by  multiplying  the  number 
obtained  in  the  experiment  by  the  specific  gravity  of  the  liquid  used  for  the 
determination. 

Suppose,  for  example,  a  determination  of  the  specific  gravity  of  potassium 
has  been  made  in  naphtha.  For  equal  volumes,  P  represents  the  weight  of 
the  potassium,  P'  that  of  the  naphtha,  and  P"  that  of  water  ;  consequently 


Fig.  91. 


—will  be  the  specific  gravity  of  the  substance  in  reference  to  naphtha,  and 
specific  gravity  of  the  naphtha  in  reference  to  water.     The  product 


-123] 


Specific  Gravity  of  Liquids. 


10; 


of  these  two  fractions  __  is  the  specific  gravity  of  the  substance  compared 
with  water. 

In  determining  the  specific  gravity  of  porous  substances,  they  are  varnished 


Specific  gravity  of  solids  at  zero  as  compared  with  distilled  water  at  4°  C. 


Platinum,  rolled     . 

.  22-069 

Statuary  marble     . 

•     2-837 

„         cast     '-'-."• 

.  20-337 

Aluminum 

J/ 

.     2-680 

Gold,  stamped 

.   19-362 

Rock  crystal  .        , 

.    2-6;^ 

„     cast      . 

.  19-258 

St.  Gobin  glass 

J*J 

.    2-488 

Lead,  cast 
Silver,  cast     . 
Bismuth,  cast 
Copper,  drawn  wire 

•   11-352 
•   10-474 
.     9-822 
.     8-878 

China  porcelain 
Sevres  porcelain     . 
Native  sulphur 
Ivory      .         . 

.    2-380 
.    2-140 
.    2-033 
.     1-917 

„       cast  .         : 

.     8-788 

Anthracite 

.     1-800 

Bronze  coinage 
German  silver 

.     8-66 
.     8-432 

Compact  coal 
Amber    . 

.     1-329 
1-078 

Brass      .         . 

•     8-383 

Sodium           .        . 

V/   \J 

.     0-970 

Steel,  not  hammered 

Melting  ice     .        t 

•    0-930 

Iron,  bar 

•     7788 

Paraffin 

.   0-874 

„    cast 

.     7-207 

Potassium       .        £Jj| 

.   0-865 

Tin,  cast 

.     7-291 

Beech     . 

.    0-852 

Zinc,  cast 

.     6-861 

Oak        .  '     I"     . 

.    0-845 

Antimony,  cast 

.     6-712 

Elm     :*.   ki. 

.    0-800 

Iodine    . 

.     4-950 

Yellow  pine    . 

.   0-657 

Heavy  spar   .         , 

•     4-430 

Lithium         <v 

.   0-585 

Diamond        .        3'53i 

to  3-501 

Common  poplar     . 

.  0-389 

Flint  glass 

•     3329 

Cork       . 

.    0-240 

In  this  table  the  different  woods  are  supposed  to  be  in  the  ordinary  air- 
dried  condition. 

123.  Specific  gravity  of  liquids. — i.  Method  of  the  hydrostatic  balance. 
From  the  pan  of  the  hydrostatic  balance  a  body  is  suspended,  on  which 
the  liquid  whose  specific  gravity  is  to  be  determined  exerts  no  chemical 
.action  ;  for  example,  a  ball  of  platinum.  This  is  then  successively  weighed 
in  air,  in  distilled  water,  and  in  the  liquid.  The  loss  of  weight  of  the  body 
in  these  two  liquids  is  noted.  They  represent  respectively  the  weights  of 
equal  volumes  of  water  and  of  the  given  liquid,  and  consequently  it  is  only 
necessary  to  divide  the  second  of  them  by  the  first  to  obtain  the  required 
specific  gravity. 

Let  P  be  the  weight  of  the  platinum  ball  in  air,  P'  its  weight  in  water,  P" 
its  weight  in  the  given  liquid,  and  let  D  be  the  specific  gravity  sought.  The 
weight  of  the  water  displaced  by  the  platinum  is  P  — P',  and  that  of  the 

P  —  P" 
second  liquid  is  P  —  P",  from  which  we  get  D  =  p— p— . 

ii.  Fahrenheit's  hydrometer.— This  instrument  (fig.  92)  resembles  Nichol- 
son's hydrometer,  but  it  is  made  of  glass,  so  as  to  be  used  in  all  liquids.  At 


io8 


On  Liquids. 


[123- 


its  lower  extremity,  instead  of  a  pan,  it  is  loaded  with  a  small  bulb  containing 
mercury.    There  is  a  standard  mark  on  the  stem. 

The  weight  of  the  instrument  is  first  accurately  determined  in  air  ;  it 
is  then  placed  in  water,  and  weights  added  to  the  scale-pan  until  the  mark 
on  the  stem  is  level  with  the  water.  It  follows,  from  the  first  principle  of 
the  equilibrium  of  floating  bodies,  that  the  weight  of  the  hydrometer,  together 
with  the  weight  in  the  scale-pan,  is  equal  to  the  weight  of  the  volume  of  the 
displaced  water.  In  the  same  manner  the  weight  of  an  equal  volume  of 

the  given  liquid  is  determined,  and  the  specific 
gravity  is  found  by  dividing  the  latter  weight  by 
the  former. 

Neither  Fahrenheit's  nor  Nicholson's  hydro- 
meters give  such  accurate  results  as  the  hydro- 
static balance  or  the  specific  gravity  bottle. 

iii.  Specific  gravity  bottle. — This  has  been 
already  described  (121).  In  determining  the.  . 
specific  gravity  of  a  liquid,  a  bottle  of  special 
construction  is  used  ;  it  consists  of  a  cylindrical 
reservoir  b  (fig.  93),  to  which  is  fused  a  capillary 
tube  <:,  and  to  this  again  a  wider  tube  <z,  closed 
with  a  stopper.  The  bottle  is  first  weighed 
empty,  and  then  successively  full  of  water  to 
the  mark  c  on  the  capillary  stem,  and  of  the 
given  liquid.  If  the  weight  of  the  bottle  be 
subtracted  from  the  two  weights  thus  obtained, 
the  result  represents  the  weights  of  equal 
volumes  of  the  liquid  and  of  water,  from  which  the  specific  gravity  is  obtained 
by  division. 

iv.  Specific  gravity  bulbs. — The  specific  gravity  of  a  liquid  is  often  de- 
termined for  technical  and  even  scientific  purposes  by  means  of  specific 
gravity  bulbs ;  these  are  small  hollow  glass  bulbs,  which  are  prepared  in 
series,  and  adjusted  so  that  they  just  float  in  a  liquid  of  a  definite  specific 
gravity.  When  carefully  prepared  they  are  susceptible  of  considerable  accu- 
racy. 

Solutions  of  certain  metallic  salts  of  high  specific  gravity  have  been  used 
for  the  mechanical  separation  of  individual  minerals  of  certain  rocks.  Such 
minerals  will  float  or  sink  according  as  their  specific  gravities  are  lower  or 
higher  than  that  of  a  given  solution.  A  saturated  solution  of  the  double 
iodide  of  barium  and  mercury,  the  specific  gravity  of  which  is  3-58,  has  been 
used  for  this  purpose. 

124.  On  the  observation  of  temperature  in  ascertaining-  specific 
' f  gravities. — As  the  volume  of  a  body  increases  with  the  temperature,  and 
as  this  increase  varies  with  different  substances,  the  specific  gravity  of  any 
given  body  is  not  exactly  the  same  at  different  temperatures  ;  and,  con- 
sequently, a  certain  fixed  temperature  is  chosen  for  these  determinations.. 
That  of  water,  for  example,  has  been  made  at  4°  C.,  for  at  this  point  it  has 
the  greatest  density.  The  specific  gravities  of  other  bodies  are  assumed  to 
be  taken  at  zero  ;  but,  as  this  is  not  always  possible,  certain  corrections  must 
be  made,  which  we  shall  consider  in  the  Book  on  Heat. 


Fig.  92. 


Fig-  93- 


-125]  Use  of  Tables  of  Specific  Gravity. 


Specific  gravities  of  liquids  at  zero,  compared  with  that  of  water  at  4°  C. 

as  unity. 

Mercury        .         .         .13-598  Sea  water      ..        ,  ;,  1-026 

Bromine        .         .         .     2-960  Urine      .        .  .     ...  ,    .  ^020 

Ethylic  iodide       .         .     r946  Distilled  water  at  4°  C.   .  rooo 

Sulphuric  acid      .         .1-841  „        „        ato°C.   .  0-999 

Chloroform            .         .     1-525  Claret      ....  0-994 

Nitric  acid   .         .         .     1-420  Olive  oil          .        .        .  0-915 

Bisulphide  of  carbon    .     1-293  Oil  of  turpentine     .        .  0-870 

Glycerine     .         .         .     1-260  Oil  of  lemon    .        .         .  0-852 

Hydrochloric  acid        .     1-240  Petroleum       .        .         .  0-836 

Blood  ....     i -060  Absolute  alcohol      .        .  0793 

Milk     ....     1-029  Ether       ....  0713 


125.  Use  of  tables  of  specific  gravity.— Tables  of  specific  gravity 
admit  of  numerous  applications.  In  mineralogy  the  specific  gravity  of  a 
mineral  is  often  a  highly  distinctive  character.  By  means  of  tables  of 
specific  gravities  the  weight  of  a  body  may  be  calculated  when  its  volume  is 
known,  and  conversely  the  volume  when  its  weight  is  known. 

With  a  view  to  explaining  the  last-mentioned  use  of  these  tables,  it  will  be 
well  to  premise  a  statement  of  the  connection  existing  between  the  British 
units  of  length,  capacity,  and  weight.  It  will  be  sufficient  for  this  purpose 
to  define  that  which  exists  between  the  yard,  gallon,  and  pound  avoirdupois, 
since  other  measures  stand  to  these  in  well-known  relations.  The  yard, 
consisting  of  36  inches,  may  be  regarded  as  the  primary  unit.  Though  it  is 
essentially  an  arbitrary  standard,  it  is  determined  by  this,  that  the  simple 
pendulum  which  makes  one  oscillation  in  a  mean  second,  at  London  on  the 
sea-level,  is  39*13983  inches  long.  The  gallon  contains  277-274  cubic  inches. 
A  gallon  of  distilled  water  at  the  standard  temperature  weighs  ten  pounds 
avoirdupois  or  70,000  grains  troy  ;  or,  which  comes  to  the  same  thing,  one 
cubic  inch  of  water  weighs  252-5  grains. 

On  the  French  system  the  metre  is  a  primary  unit,  and  is  so  chosen 
that  10,000,000  metres  are  the  length  of  a  quadrant  of  the  meridian  from 
either  pole  to  the  equator.  The  metre  contains  10  decimetres,  or  100  centi- 
metres, or  1,000  millimetres',  its  length  equals  1-0936  yards.  The  unit 
of  the  measure  of  capacity  is  the  litre  or  cubic  decimetre.  The  unit  of 
weight  is  the  gramme,  which  is  the  weight  of  a  cubic  centimetre  of  distilled 
water  at  4°  C.  The  kilogramme  contains  1,000  grammes,  or  is  the  weight 
of  a  decimetre  of  distilled  water  at  4°  C.  The  gramme  equals  15-443 

grains. 

If  V  is  the  number  of  cubic  centimetres  (or  decimetres)  in  a  certain 
quantity  of  distilled  water  at  4°  C.,  and  P  its  weight  in  grammes  (or  kilo- 
grammes), it  is  plain  that  P  =  V.  Now  consider  a  substance  whose  specific 
o-ravity  is  U  ;  every  cubic  centimetre  of  this  substance  will  weigh  as  much 
as  D  cubic  centimetres  of  water,  and  therefore  V  centimetres  of  this  sub- 
stance will  weigh  as  much  as  DV  centimetres  of  water.  Hence  i 
the  weight  of  the  substance  in  grammes,  we  have  P  =  DV.  If,  however,  V 


no 


On  Liquids. 


[125- 


is  the  volume  in  cubic  inches,  and  P  the  weight  in  grains,  we  shall  have 
P  =  252-5  DV. 

As  an  example,  we  may  calculate  the  internal  diameter  of  a  glass  tube. 
Mercury  is  introduced,  and  the  length  and  weight  of  the  column  at  4°  C. 
are  accurately  determined.  As  the  column  is  cylindrical,  we  have  V  =  TIT-/, 
where  r  is  the  radius,  and  /  the  length  of  the  column  in  centimetres.  Hence 
if  D  is  the  specific  gravity  of  mercury,  and  P  the  weight  of  the  column  in 
grammes,  we  have  P  =  TrrYD,  and  therefore 


If  r  and  /  are  in  inches  and  P  in  grains,  we  shall  have 
and  therefore 

-V* p 


In  a  similar  manner  by  weighing  a  given  length,  the  diameter  of  very  fine 
metal  wires  can  be  determined  with  great  accuracy. 

126.  Hydrometers    of     variable    immersion. — The    hydrometers    of 
Nicholson  and  Fahrenheit  are  called  hydrometers  of  constant  immersion 
but  variable  weight,  because  they  are  always  immersed  to  the  same  extent, 
but  carry  different  weights.     There  are  also  hydrometers  of  variable  immer- 
sion but  of  constant  weight. 

127.  Beaume's  hydrometer. — This,  which  was  the  first  of  these  instru- 
ments, may  serve  as  a  type  of  them.     It  consists  of  a  glass  tube  (fig.  94) 
loaded  at  the  bottom  with  mercury,  and  with  a  bulb  blown  in   the  middle. 
The  stem,  the  external  diameter  of  which  is  as  regular  as  possible,  is  heUtTW, 
and  the  scale  is  marked  upon  it. 

The  graduation  of  the  instrument  differs  according  as  the  liquid,  for 
which  it  is  to  be  used,  is  heavier  or  lighter  than  water.  In 
the  first  case,  it  is  so  constructed  that  it  sinks  in  water 
nearly  to  the  top  of  the  stem,  to  a  point  A,  which  is  marked 
zero.  A  solution  of  fifteen  parts  of  salt  in  eighty-five  parts  of 
water  is  made,  and  the  instrument  immersed  in  it.  It  sinks 
to  a  certain  point  on  the  stem,  B,  which  is  marked  1 5  ;  the 
distance  between  A  and  B  is  divided  into  1 5  equal  parts,  and 
the  graduation  continued  to  the  bottom  of  the  stem.  Some- 
times the  graduation  is  on  a  piece  of  paper  inside  the 
stem. 

The  hydrometer  thus  graduated  only  serves  for  liquids 
of  a  greater  specific  gravity  than  water,  such  as  acids  and 
saline  solutions.  For  liquids  lighter  than  water  a  different 
plan  must  be  adopted.  Beaumd  took  for  zero  the  point  to 
which  the  apparatus  sank  in  a  solution  of  10  parts  of  salt  in 
90  of  water,  and  for  10°  he  took  the  level  in  distilled  water. 
This  distance  he  divided  into  10°,  and  continued  the  division 
to  the  top  of  the  scale. 

TlvtddelFs  hydrometer  is   in   common  use  in  England 
for  testing  liquids  denser  than  water.     It  is  graduated  in  such  a  manner 


Fig.  94. 


-129]  .Salimeters.  ril 

that  the  reading  or  number  of  degrees  multiplied  by  5  and  added  to  1,000 
gives  the  specific  gravity  with  reference  to  water  at  1,000.  Thus'io0 
Tweddell  represents  the  specific  gravity  1050,  and  90°  represents  1450. 

The  graduation  of  these  hydrometers  is  entirely  conventional,  and  they 
give  neither  the  densities  of  the  liquids  nor  the  quantities  dissolved.  But 
they  are  very  useful  in  making  mixtures  or  solutions  in  given  proportions, 
and  in  evaporating  acids,  alkaline  liquids,  solutions  of  salts,  worts,  syrups, 
and  the  like  to  a  proper  degree  of  concentration,  the  results  they  give  being 
sufficiently  near  in  the  majority  of  cases. 

y    128.  Gay-Xiussac's  alcoholometer. — This  instrument  is  used  to  deter- 
/  mine  the  strength   of  spirituous  liquors  ;   that  is,  the  proportion  of  pure 
alcohol  which  they  contain.     It   differs  from   Beaume's  hydrometer  in  the 
graduation. 

The  alcoholometer  is  so  constructed  that,  when  placed  in  pure  distilled 
water,  the  bottom  of  its  stem  is  level  with  the  water,  and  this  point  is  zero. 
It  is  next  placed  in  absolute  alcohol,  which  marks  100°,  and  then  successively 
in  mixtures  of  alcohol  and  water  containing  10,  20,  30,  &c.,  per  cent.  The 
divisions  thus  obtained  are  not  exactly  equal,  but  their  difference  is  not  great, 
and  they  are  subdivided  into  10  divisions,  each  of  which  marks  one  per  cent, 
of  absolute  alcohol  in  a  liquid.  Thus  a  brandy  in  which  the  alcoholometer 
stood  at  48°  would  contain  48  per  cent,  of  absolute  alcohol,  and  the  rest 
would  be  water. 

All  these  determinations  are  made  at  15°  C.,  and  for  that  temperature 
only  are  the  indications  correct.  For,  other  things  being  the  same,  if  the 
temperature  rises,  the  liquid  expands,  and  the  alcoholometer  will  sink,  and 
the  contrary  if  the  temperature  fall.  To  obviate  this  error,  Gay-Lussac  con- 
structed a  table  which  for  each  percentage  of  alcohol  gives  the  reading  of 
the  instrument  for  each  degree  of  temperature  from  o°  up  to  30°.  When  the 
exact  analysis  of  an  alcoholic  mixture  is  to  be  made,  the  temperature  of  the 
liquid  is  first  determined,  and  then  the  point  to  which  the  alcoholometer  sinks 
in  it.  The  number  in  the  table  corresponding  to  these  data  indicates  the 
percentage  of  alcohol.  From  its  giving  the  percentage  of  alcohol,  this  is 
often  called  the  centesimal  alcoholometer. 

129.  Salimeters. — Salimeters^  or  instruments  for  indicating  the  per- 
centage  of  a  salt  contained  in  a  solution,  are  made  on  the  principle  of  the 
centesimal  alcoholometer.  They  are  graduated  by  immersing  them  in  pure 
water  which  gives  the  zero,  and  then  in  solutions  containing  different  percent- 
ages of  the  salt,  and  marking  on  the  scale  the  corresponding  points.  These 
instruments  are  open  to  the  objection  that  every  salt  requires  a  special 
instrument.  Thus  one  graduated  for  common  salt  would  give  false  indications 
in  a  solution  of  nitre. 

Lactometers  are  similar  instruments,  and  are  based  on  the  fact  that 
the  average  density  of  a  good  natural  quality  of  milk  is  1-029.  Hence  if 
water  is  added  to  milk,  it  will  indicate  a  lower  specific  gravity.  But  a 
common  plan  of  adulteration  is  to  remove  cream  from  the  milk,  by  which 
its  specific  gravity  is  increased,  and  then  add  water  so  as  to  reproduce  the 
original  density  ;  the  lactometer  will  not  reveal  a  fraud  of  this  kind.  Urino- 
meters  are  frequently  used  in  medicine  to  test  the  variations  in  the  density 
of  urine,  which  accompany  and  characterise  certain  forms  of  disease. 


112 


On  Liquids.. 


[130- 


-  130.  Densimeter. — Rosseads  densimeter  (fig.  95)  is  of  great  use,  in  many 
scientific  investigations,  in  determining  the  specific  gravity  of  a  small 
quantity  of  a  liquid.  It  has  the  same  form  as  Beaume's 
hydrometer,  but  there  is  a  small  tube  AC  at  the  top 
of  the  stem,  in  which  is  placed  the  substance  to  be  de- 
termined. A  mark  A  on  the  side  of  the  tube  indicates 
a  measure  of  a  cubic  centimetre. 

The  instrument  is  so  constructed  that  when  AC  is 
empty  it  sinks  in  distilled  water  to  a  point,  B,  just  at 
the  bottom  of  the  stem.  It  is  then  filled  with  distilled 
water  to  the  height  measured  on  the  tube  AC,  which 
indicates  a  cubic  centimetre,  and  the  point  to  which  it 
now  sinks  is  20°.  The  interval  between  o  and  20  is 
divided  into  20  equal  parts,  and  this  graduation  is 
continued  to  the  top  of  the  scale.  As  this  is  of  uniform 
bore,  each  division  corresponds  to  ~  gramme  or  0-05. 
To  obtain  the  density  of  any  liquid,  bile  for  ex- 
ample, the  tube  is  filled  with  it  up  to  the  mark  A ;  if 
the  densimeter  sinks  to  20^  divisions,  its  weight  is 

0-05  x  20-5  =  1-025  5  that  is  to  saY)  that  w^th  equal  volumes,  the  weight  of  water 
being  i,  that  of  bile  is  1-025.     The  specific  gravity  of  bile  is  therefore  1-025. 


Fig.  95- 


-132] 


Capillary  Phenomena. 


CHAPTER   II. 

CAPILLARITY,    ENDOSMOSE,   EFFUSION,   AND   ABSORPTION. 

131.  Capillary  phenomena.— When  solid  bodies  are  placed  in  contact 
with  liquids,  phenomena  are  produced  which  are  classed  under  the  general  head 
of  capillary  phenomena,  because  they  are  best  seen  in  tubes  whose  diameters 
are  so  small  as  to  be  comparable  with  that  of  a  hair.  These  phenomena  are 
treated  of  in  physics  under  the  head  of  capillarity  or  capillary  attraction  ;  the 
latter  expression  is  also  applied  to  the  force  which  produces  the  phenomena. 

The  phenomena  of  capillarity  are  very  various,  but  may  all  be  referred 
to  the  relation  of  the  attraction  of  the  liquid  molecules  for  each  other,  to  the 
attraction  between  these  molecules  and  solid  bodies.  The  following  are 
some  of  these  phenomena  : — 

When  a  body  is  placed  in  a  liquid  which  wets  it— for  example,  a  glass 
rod  in  water — the  liquid,  as  if  not  subject  to  the  laws  of  gravitation,  is  raised 
upwards  against  the  sides  of  the  solid,  and  its  surface,  instead  of  being  hori- 
zontal, becomes  slightly  concave  (fig.  96).  If,  on  the  contrary,  the  solid  is 


Fig.  96. 


Fig,  97. 


Fig.  98. 


Fig.  99. 


one  which  is  not  moistenened  by  the  liquid,  as  glass  by  mercury,  the  liquid  is 
depressed  against  the  sides  of  the  solid,  and  assumes  a  convex  shape,  as 
represented  in  fig.  97.  The  surface  of  the  liquid  exhibits  the  same  concavity 
•or  convexity  against  the  sides  of  a  vessel  in  which  it  is  contained,  accord- 
ing as  the  sides  are  or  are  not  moistened  by  the  liquid. 

These  phenomena  are  much  more  apparent  when  a  tube  of  small 
diameter  is  placed  in  a  liquid.  And  according  as  the  tubes  are  or  are  not 
moistened  by  the  liquid,  an  ascent  or  a  depression  of  the  liquid  is  produced, 
which  is  greater  in  proportion  as  the  diameter  is  less  (figs.  98  and  99). 

When  the  tubes  are  moistened  by  the  liquid,  its  surface  assumes  the 
form  of  a  concave  hemispherical  segment,  called  the  concave  meniscus 
(fig.  98)  ;  when  the  tubes  are  not  moistened,  there  is  a  convex  meniscus 

(fig-  99)- 

132.  laws  of  the  ascent  and  depression  in  capillary  tubes. — The 

most  important  law  in  reference  to  capillarity  is  known  as  JuriiUs  law.     It 

I 


114  On  Liquids.  [132- 

is  that  the  height  of  the  ascent  of  one  and  the  same  liquid  in  a  capillary  tube 
is  inversely  as  the  diameter  of  the  tube.  Thus,  if  water  rises  to  a  height  of 
30  mm.  in  a  tube  I  mm.  in  diameter,  it  will  only  rise  to  a  height  of  1 5  mm. 
in  a  tube  2  mm.  in  diameter,  but  to  a  height  of  300  mm.  in  a  tube  cri  mm. 
in  diameter.  This  law  has  been  verified  with  tubes  whose  diameters  ranged 
from  5  mm.  to  0-07  mm.  It  presupposes  that  the  liquid  has  previously 
moistened  the  tube. 

The  nature  of  the  liquid  is  of  prime  importance ;  of  all  liquids  water  rises 
the  highest ;  thus  in  a  glass  tube  1-29  mm.  in  diameter,  the  heights  of  water, 
alcohol,  and  turpentine  are  respectively  23*16,  9-18,  and  9-85  mm. 

The  height  to  which  a  liquid  rises  in  a  tube  diminishes  as  the  tempera- 
ture rises.  Thus  in  a  capillary  tube  in  which  water  stood  at  a  height  of 
307  mm.  at  o°,  it  stood  at  28-6  mm.  at  35°,  and  at  26  mm.  at  80°. 

Provided  the  liquid  moistens  the  tube,  neither  its  thickness  nor  its  nature 
has  any  influence  on  the  height  to  which  the  liquid  rises.  Thus  water  rises 
to  the  same  height  in  tubes  of  different  kinds  of  glass  and  of  rock  crystal,, 
provided  the  diameters  are  the  same. 

In  regard  to  the  depression  of  liquids  in  tubes  which  they  do  not 
moisten,  Jurin's  law  has  not  been  found  to  hold  with  the  same  accuracy. 
The  reason  for  this  is  probably  to  be  found  in  the  following  circumstances : — 
When  a  liquid  moistens  a  capillary  tube,  a  very  thin  layer  of  liquid  is  formed 
against  the  sides,  and  remains  adherent  even  when  the  liquid  sinks  in  the 
tube.  The  ascent  of  the  column  of  liquid  takes  place  then,  as  it  were,  inside 
a  central  tube,  with  which  it  is  physically  and  chemically  identical.  The 
ascent  of  the  liquid  is  thus  an  act  of  cohesion.  It  is  therefore  easy  to 
understand  why  the  nature  of  the  sides  of  the  capillary  tube  should  be 
without  influence  on  the  height  of  the  ascent,  which  only  depends  on  the 
diameter. 

With  liquids,  on  the  contrary,  which  do  not  moisten  the  sides  of  the  tube,. 
the  capillary  action  takes  place  between  the  sides  and  the  liquid.  The 
nature  and  structure  of  the  sides  are  never  quite  homogeneous,  and  there  is 
always,  moreover,  a  layer  of  air  on  the  inside,  which  is  not  dissolved  by  the 
liquid.  These  two  causes  undoubtedly  exert  a  disturbing  influence  on  the 
law  of  Jurin. 

133.  Ascent  and  depression  between  parallel  or  inclined  surfaces. — 
When  two  bodies  of  any  given  shape  are  dipped  in  water,  analogous  phe- 
nomena are  produced,  provided  the  bodies  are  sufficiently  near.  If,  for 
example,  two  parallel  glass  plates  are  immersed  in  water  at  a  very  small 
distance  from  each  other,  water  will  rise  between  the  two  plates  in  the 
inverse  ratio  of  the  distance  which  separates  them.  The  height  of  the 
ascent  for  any  given  distance  is  half  what  it  would  be  in  a  tube  whose  dia- 
meter is  equal  to  the  distance  between  the  plates. 

If  the  parallel  plates  are  immersed  in  mercury,  a  corresponding  depression 
is  produced,  subject  to  the  same  laws. 

If  two  glass  plates  AB  and  AC,  with  their  planes  vertical  and  inclined  to 
one  another  at  a  small  angle,  as  represented  in  fig.  100,  have  their  ends 
dipped  into  a  liquid  which  wets  them,  the  liquid  will  rise  between  them. 
The  elevation  will  be  greatest  at  the  line  of  contact  of  the  plates  and  from 
thence  gradually  less,  the  surface  taking  the  form  of  an  equilateral  hyperbola. 


-134] 


Curvature  of  Liquid  Surfaces. 


whose  asymptotes  are  respectively  the  line  of  intersection  of  the  plates,  and 
the  line  in  which  the  plates  cut  the  horizontal  surface  of  the  liquid. 

If  a  drop  of  water  be  placed  within  a  conical  glass  tube  whose  angle  is 
small  and  axis  horizontal,  it  will  have  a  concave  meniscus  at  each  end 


Fig.  ic 


Fig. 


Fig.  102. 


(fig.  101),  and  will  tend  to  move  towards  the  vertex.  But  if  the  drop  be  of 
mercury  it  will  have  a  convex  meniscus  at  each  end  (fig.  102),  and  will  tend 
to  move  from  the  vertex. 

134.  Cause  of  the  curvature  of  liquid  surfaces  in  contact  with  solids. 

The  form  of  the  surface  of  a  liquid  in  contact  with  a  solid  depends  on  the 
relation  between  the  attraction  of  the  solid  for  the  liquid,  and  of  the  mutual 
attraction  between  the  molecules  of  the  liquid. 

Let  m  be  a  liquid  molecule  (fig.  103)  in  contact  with  a  solid.  This 
molecule  is  acted  upon  by  three  forces  :  by  gravity,  which  attracts  it  in  the 
direction  of  the  vertical  m?  ;  by  the  attraction  of  the  liquid  F,  which  acts  in 
the  direction  m¥  ;  and  by  the  attraction  of  the  plate  n,  which  is  exerted  in 
the  direction  mn.  According  to  the  relative  intensities  of  these  forces,  their 
resultant  can  take  three  positions  : — 

i.  The  resultant  is  in  the  direction  of  the  vertical  mR  (fig.  103).  In  this 
case  the  surface  m  is  plane  and  horizontal  ;  for,  from  the  condition  of  the 
equilibrium  of  liquids,  the  surface  must  be  perpendicular  to  the  force  which 
acts  upon  the  molecules. 

ii.  If  the  force  n  increases  or  F  diminishes,  the  resultant  R  is  within  the 
angle  nmP  (fig.  104) ;  in  this  case  the  surface  takes  a  direction  perpendicular 
to  mR,  and  becomes  concave. 

iii.  If  the  force  F  increases  or  n  diminishes,  the  resultant  R  takes  the 


Fig.  103.  Fig.  104.  Fig.  105. 

direction  mR  (fig.  105)  within  the  angle  P;;zF,  and  the  surface,  becoming 
perpendicular  to  this  direction,  is  convex. 


I  2 


u6 


On  Liquids. 


[135- 


135.  Influence  of  curvature  on  capillary  phenomena. — The  elevation 
or  depression  of  a  liquid    in  a  capillary  tube  depends  on  the  concavity  or 

convexity   of  the 
In    a 


Fig.  1 06. 


Fig.  107. 


meniscus. 
concave  menis- 
cus, abed  (fig. 
106),  the  liquid 
molecules  are 
sustained  in  equi- 
librium by  the 
forces  acting  on 
them,  and  they 
exert  no  down- 
ward pressure  on  the  inferior  layers.  On  the  contrary,  in  virtue  of 
molecular  attraction,  they  act  on  the  nearest  inferior  layers,  from  which  it 
follows  that  the  pressure  on  any  layer,  mn,  in  the  interior  of  the  tube,  is  less 
than  if  there  were  no  meniscus.  The  consequence  is  that  the  liquid  rises 
in  the  tube  until  the  internal  pressure  on  the  layer  mn  is  equal  to  the  pressure. 
op,  which  acts  externally  on  a  point  p  of  the  same  layer. 

Where  the  meniscus  is  convex  (fig.  107),  equilibrium  exists  in  virtue  of 
the  molecular  forces  acting  on  the  liquid  ;  but  as  the  molecules  which 
would  occupy  the  same  space  ghik,  if  there  were  no  molecular  action,  do 
not  exist,  they  exert  no  attraction  on  the  lower  layers.  Consequently,  the 
pressure  on  any  layer  mn,  in  the  interior  of  the  tube,  is  greater  than  if  the  ' 
space  ghik  were  filled,  for  the  molecular  forces  are  more  powerful  than 
gravity.  The  liquid  ought,  therefore,  to  sink  in  the  tube  until  the  internal 
pressure  on  a  layer,  mn,  is  equal  to  the  external  pressure  on  any  point,  p,  of 
this  layer. 

136.  Tension  of  the  free  surface  of  liquids. — The  free  surface  of  a 
liquid  is  that  which  is  bounded  by  a  gas  or  by  vacuum  ;  it  has  greater 
cohesion  than  any  layer  of  the  liquid  in  the  interior.  For  consider  any  par- 
ticle at  the  surface,  it  will  be  attracted  by  the  adjacent  particles  in  all  directions 
except  in  those  above  the  surface.  The  attractions  acting  laterally  will  com- 
pensate each  other  ;  and  as  there  are  no  attractions  exerted  by  the  particles 
of  the  liquid  above  the  surface  to  counteract  those  acting  from  the  interior, 
the  latter  will  exercise  a  considerable  pull  towards  the  interior.  The  effect 
of  this  is  to  lessen  the  mobility  of  particles  on  the  surface,  while  those  in  the 
interior  are  quite  mobile  ;  the  surface  is  stretched,  as  it  were,  by  an  elastic 
skin,  the  effect  being  the  same  as  if  the  surface  layer  exerted  a  pressure  on 
the  interior.  This  surface  tension,  as  it  is  called,  is  greater,  the  greater  the 
cohesion  of  the  liquid. 

When  the  surface  of  a  liquid  increases,  more  particles  enter  into  the 
condition  of  the  surface  layer,  to  effect  which  a  certain  amount  of  work  is 
required.  On  the  other  hand,  when  the  surface  is  diminished,  the  molecules 
pass  into  the  state  of  the  internal  layer,  and  they  perform  work.  The  work 
done  when  a  square  mm.  of  surface  passes  into  the  interior  is  called  the 
coefficient  of  surface  tension. 

The  surface  tension  depends  on  the  form  of  the  surface.  It  has  been 
determined  in  the  case  of  spheroidal  bodies.  If  the  pressure  which  is  exerted 


~137]  Various  Capillary  Phenomena.  !  x ; 

on  *  plane  surface  be  called  P,  the  pressure  /,  on  a  spherical  surface  of 
radius  p,  is  p  =  P  4  ^  for  convex,  and  p  =  P  -  ^  for  concave  surfaces> 

Hence  for  a  spheroidal  shell,  the  internal  radius  OA  of  which  is  p,  and 
its  thickness  AB  =  d,  the  pressure  of  the  outer  layer  is  p  =  P  +  2*.     and  of 

'  p  +  tf 

the  inner  layer  ^  =  P  -  ??,  and  the  resultant  is  their 
P 

difference  ^J*  +20;   a  pressure    exerted    inwards, 


since  psfa.  This  is  well  illustrated  by  blowing  a  soap- 
bubble  on  a  glass  tube.  So  long  as  the  other  end  of 
the  tube  is  closed,  the  bubble  remains,  the  elastic  force 
of  the  enclosed  air  counterbalancing  the  tension  of 
the  surface  ;  but  when  the  tube  is  opened,  the  tension 

of  the  surface  being  unchecked,  the  bubble  gradually  contracts  and  finally 
disappears. 

Insects  can  often  move  on  the  surface  of  water  without  sinking.  This 
phenomenon  is  caused  by  the  fact  that,  as  their  feet  are  not  wetted  by  the 
water,  a  depression  is  produced,  and  the  elastic  reaction  of  the  surface  layer 
keeps  them  up  in  spite  of  their  weight.  Similarly  a  sewing-needle,  gently 
placed  on  water,  does  not  sink,  because  its  surface,  being  covered  with  an 
oily  layer,  does  not  become  wetted.  The  pressure  of  the  needle  brings 
about  a  concavity,  the  surface  tension  of  which  acts  in  opposition  to  the 
weight  of  the  needle.  But  if  washed  in  alcohol  or  in  potash,  the  metal  is 
wetted  and  at  once  sinks  to  the  bottom. 

Among  the  phenomena  due  to  surface  tension  may  be  mentioned  the  well- 
known  one  of  the  '  tears  of  wine.'  The  surface  tension  of  water  in  contact 
with  air  is  greater  than  that  of  any  other  liquid  except  mercury.  It  is  more 
than  three  times  as  great  as  that  of  alcohol.  When  a  wine-glass  is  half-filled 
with  a  strong  wine,  the  wine  rises  up  against  the  sides  like  any  other  liquor  ; 
but  the  alcohol  evaporates  rapidly  from  the  surface,  the  consequence  of  which 
is  that  the  liquid  layer  becomes  more  watery.  Near  the  surface  of  the 
liquid  the  strength  of  the  liquid  layer  is  kept  up  by  diffusion,  but  higher  up, 
owing  to  the  increased  surface  tension  of  the  more  aqueous  wine,  it  creeps  up 
the  sides  and  draws  with  it  some  of  the  stronger  alcoholic  liquid  below,  the 
increasing  weight  of  which  ultimately  causes  it  to  break  and  run  down  in 
drops. 

If  a  thin  layer  of  water  be  spread  on  a  plate,  and  a  drop  of  ether  be 
placed  upon  it,  the  water  retreats  from  the  drop.  Here,  instead  of  the  sur- 
face tension  between  water  and  air,  we  have  that  between  water  and  ether, 
which  is  smaller ;  the  effect  is  much  the  same  as  if  there  were  a  tightly 
stretched  india-rubber  skin,  and  a  portion  of  it  were  then  softened  or  made 
thinner. 

137.  Various  capillary  phenomena. — The  attractions  and  repulsions 
observed  between  bodies  floating  on  the  surface  of  liquids  find  their  expla- 
nation in  the  concave  or  convex  curvature  which  the  liquid  assumes  in  con- 
tact with  the  solid.  The  following  are  some  of  them. 

When  two  floating  balls  both  moistened  by  the  liquid — for  example,  cork 


Il8  On  Liquids.  [137- 

upon  water — are  so  near  that  the  liquid  surface  between  them  is  not  level, 
an  attraction  takes  place.  The  same  effect  is  produced  when  neither  of  the 
balls  is  moistened,  as  is  the  case  with  balls  of  wax  on  water. 

Lastly,  if  one  of  the  balls  is  moistened  and  the  other  not,  as  a  ball  of  cork 
and  a  ball  of  wax  in  water,  they  repel  each  other  if  the  curved  surfaces  of  the 
liquid  in  their  respective  neighbourhoods  intersect. 

A  drop  of  mercury  on  a  table  has  a  spherical  shape,  which,  like  that  of 
the  heavenly  bodies,  is  due  to  attraction.  The  globule  of  mercury  behaves 
as  if  its  molecules  had  no  weight,  since  it  remains  spherical.  That  is,  the 
molecular  attraction  is  far  greater  than  the  weight,  which  only  alters  the 
shape  of  the  globule  if  the  quantity  of  mercury  is  much  greater  ;  it  then 
flattens,  but  always  retains  at  its  edge  the  convex  form  which  molecular 
attraction  imparts  to  it.  A  liquid  immersed  in  another,  with  which  it  does 
not  mix,  of  exactly  the  same  specific  gravity,  such  as  olive  oil  in  a  mixture 
of  alcohol  and  water,  assumes  the  spherical  form. 

To  this  cause  also  is  due  the  spherical  form  acquired  by  small  masses  of 
liquid  which  fall  through  great  heights,  such  as  rain-drops,  and  molten  lead  in 
casting  small  shot. 

When  a  capillary  tube  is  immersed  in  a  liquid  which  moistens  it,  and 
is  then  carefully  removed,  the  column  of  liquid  in  the  tube  is  seen  to  be  twice 
as  long  as  while  the  tube  was  immersed  in  the  liquid.  This  arises  from 
the  fact  that  a  drop  adheres  to  the  lower  extremity  of  the  tube  and  forms  a 
convex  meniscus,  which  concurs  with  that  of  the  upper  meniscus  to  form  a 
longer  column  (131). 

For  the  same  reason  a  liquid  does  not  overflow  in  a  capillary  tube, 
although  the  latter  may  be  shorter  than  the  liquid  column  which  would 
otherwise  be  formed  in  it.  For  when  the  liquid  reaches  the  top  of  the  tube, 
its  upper  surface,  though  previously  concave,  becomes  convex,  and,  as  the 
downward  pressure  becomes  greater  than  if  the  surface  were  plane,  the 
ascending  motion  ceases. 

It  is  from  capillarity  that  oil  ascends  in  the  wicks  of  lamps,  that  water 
rises  in  woods,  sponge,  bibulous  paper,  sugar,  sand,  and  in  all  bodies  which 
possess  pores,  of  a  perceptible  size.  In  the  cells  of  plants  the  sap  rises  with 
great  force,  for  here  we  have  to  do  with  vessels  whose  diameter  is  less  than 
o-oi  mm.  Efflorescence  of  salts  is  also  due  to  capillarity  ;  a  solution  rising 
against  the  side  of  a  vessel,  the  water  evaporates,  and  the  salt  forms  on  the 
side  a  means  of  furthering  still  more  the  ascent  of  a  liquid.  Capillarity  is, 
moreover,  the  cause  of  the  following  phenomenon  : — When  a  porous  sub- 
stance, such  as  gypsum,  or  chalk,  or  even  earth,  is  placed  in  a  porous  vessel 
of  unbaked  porcelain,  and  the  whole  is  dipped  in  water,  the  water  penetrates 
into  the  pores,  and  the  air  is  driven  inwards,  so  that  it  is  under  four  or  five 
times  its  usual  pressure  and  density.  Jamin  has  proved  this  by  cementing 
a  manometer  into  blocks  of  chalk,  gypsum,  £c.,  and  he  has  made  it  probable 
that  a  pressure  of  this  kind,  exerted  upon  the  roots,  promotes  the  ascent  of 
sap  in  plants. 

138.  Determination  of  the  constant  of  capillarity. — This  determination 
may  be  effected  in  various  ways,  of  which  the  simplest  and  perhaps  the  most 
accurate  is  that  of  the  measuring  the  ascent  of  a  liquid  in  capillary  tubes. 


-139] 


Endosmose  and  Exosmose. 


119 


For  this  purpose  capillary  tubes  of  glass  are  used,  the  diameter  of  which  is 
determined  by  introducing  a  thread  of  mercury  into  the  tube 
and  ascertaining  the  weight  of  a  given  length  (125). 

The  height  to  which  the  liquid  rises  in  the  capillary 
tube  may  be  read  off  by  a  cathetometer.  A  simpler  ar- 
rangement is  the  following  (fig.  109).  The  capillary  tube 
is  fixed  to  a  strip  of  opaque  glass,  graduated  in  milli- 
metres. The  lower  end  of  the  tube,  which  is  fixed  in  a 
suitable  support,  is  first  dipped  in  a  small  vessel  of  the 
liquid  and  then  the  movable  steel  point  p,  being  placed 
•opposite  the  zero  of  the  graduation,  liquid  is  added  drop 
by  drop  until  its  level  just  grazes  the  point.  In  order  that 
the  liquid  may  properly  moisten  the  tube  completely  it  is 
sucked  up  by  means  of  a  caoutchouc  tube  beyond  the  height 
at  which  it  finally  stands.  This  height  may  be  read  off  by  a 
lens. 

In  the  case  of  a  liquid  which  wets  the  tube,  the  force 
which  holds  up  the  liquid  in  the  tube  is  the  surface  tension, 
a  ;  acting  along  the  cross-section  of  the  tube  ;  that  is, 
27rra,  where  r  is  the  diameter  of  the  tube.  This  force  is 
•equal  to  the  weight  of  the  column  of  liquid,  which  is 
where  h  is  the  height  of  the  column  of  liquid,  and 


ts 


.specific  gravity.     From  this  we  get   a  =  —,  and  for  water, 


where  s  is  unity,  a 


hr 


This,  which  is  known  as  the  capil- 


Fig.  109. 


.lary  constant,  gives  the  weight  supported  by  the  unit  of 
length,  which  is  usually  taken  at  a  millimetre.  The  following 
.are  some  of  the  values  expressed  in  milligrammes  : — 

Water  ....  7-24  Turpentine  ....  277 
Hydrochloric  acid  .  7*15  Petroleum  ....  2*57 
Olive  oil  "  .  '•*  .  3*27  Alcohol  .  .  .  2-27 

139.  Endosmose  and  ezosmose. — When  two  different  liquids  are  sepa- 
rated by  a  thin  porous  partition,  either  inorganic  or  organic,  a  current  sets 
in  from  each  liquid  to  the  other  ;  to  these  currents  the  names  endosmose 
and  exosmose  are  respectively  given.  These  terms,  which  signify  impulse 
Jrom  within  and  impulse  from  without^  were  originally  introduced  by 
Dutrochet,  who  first  drew  attention  to  these  phenomena.  The  general 
phenomenon  may  be  termed  diosmose.  They  may  be  well  illustrated  by 
means  of  the  etidosmometer.  This  consists  of  a  long  tube,  at  the  end  of 
which  a  membranous  bag  is  firmly  bound  (fig.  no).  The  bag  is  then  filled 
with  a  strong  syrup,  or  some  other  solution  denser  than  water,  such  as  milk 
or  albumen,  and  is  immersed  in  water.  The  liquid  is  found  gradually  to  rise 
in  the  tube,  to  a  height  which  may  attain  several  inches  ;  at  the  same  time 
the  level  of  the  liquid  in  which  the  endosmometer  is  immersed  becomes 
lower.  It  follows,  therefore,  that  some  of  the  external  liquid  has  passed 
through  the  membrane  and  has  mixed  with  the  internal  liquid.  The 


120 


On  Liquids. 


[139- 


external  liquid,  moreover,  is  found  to  contain  some  of  the  internal  liquid. 
Hence  two  currents  have  been  produced  in  opposite  directions.  The  flow 
of  the  liquid  towards  that  which  increases  in  volume  is  endosmose,  and  the 
current  in  the  opposite  direction  is  exosmose.  If  water  is  placed  in  the  bag, 
and  immersed  in  the  syrup,  endosmose  is  produced  from  the  water  towards 
the  syrup,  and  the  liquid  in  the  interior  diminishes  in  volume  while  the  level 
of  the  exterior  is  raised. 

The  phenomena  of  endosmose  are  explained  as  follows  : — The  diaphragm 
is  made  up  of  numerous  capillary  apertures,  and  according  to  the  difference 
in  the  molecular  attraction  of  its  material  for  different  liquids  it  absorbs 
different  quantities  of  them.  Thus  Liebig  found  that  in  24  hours  100 
grammes  of  dry  ox-bladder  absorbed  268  grammes  of  water,  or  133  grammes 
of  solution  of  chloride  of  sodium.  If,  therefore,  such  a  bladder  separates 
water,  and  solution  of  salt,  it  will  absorb  both,  but  water  in  larger  quanti- 
ties. These  liquids  will  now  be  withdrawn  from  the  bladder  by  the  different 
liquids  on  the  two  sides,  but  in  unequal  quantities,  for  the  quantities  present 
in  the  bladder  are  different.  Hence  more  water  will  pass  in  one  direction 
than  in  the  other. 

The  height  of  the  ascent  in  the  endosmometer  varies  with  different  liquids. 
Of  all  vegetable  substances,  sugar  is  that  which,  for  the  same  density,  has 

the  greatest  power  of  endosmose,  while 
albumen  has  the  highest  power  of  all  animal 
substances.  In  general  it  may  be  said  that 
endosmose  takes  place  towards  the  denser 
liquid.  Alcohol  and  ether  form  an  exception 
to  this  ;  they  behave  like  liquids  which  are 
denser  than  water.  With  acids,  according 
as  they  are  more  or  less  dilute,  the  endosmose 
is  from  the  water  towards  the  acid,  or  from 
the  acid  towards  the  water. 

It  is  necessary  for  the  production  of 
endosmose — (i.)  that  the  liquids  be  different 
but  capable  of  mixing,  as  alcohol  and  water 
— 'there  is  no  diosmose,  for  instance,  with 
water  and  oil  ;  (ii.)  that  the  liquids  be  of 
different  densities  ;  and  (iii.)  that  the  mem- 
brane must  be  permeable  to  at  least  one  of 
the  substances. 

The  current  through  thin  inorganic  plates 
is  feeble,  but  continuous,  while  organic  mem- 
|jji  branes  are  rapidly  decomposed,  and  diosmose 
then  ceases. 

The  well-known  fact  that  dilute  alcohol 
Fig.  no.  kept   in   a  porous  vessel  becomes   concen- 

trated depends  on  endosmose.     If  a  mixture 

of  alcohol  and  water  be  kept  for  some  time  in  a  bladder,  the  volume: 
diminishes,  bnt  the  alcohol  becomes  much  more  concentrated.  The  reason 
doubtless  is  that  the  bladder  permits  the  diosmose  of  water  rather  than  that 
of  alcohol. 


-140] 


Diffusion  of  Liquids. 


121 

Dutrochet's  method  is  not  adapted  for  quantitative  measurements,  for  it 
does  not  take  into  account  the  hydrostatic  pressure  produced  by  the  column. 
Jolly  has  examined  the  endosmose  of  various  liquids  by  determining  the 
weights  of  the  bodies  diffused.     He  calls  the  endosmotic  equivalent  of  a  sub- 
stance the  number  which  expresses  how  many  parts  by  weight  of  water  pass 
through  the  bladder  in  exchange  for  one  part  by  weight  of  the  substance.  The 
following  are  some  of  the  endosmotic  equivalents  which  he  determined — 
Sulphuric  acid       .         .       0-4         Sulphate  of  copper  .        .        9-5 
Alcohol.         .        .        .4*2  „  magnesium  .       117 

Chloride  of  sodium        .      4-3         Caustic  potass .        .        .     215.0 
Sugar     .         .        .        .  •   7-1 

He  also  found  that  the  endosmotic  equivalent  increases  with  the  temperature, 
and  that  the  quantities  of  substances  which  pass  in  equal  times  through  the 
bladder  are  proportional  to  the  strengths  of  the  solutions. 

140.  Diffusion  of  liquids. — If  oil  be  poured  on  water  no  tendency  to 
intermix  is  observed,  and  even  if  the  two  liquids  be  violently  agitated  to- 
gether, on  allowing  them  to  stand,  two  separate  layers  are  formed.  With 
alcohol  and  water  the  case  is  different ;  if  alcohol,  which  is  specifically 
lighter,  be  poured  upon  water,  the  liquids  gradually  intermix,  in  spite  of  the 
difference  of  the  specific  gravities  :  they  diffuse  into  one  another. 

This  point  may  be  illustrated  by  the  experiment  represented  in  fig.  in. 
A  tall  jar  contains  water  coloured  by  solution  of  blue  litmus  ;  by  means  of 
a  funnel  some  dilute  sulphuric  acid  is  carefully  poured  in,  so  as  to  form  a 
layer  at  the  bottom  ;  the  colour  of  the  solution  is  changed  into  red,  pro- 
gressing upwards,  and  after  forty-eight  hours  the  change  is  complete — a 


Fig.  112. 

result  of  the  action  of  the  acid,  and  a  proof,  therefore,  that  it  has  diffused 
throughout  the  entire  mass. 

The  laws  of  this  diffusion,  in  which  no  porous  diaphgram  is  used 
been  completely  investigated  by  Graham.     The  method  by  which  his  latest 
experiments  were  made  was  the  following  :— A  small  wide-necked  bottle  A 
(fig.  in)  filled  with  the  liquid  whose  rate  of  diffusion  was  to  be  exami 


J22  On  Liquids.  [140 

was  closed  by  a  thin  glass  disc  and  placed  in  a  larger  vessel  B,  in  which 
water  was  poured  to  a  height  of  about  an  inch  above  the  top  of  the  bottle. 
The  disc  was  carefully  removed,  and  then  'after  a  given  time  successive 
layers  were  carefully  drawn  off  by  means  of  a  siphon  or  pipette,  and  their 
contents  examined. 

The  general  results  of  these  investigations  may  be  thus  stated  : — 

i.  When  solutions  of  the  same  substance,  but  of  different  strengths,  are 
taken,  the  quantities  diffused  in  equal  times  are  proportional  to  the  strengths 
of  the  solutions. 

ii.  In  the  case  of  solutions  containing  equal  weights  of  different  substances, 
the  quantities  diffused  vary  with  the  nature  of  the  substances.  Saline 
substances  may  be  divided  into  a  number  of  equidiffusive  groups,  the  rates 
of  diffusion  of  each  group  being  connected  with  the  others  by  a  simple 
numerical  relation. 

iii.  The  quantity  diffused  varies  with  the  temperature.  Thus,  taking  the 
rate  of  diffusion  of  hydrochloric  acid  at  15°  C.  as  unity,  at  49°  C.  it  is  2-18. 

iv.  If  two  substances  which  do  not  combine  be  mixed  in  solution,  they 
may  be  partially  separated  by  diffusion,  the  more  diffusive  one  passing  out 
most  rapidly.  In  some  cases  chemical  decomposition  even  may  be  effected 
by  diffusion.  Thus,  bisulphate  of  potassium  is  decomposed  into  free  sulphuric 
acid  and  neutral  sulphate  of  potassium. 

v.  If  liquids  be  dilute,  a  substance  will  diffuse  into  water  containing 
another  substance  dissolved,  as  into  pure  water  ;  but  the  rate  is  materially 
reduced  if  a  portion  of  the  same  diffusing  substance  be  already  present. 

The  following  table  gives  the  approximate  times  of  equal  diffusion  : — 

Hydrochloric  acid  .  .  ro  Sulphate  of  magnesium  .  7-0 
Chloride  of  sodium  .  .2-3  Albumen.  .  .  .  49-0 
Sugar .  .  .  .  .7-0  Caramel  ....  98-0 

It  will  be  seen  from  the  above  table  that  the  difference  between  the  rates 
of  diffusion  is  very  great.  Thus  sulphate  of  magnesium,  one  of  the  least 
diffusible  saline  substances,  diffuses  7  times  as  rapidly  as  albumen  and  14 
times  as  rapidly  as  caramel.  These  last  substances,  like  hydrated  silicic 
acid,  starch,  dextrine,  gum,  &c.,  constitute  a  class  of  substances  which  are 


Fig.  113.  Fig.  114. 

characterised  by  their  incapacity  for  taking  the  crystalline  form,  and  by-  the 
mucilaginous  character  of  their  hydrates.  Considering  gelatine  as  the  type 
of  this  class,  Graham  has  proposed  to  call  them  colloids  (^oXA?;,  glue),  in  con- 


140]  Diffusion  of  Liquids.  123 

tradistinction  to  the  far  more  easily  diffusible  crystalloid  substances.  Colloids 
.are  for  the  most  part  bodies  of  high  molecular  weight,  and  it  is  probably  the 
larger  size  of  their  molecules  which  hinders  their  passing  through  minute 
apertures. 

Graham  has  proposed  a  method  of  separating  bodies  based  on  their  un- 
•equal  diffusibility,  which  he  calls  dialysis.  His  dialyser  (fig.  113)  consists  of 
a  ring  of  gutta-percha,  over  which  is  stretched  while  wet  a  sheet  of  parch- 
ment-paper, forming  thus  a  vessel  about  two  inches  high  and  ten  inches  in 
diameter,  the  bottom  of  which  is  of  parchment-paper.  After  pouring  in  the 
mixed  solution  to  be  dialysed,  the  whole  is  floated  on  a  vessel  containing  a 
very  large  quantity  of  water  (fig  114).  In  the  course  of  one  or  two  days  a 
more  or  less  complete  separation  will  have  been  effected.  Thus  a  solution 
of  arsenious  acid  mixed  with  various  kinds  of  food  readily  diffuses  out.  The 
process  has  received  important  applications  to  laboratory  and  pharmaceutical 
purposes. 

Diosmose  plays  a  most  important  part  in  organic  life  ;  the  cell-walls  are 
diaphragms,  through  which  the  liquids  in  the  cells  set  up  diosmotic  com- 
munications. 


1 24  On  Liquids.  [141- 


CHAPTER   III. 

HYDRODYNAMICS. 

141.  Hydrodynamics.  —  The  science  which  treats  of  the  motion  of  liquids 
is  called  hydrodynamics  •  and  the  application  of  the  principles  of  this  science 
to  conducting  and  raising  water  in  pipes  and  to  the  use  of  water  as  a  motive 
power  is  known  by  the  name  of  hydraulics. 

142.  Velocity  of  efflux.     Torricelli's  theorem.  —  Let  us    imagine  an 
aperture  made  in  the  bottom  of  any  vessel,  and  consider  the  case  of  a  par- 
ticle of  liquid  on  the  surface,  without  reference  to  those  which  are  beneath. 
If  this  particle  fell  freely,  it  would  have  a  velocity  on  reaching  the  orifice 
equal  to  that  of  any  other  body  falling  through  the   distance  between  the 
level  of  the  liquid  and  the  orifice.     This,  from  the  laws  of  falling  bodies,  is 
x/2£->#,  in  which  g  is  the  accelerating  force  of  gravity,  and  h  the  height.     If 
the  liquid  be  maintained  at  the  same  level,  for  instance  by  a  stream  of  water 
running  into  the  vessel  sufficient  to  replace  what  has  escaped,  the  particles 
will  follow  one  another  with  the  same  velocity,  and  will  issue  in  the  form  of 
a  stream.     Since  pressure  is  transmitted  equally  in  all  directions,  a  liquid 
would  issue  from  an  orifice  in  the  side  with  the  same  velocity  provided  the 
depth  were  the  same. 

The  law  of  the  velocity  of  efflux  was  discovered  by  Torricelli.  It  may  be 
enunciated  as  follows  :  —  The  velocity  of  efflux  is  the  velocity  which  a  freely 
falling  body  would  have  on  reaching  the  orifice  after  having  started  from 
a  state  of  rest  at  the  surface.  It  is  algebraically  expressed  by  the  formula 


It  follows  directly  from  this  law  that  the  velocity  of  efflux  depends  on  the 
depth  of  the  orifice  below  the  surface,  and  not  on  the  nature  of  the  liquid. 
Through  orifices  of  equal  size  and  of  the  same  depth,  water  and  mercury 
would  issue  with  the  same  velocity,  for  although  the  density  of  the  latter 
liquid  is  greater,  the  weight  of  the  column,  and  consequently  the  pressure,  is 
greater  too.  It  follows  further  that  the  velocities  of  efflux  are  directly  pro- 
portional to  the  square  roots  of  the  depth  of  the  orifices.  Water  would  issue 
from  an  orifice  100  inches  below  the  surface  with  ten  times  the  velocity  with 
which  it  would  issue  from  one  an  inch  below  the  surface. 

The  quantities  of  water  which  issue  from  orifices  of  different  areas  are 
very  nearly  proportional  to  the  size  of  the  orifice,  provided  the  level  remains 
constant. 

143.  Direction  of  the  jet  from  lateral  orifices.  —  From  the  principle  of 
the  equal  transmission  of  pressure,  water  issues  from  an  orifice  in  the  side  of 
a  vessel  with  the  same  velocity  as  from  an  aperture  in  the  bottom  of  a  vessel 


-145] 


Quantity  of  Efflux.     Vena  Contracts 


12$ 


at  the  same  depth.   ^  Each  particle  of  a  jet  issuing  from  the  side  of  a  vessel 

begins  to  move  horizontally  with  the  velocity  above  mentioned,  but  it  is  at 

once  drawn  downward  by  the  force 

of  gravity  in  the  same  manner  as 

a  bullet,  fired  from  a  gun,  with  its 

axis  horizontal.     It  is  well  known 

that  the  bullet  describes  a  parabola 

(51)  with  a  vertical  axis,  the  vertex 

being  the  muzzle  of  the  gun.    Now, 

since  each  particle  of  the  jet  moves 

in  the  same  curve,  the  jet    itself 

takes  the  parabolic  form,  as  shown 

in  fig.  115. 

In  every  parabola  there   is   a 
certain  point  called  the  focus,  and 


Fig.  115. 


the  distance  from  the  vertex  to  the  focus  fixes  the  magnitude  of  a  parabola 
in  much  the  same  manner  as  the  distance  from  the  centre  to  the  circum- 
ference fixes  the  magnitude  of  a  circle.  Now  it  can  easily  be  proved  that 
the  focus  is  as  much  below,  as  the  surface  of  the  water  is  above,  the  orifice. 
Accordingly,  if  water  issues  through  orifices  which  are  small  in  comparison 
with  the  contents  of  the  vessel,  the  jets  from  orifices  at  different  depths 
below  the  surface  take  different  forms,  as  shown  in  fig.  1 1 5. 

144.  Height  of  tne  jet. —  If  a  jet  issuing  from  an  orifice  in  a  vertical 
direction  has  the  same  velocity  as  a  body  would  have  which  fell  from  the 
surface  of  the  liquid  to  that  orifice,  the  jet  ought  to  rise  to  the  level  of  the 
liquid.    It  does  not,  however,  reach  this  ;  for  the  particles  which  fall  hinder 
it.     But  by  inclining  the  jet  at  a  small  angle  with  the  vertical,  it  reaches 
about  ~  of  the  theoretical  height,  the  difference  being  due  to  friction  and 
to  the  resistance  of  the  air.     By  experiments  of  this  nature  the  truth   of 
Torricelli's  law  has  been  demonstrated. 

145.  Quantity  of  efflux.     Vena  contracta. — If  we  suppose  the  sides  of 
a  vessel  containing  water  to  be  thin,  and  the  orifice  to  be  a  small  circle  whose 
area  is  A,  we  might  think  that  the  quantity  of  water  E  dis- 
charged  in   a   second   would   be  given  by  the  expression         ^^  v  y 
P±^2gh,  since  each  particle  has,  on  the  average,  a  velocity 

equal  to  \/2g7z,  and  particles  issue  from  each  point  of  the 
orifice.     But  this  is  by  no  means  the  case.     This  may  be 
explained  by  reference  to  fig.  116,  in  which  AB  represents  an 
orifice  in  the  bottom  of  a  vessel — what  is  true  in  this  case 
being  equally  true  of  an  orifice   in  the  side  of  the  vessel. 
Every  particle  above  AB  endeavours  to  pass  out  of  the 
vessel,  and  in  so  doing  exerts  a  pressure  on  those  near  it.          Fig.  Il6. 
Those   that   issue   near  A  and   B  exert  pressures    in  the 
directions  MM  and  NN  ;  those  near  the  centre  of  the  orifice  in  the  direction 
RQ,  those  in  the  intermediate  parts  in  the  directions  PO,  PQ.     In  conse- 
quence, the  water  within  the  space  PQP  is  unable  to  escape,  and  that  which 
does  escape,  instead  of  assuming  a  cylindrical  form,  at  first  contracts,  and 
takes  the  form  of  a  truncated  cone.      It  is  found  that  the  escaping  jet 
continues  to  contract,  until  at  a  distance  from  the  orifice  about  equal  to  the 


126  On  Liquids.  [145— 

diameter  of  the  orifice.  This  part  of  the  jet  is  called  the  vena  contracta.  It 
is  found  that  the  area  of  its  smallest  section  is  about  %  or  0-62  of  that  of  the 
orifice.  Accordingly,  the  true  value  of  the  efflux  per  second  is  given  approxi- 
mately by  the  formula 


or  the  actual  value  of  E  is  about  0*62  of  its  theoretical  amount. 

146.  Influence  of  tubes  on  the  quantity  of  efflux. — The  result  given 
in  the  last  article  has  reference  to'v'an  aperture  in  a  thin  wall.  If  a  cylindrical 
or  conical  efflux  tube  or  ajutage  is  fitted  to  the  aperture,  the  amount  of  the 
efflux  is  considerably  increased,  and  in  some  cases  falls  but  a  little  short  of 
its  theoretical  amount. 

A  short  cylindrical  ajutage,  whose  length  is  from  two  to  three  times  its  dia- 
meter, has  been  found  to  increase  the  efflux  per  second  to  about  o%82A  \/?.gh. 
In  this  case  the  water  on  entering  the  ajutage  forms  a  contracted  vein  (fig. 
117),  just  as  it  would  do  on  issuing  freely  into  the  air  ;  but  afterwards  it  ex- 
pands, and,  in  consequence  of  the  adhesion  of  the  water  to  the  interior  surface 
of  the  tube,  has,  on  leaving  the  ajutage,  a  section  greater  than  that  of  the 
contracted  vein  The  contraction  of  the  jet  within  the  ajutage  causes  a  par- 
tial vacuum.  If  an  aperture  is  made  in  the  ajutage,  near  the  point  of  greatest 
contraction,[and  is  fitted  with  a  vertical  tube,  the 
other  end  of  which  dips  into  water  (fig.  117),  it  is 
found  that  water  rises  in  the  vertical  tube,  thereby 
proving  the  formation  of  a  partial  vacuum. 

If  the  ajutage  has  the  form  of  a  conic  frustrum 
whose  larger  end  is  at  the  aperture,  the  efflux  in 
a  second  may  be  raised  to  0-92 A  *J 2gh,  provided 
the  dimensions  are  properly  chosen.  If  the 
smaller  end  of  a  frustrum  of  a  cone  of  suitable 
dimensions  be  fitted  to  the  orifice,  the  efflux 
may  be  still  further  increased,  and  fall  very  little 
short  of  the  theoretical  amount. 

When  the  ajutage  has  more  than  a  certain 
^  length,  a  considerable  diminution  takes  place  in 

the  amount  of  the  efflux  :  for  example,  if  its  length 

is  48  times  its  diameter,  the  efflux  is  reduced  to  o'63AN/2^.  This  arises  from 
the  fact  that,  when  water  passes  along  cylindrical  tubes,  the  resistance  in- 
creases with  the  length  of  the  tube  ;  for  a  thin  layer  of  liquid  is  attracted  to 
the  walls  by  adhesion,  and  the  internal  flowing  liquid  rubs  against  this. 
The  resistance  which  gives  rise  to  this  result  is  called  hydraulic  friction  :  it 
is  independent  of  the  material  of  the  tube,  provided  it  be  not  roughened  ; 
but  depends  in  a  considerable  degree  on  the  viscosity  of  the  liquid  ;  for 
instance,  ice-cold  water  experiences  a  greater  resistance  than  lukewarm  water. 
According  to  Prony,  the  mean  velocity  v  of  water  in  a  cast-iron  pipe  of 
the  length  /,  and  the  diameter  d,  under  the  pressure  /,  is  in  metres 

Z/=26' 

This  is  on  the  assumption  that  the  tubes  are  straight.  Any  angle  or 
curvature  of  the  tube  diminishes  it,  seeing  that  part  of  the  motion  is  used  up 


-148] 


Form  of  the  Jet. 


127 


m  pressure  against  the  sides.  Thus  Venturi  found  the  time  requisite  to  fill 
a  small  vessel  by  means  of  a  tube  38  inches  in  length  by  3-3  in  diameter  was 
45,  So,  or  70  seconds,  according  as  the  tube  was  straight,  curved  or  bent 

By  means  of  hydraulic  pressure  Tresca  submitted  solids  such  as  silver 
lead,  iron  and  steel,  powders  like  sand,  soft  plastic  substances  such  as  clay 
and  brittle  bodies  like  ice,  to  such  enormous  pressures  as  100  ooo  kilo 
grammes,  and  has  found  that  they  then  behave  like  fluid  bodies.'  His  ex- 
periments show  also  that  these  bodies  transmit  pressure  equally  in  all 
directions  when  the  pressure  is  considerable  enough. 

147-  Efflux  through  capillary  tubes.—  This  was  investigated  by 
Poissemlle  by  means  of  the  apparatus  represented  in  fig.  118,  in  which  the 
capillary  tube  AB  is  sealed  to  a  glass  tube  on  which  a  bulb  is  blown.  The 
volume  of  the  space  between  the  marks  M  and  N  is  accurately  determined 
and  the  apparatus  having  been  filled  with  the  liquid  under  examination  by 
suction,  the  apparatus  is  connected  at  the  end  M  with  a  reservoir  of  com- 
pressed air,  in  which  the  pressure  is  measured  by  means  of  a  mercury  mano- 
meter (183).  The  time  is  then  noted  which  is  required  for  the  level  of  the 
liquid  to  sink  from  M  to  N,  the  pressure  remaining  constant.  It  is  thus  found 
that  v,  the  volume  which  flows  out  in  a  given  time,  is  represented  by  the 
formula 


M 


where  /  is  the  length  and  r  the  diameter  of  the  tube,  p  the  pressure,  and  e  the 

coefficient  of  internal  friction  ;  which  may  be  defined  as   the  resistance  to 

motion  offered  by  two  layers 

of  the  liquid  of  unit  surface, 

at  unit  distance,  and  moving 

away  from  each  other  with 

unit  velocity.     Knowing  the 

dimensions,  a  determination 

of  the  volume   which  flows 

out   is    a    ready    means    of 

obtaining  this  coefficient.     If 

the  experiment  be  made  with 

water,  then,  using  the  same 

apparatus,  other  liquids  may 

be  compared  with  it,  which 

has  thus  the  ad  vantage  of  dis- 

pensing with  a  separate  deter-  Fig.  -n8. 

mination  of  the  diameter  of 

the  tube,  a  matter  of  importance,  as  its  fourth  power  occurs  in  the  formula. 

The  coefficient  of  internal  friction  is  greater  in  the  case  of  solution  of  salts 

than  with  water,  and  increases  with  the  strength  of  the  solution.     It  greatly 

diminishes  with  the  temperature,  and  at  60°  is  one-third  what  it  is  at  zero. 

148.  Form  of  the  jet.  —  After  the  contracted  vein,  the  jet  has  the  form 
of  a  solid  rod  for  a  short  distance,  but  then  begins  to  separate  into  drops, 
which  present  a  peculiar  appearance.  They  seem  to  form  a  series  of  ventral 
and  nodal  segments  (fig.  119).  The  ventral  segments  consist  of  drops  extended 


128 


On  Liquids. 


[148- 


in  a  horizontal  direction,  and  the  nodal  segments  in  a  longitudinal  direction. 
And  as  the  ventral  and  nodal  segments  have  respectively  a  fixed  position, 
each  drop  must  alternately  become  elongated  and  flattened  while  it  is 
falling  (fig.  120).  Between  any  two  drops  there  are  smaller  ones,  so  that  the 
whole  jet  has  a  tube-like  appearance. 

If  the  jet  is  momentarily  illuminated  by  the  electric  spark  its  structure  is 
well  seen  ;  the  drops  appear  then  to  be  stationary,  and  separate  from  each 
other.  If  the  aperture  is  not  circular  the  form  of  the  jet  undergoes  curious 
changes. 

149.  Hydraulic  tourniquet. — If  water  be  contained  in  a  vessel,  and  an 
aperture  be  made  in  one  of  the  sides,  the  pressure  at  this  point  is  removed, 
foriit  is  expended  in  sending  out  the  water :  but  it  remains  on  the  other  side ; 
and  if  the  vessel  were  movable  in  a  horizontal  direction,  it  would  move  in  a 
direction  opposite  that  of  the  issuing  jet.  This  is  illustrated  by  the  appa- 
ratus known  as  the  hydraulic  tourniquet  or  Barker's  mill  (fig.  121).  It  con- 
sists of  a  glass  vessel,  M,  containing  water,  and  capable  of  moving  about  its 
vertical  axis.  At  the  lower  part  there  is  a  tube,  C,  bent  horizontally  in  oppo- 


• 


I 


Fig.  119. 


Fig.  120. 


Fig.  121. 

site  directions  at  the  two  ends.  If  the  vessel  were  full  of  water  and  the  tubes 
closed,  the  pressure  on  the  sides  of  C  would  balance  each  other,  being  equal 
and  acting  in  contrary  directions  ;  but,  being  open,  the  water  runs  out,  and  the 
pressure  is  not  exerted  on  the  open  part,  but  only  on  the  opposite  side,  as 
shown  in  the  figure  A.  And  this  pressure,  not  being  neutralised  by  an 
opposite  pressure,  imparts  a  rotatory  motion  in  the  direction  of  the  arrow, 
the  velocity  of  which  increases  with  the  height  of  the  liquid  and  the  size  of 
the  aperture. 

The  same  principle  may  be  illustrated  by  the  following  experiment.     A 


Water-wheels.  I2Q 

tall  cylinder  containing  water,  and  provided  with  a  lateral  stop-cock  n< 
bottom,  is  placed  on  a  light  shallow  dish  on  water,  so  that  it  easily  floa? 
On  opening  the  stop-cock  so  as  to  allow  water  to  flow  out,  the  vessel  i- 
observed  to  move  in  a  direction  diametrically  opposite  to  that  in  which  the 
water  is  issuing.     Similarly,  if  a  vessel  containing  water  be  suspended  by  a 
string,  on  opening  an  aperture  in  one  of  the  sides,  the  water  will  jet  out,  and 
the  vessel  be  deflected  away  from  the  vertical  in  the  opposite  direction 

Segner's  water-wheel  and  the  reaction  machine  depend  on  this  principle 
So  also  do  rotating  fireworks  ;  that  is,  an  unbalanced  reaction  from  the 
heated  gases  which  issue  from  openings  in  them,  gives  them  motion  in  the 
opposite  direction. 

150.  Water-wheels.  Turbines.— When  water  is  continuously  flowing 
from  a  higher  to  a  lower  level,  it  may  be  used  as  a  motive  power  The 
motive  power  of  water  is  generally  utilised  either  by  means  of  water-wheels 
turbines,  rams,  or  hydraulic  engines. 

Water-wheels  are  wheels  provided  with  buckets  or  float-boards  at  the 
circumference,  and  on  which  the  water  acts  either  by  pressure  or  by  impact. 
They  are  made  to  turn  in  a  vertical  plane  round  a  horizontal  axis,  and  are 
of  two  principal  kinds,  undershot  and  overshot.  In  tmdershot  wheels  the 
float-boards  are  placed  radially,  that  is  at  right  angles  to  the  circumference 
of  the  wheel.  The  lowest  float-boards  are  immersed  in  the  water,  which 
flows  with  a  velocity  depending  on  the  height  of  the  fall.  Such  wheels  are 
applicable  where  the  quantity  of  water  is  great,  but  the  fall  inconsiderable. 
Overshot  wheels  are  used  with  a  small  quantity  of  water  which  has  a  high 
fall,  as  with  small  mountain  streams.  On  the  circumference  of  the  wheel 
there  are  buckets  of  a  peculiar  shape.  The  water  falls  into  the  buckets  on 
the  upper  part  of  the  wheel,  which  is  thus  moved  by  the  weight  of  the  water, 
and  as  each  bucket  arrives  at  the  lowest  point  of  revolution  it  discharges  all 
the  water,  and  ascends  empty. 

An  overshot  wheel  driven  by  an  extraneous  force  may  be  used  for  raising 
water,  as  in  dredging  machines  ;  and  an  undershot  one  for  moving  a  vessel 
to  which  its  axis  is  fixed,  as  in  the  paddles  of  steam-vessels. 

The  turbine  is  a  horizontal  water-wheel,  and  is  similar  in  principle  to  the 
hydraulic  tourniquet  or  reaction  wheel  (149).  It  consists  of  a  pair  of  discs, 
-one  above  the  other,  connected  together  by  a  number  of  specially  shaped  thin 
arms  or  blades,  which  divide  the  space  between  the  discs  into  an  equal 
number  of  curved  radial  chambers.  The  wheel  works  generally  upon  a 
vertical  axis,  and  one  of  the  discs  is  cut  away  at  the  centre.  In  an  outward 
flow  turbine,  the  water  enters  through  the  opening  so  made  into  the  space 
between  the  discs,  and  passes  outwards  radially  through  the  chambers  above 
mentioned,  causing  the  wheel  to  rotate  by  its  reaction  upon  their  curved 
walls.  In  order  to  prevent  waste  of  energy  in  giving  useless  rotation  to  the 
water,  the  peripheral  openings  of  the  wheel  are  surrounded  by  a  series  of 
•corresponding  fixed  chambers,  whose  sides  (guide-blades)  are  so  curved  that 
the  water  when  it  leaves  them  has  lost  all  its  rotational  motion,  and  simply 
•flows  away  at  right  angles. to  the  axis.  In  an  inward  flow  turbine  the  water 
enters  the  peripheral  opening  of  the  wheel  through  the  guide-blades,  and 
leaves  the  wheel  at  the  centre. 

The  total  theoretical  effect  of  a  fall  of  water  is  never  realised  ;  for  the 

K 


130 


On  Liquids. 


[150- 


water,  after  acting  on  the  wheel,  still  retains  some  velocity,  and  therefore 
does  not  impart  the  whole  of  its  velocity  to  the  wheel.  In  many  cases  water 
flows  past  without  acting  at  all  ;  if  the  water  acts  by  impact,  vibrations  are 
produced  which  are  transmitted  to  the  earth  and  lost  ;  the  same  effect  is 
produced  by  the  friction  of  water  over  an  edge  of  the  sluice,  in  the  channel' 
which  conveys  it,  or  against  the  wheel  itself,  as  well  as  by  the  friction  of 
this  latter  against  the  axle.  A  wheel  working  freely  in  a  stream,  as  with  the 
corn-mills  on  the  Rhine  near  Mainz,  does  not  utilise  more  than  20  per  cent, 
of  the  theoretical  effect.  One  of  the  more  perfect  forms  of  turbines  will 
work  up  to  over  80  per  cent.  Turbines  also,  when  properly  designed,  may 
be  made  to  have  a  very  high  efficiency  either  with  high  or  low  falls ;  while,  on 
account  of  the  great  speed  at  which  they  run,  they  are  very  much  smaller 
than  water-wheels  in  proportion  to  their  power.  They  are  thus  more  '  effi- 
cient '  motors  than  steam-engines,  which,  even  if  perfect,  can  only  transform 
into  work  from  25  to  30  per  cent,  of  the  energy  represented  by  the  coal  they 
burn,  and  seldom  in  practice  utilise  more  than  half  of  this  percentage. 

The  hydraulic  ram,  often  called  Montgolfier's  Ram,  is  simply  a  pumping 
machine  by  which  a  large  quantity  of  water,  falling  through  a  small  distance, 
is  made  to  lift  a  small  quantity  through  a  greater  height. 

151.  Hydraulic  Engine. — Historically,  falling  water  was  one  of  the 
earliest  sources  of  power  ;  but  it  is  only  lately  that  attention  has  been  called 
(first  by  Sir  W.  Armstrong)  to  the  advantage  of  using  hydraulic  power  in 
towns  and  other  places  where  there  is  no  natural  fall  of  water  for  driving 
certain  classes  of  machines,  in  those  cases  more  especially  where  the  use  of 
the  machinery  is  only  intermittent. 


Fig.  122. 

For  this  purpose  the  most  important  docks  and  large  warehouses  are 
now  generally  furnished  with  means  of  obtaining  a  water-supply  at  a  very 
high  pressure,  generally  about  700  pounds  to  the  square  inch.  Steam- 
pumping  engines  are  employed  to  pump  water  more  or  less  continuously 


-151]  Hydraulic  Engine.  131 

into  what  are  practically  large  cylinders  with  immensely  heavy  pistons  loaded 
to  the  required  pressure.  These  vessels  are  called  accumulators,  and  pipes 
from  them  are  led  away  to  the  various  places  (lock  gates,  sluice  valves, 
cranes,  capstans,  &c.)  where  power  may  be  wanted.  At  each  of  these  places 
there  is  some  kind  of  hydraulic  motor  suitable  to  the  particular  work  to  be 
done,  and  this  motor  can  be  instantaneously  set  to  work  by  opening  the 
communication  between  it  and  the  high-pressure  water  in  the  accumulator. 
The  motor  used  is  not  uncommonly  a  small  engine  similar  in  principle  to  a 
steam-engine,  and  one  of  the  best  of  these  engines  is  that  illustrated  in 
fig.  122,  which  is  the  invention  of  Schmidt  of  Zurich.  It  consists  of  a 
cylinder  fitted  with  a  piston  c,  whose  rod  is  connected  directly  to  a  crank 
upon  a  horizontal  shaft.  The  cylinder  has  two  ports  or  passages,  a  and  ^, 
one  at  each  end,  both  terminating  below  in  openings  upon  a  convex  curved 
face,  which  is  kept  continually  pressed  against  a  similar  concave  face  upon 
the  framing  of  the  engine.  In  this  fixed  face  is  also  an  inlet  port  or  passage 
A,  and  outlet  passages  B.  When  the  cylinder  is  in  the  position  shown 
in  the  figure  the  high-pressure  water  is  passing  through  A  and  b,  forcing 
the  piston  along,  and  driving  out  the  already  used  water  away  through  a 
and  B.  As  the  piston  moves  and  turns  the  crank,  the  cylinder  oscillates  on 
its  bearings,  and  by  the  time  the  piston  has  got  to  the  end  of  its  stroke, 
the  cylinder  being  then  horizontal,  the  process  is  just  being  reversed,  water 
passing  in  through  A  and  «,  and  out  through  b  and  B.  W  is  an  air-vessel 
for  preventing  shocks. 

The  chief  drawback  about  the  use  of  water  power,  except  where  there  is 
a  large  natural  supply  under  pressure,  is  its  expense.  For  each  revolution 
of  the  crank  shaft,  two  complete  cylinders  full  of  water  must  be  passed 
through  such  an  engine,  as,  whether  the  power  be  wanted  or  not,  the  water 
cannot  be  expanded  like  steam. 

With  any  given  pressure  it  is  easy  to  find  out  how  much  water  will  be 
required  for  a  given  power.  At  a  pressure  of  30  pounds  per  square  inch, 
for  instance,  one  horse-power  will  require,  supposing  the  efficiency  of  the 


machine  to  be  70  per  cent.  (472)  ~~^J~=  =  about  8*5  cubic  feet  or  4>°°° 
gallons  per  hour,  a  quantity  the  cost  of  which  would  in  most  cases  put  the  use 
of  this  power  out  of  the  question.  The  pressure  in  town  mains  generally 
lies  between  20  and  40  pounds  per  square  inch,  and  it  is  therefore  only  in 
cases  where  a  special  high-pressure  supply  is  available  that  the  power  can 
be  economically  used. 

Water-power  is  usually  represented  by  the  weight  of  the  water  multiplied 
into  the  height  of  the  available  fall  ;  or  it  may  also  be  represented  by  half 
the  product  of  the  mass  into  the  square  of  the  velocity.     Both  measurement 
give  the  same  result  (60).     The  water-power  of  the  Niagara  Falls  is  calci 
lated  to  be  equal  to  four  and  a  half  millions  of  horse-power. 


K  2 


132  On  Gases.  [152 


BOOK    IV. 

ON   GASES. 


CHAPTER    I. 
PROPERTIES   OF  GASES.      ATMOSPHERE.      BAROMETERS. 

152.  Physical  properties  of  gases. — Gases  are  bodies  which,  unlike 
solids,  have  no  independent  shape,  and  unlike  liquids,  have  no  independent 
volume.  Their  molecules  possess  almost  perfect  mobility  ;  they  are  con- 
ceived as  darting  about  in  all  directions,  and  are  continually  tending  to 
occupy  a  greater  space.  This  property  of  gases  is  known  by  the  names 
expansibility,  tension,  or  elastic  force,  from  which  they  are  often  called  elastic 
fluids. 

Gases  and  liquids  have  several  properties  in  common,  and  some  in  which 
they  seem  to  differ  are  in  reality  only  different  degrees  of  the  same  property. 
Thus,  in  both,  the  particles  are  capable  of  moving  :  in  gases  with  almost 
perfect  freedom  ;  in  liquids  not  quite  so  freely,  owing  to  a  greater  degree  of 
viscosity.  Both  are  compressible,  though  in  very  different  degrees.  If  a 
liquid  and  a  gas  both  exist  under  the  pressure  of  one  atmosphere,  and  then 
the  pressure  be  doubled,  the  water  is  compressed  by  about  the  goibo  Part> 
while  the  gas  is  compressed  by  one-half.  In  density  there  is  a  great  dif- 
ference ;  water,  which  is  the  type  of  liquids,  is  770  times  as  heavy  as  air,  the 
type  of  gaseous  bodies,  while  under  the  pressure  of  one  atmosphere.  The 
property  by  which  gases  are  distinguished  from  liquids  is  their  tendency  to 
indefinite  expansion. 

Matter  assumes  the  solid,  liquid,  or  gaseous  form  according  to  the  rela- 
tive strength  of  the  cohesive  and  repulsive  forces  exerted  between  their 
molecules.  In  liquids  these  forces  balance  ;  in  gases  repulsion  preponderates. 

By  the  aid  of  pressure  and  of  low  temperatures,  the  force  of  cohesion 
may  be  so  far  increased  in  many  gases  that  they  are  readily  converted  into 
liquids,  and  we  know  now  that  with  sufficient  pressure  and  cold  they  may  all 
be  liquefied.  On  the  other  hand,  heat,  which  increases  the  vis  viva  of  the 
molecules,  converts  liquids,  such  as  water,  alcohol,  and  ether,  into  the  aeriform 
state  in  which  they  obey  all  the  laws  of  gases.  The  aeriform  state  of  liquids 
is  known  by  the  name  of  vapour ;  while  gases  are  bodies  which,  under  ordi- 
nary temperature  and  pressure,  remain  in  the  aeriform  state. 


-155] 


Weight  of  Gases. 


133 


In   describing  exclusively  the  properties  of  gases  we  shall,  for  obvious 
reasons,  refer  to  atmospheric  air  as  their  type. 

153-  Expansibility  of  gases.-This  property  of  gases,  their  tendency  to 
assume  continually  a  greater  volume,  is  exhibited  by  means  of  the  following 
experiment :— A  bladder,  closed  by  a  stop-cock  and  about  half-full  of  air  is 
placed  under  the  receiver  of  the  air-pump  (fig.  123),  and  a  vacuum  is  produced, 
on  which  the  bladder  immediately  distends. 
This  arises  from  the  fact.,  that  the  molecules 
of  air  flying  about  in  all  directions  (293) 
press  against  the  sides  of  the  bladder.  Under 
ordinary  conditions  this  internal  pressure  is 
counterbalanced  by  the  air  in  the  receiver, 
which  exerts  an  equal  and  contrary  pressure. 
But  when  this  pressure  is  removed,  by  ex- 
hausting the  receiver,  the  internal  pressure 
becomes  evident.  When  air  is  admitted  into 
the  receiver,  the  bladder  resumes  its  original 
form. 

154.  Compressibility  of  gases.— The 
compressibility  of  gases  is  readily  shown  by 
the  pneumatic  syringe  (fig.  124).  This  con- 
sists of  a  stout  glass  tube  closed  at  one  end, 
and  provided  with  a  tight-fitting  solid  piston. 
When  the  rod  of  the  piston  is  pressed  it 
moves  down  in  the  tube,  and  the  air  becomes 

compressed  into  a  smaller  volume  ;  but  as  soon  as  the  force  is  removed  the 
air  regains  its  original  volume,  and  the  piston  rises  to  its  former  position. 


Fig.  124. 

155.  Weight  of  gases. — From  their  extreme  fluidity  and  expansibility, 
gases  seem  to  be  uninfluenced  by  the  force  of  gravity  :  they  nevertheless 
possess  weight  like  solids  and  liquids.  To  show  this,  a  glass  globe  of  3  or  4 
quarts  capacity  is  taken  (fig.  125),  the  neck  of  which  is  provided  with  a  stop- 
cock, which  hermetically  closes  it,  and  by  which  it  can  be  screwed  to  the 
plate  of  the  air-pump.  The  globe  is  then  exhausted,  and  its  weight  deter- 
mined by  means  of  a  delicate  balance.  Air  is  now  allowed  to  enter,  and  the 
globe  again  weighed.  The  weight  in  the  second  case  will  be  found  to  be 
greater  than  before,  and  if  the  capacity  of  the  vessel  is  known,  the  increase 
will  obviously  be  the  weight  of  that  volume  of  air. 

By  a  modification  of  this  method,  and  with  the  adoption  of  certain  pre- 


134  On  Gases.  [155- 

cautions,  the  weight  of  air  and  of  other  gases  has  been  determined.  Perhaps 
the  most  accurate  are  those  of  Regnault,  who  found  that  a  litre  of  dry  air  at 
o°  C,  and  under  a  pressure  of  760  millimetres,  weighs  1-293187  grammes. 
•Since  a  litre  of  water  (or  1,000  cubic  centimetres)  at  o°  weighs  0-999877 
gramme,  the  density  of  air  is  0-00129334  that  of  water  under  the  same  circum- 
stances ;  that  is,  water  is  773  times  as  heavy  as  air.  Expressed  in  English 
measures,  100  cubic  inches  of  dry  air  under  the  ordinary  at- 
mospheric pressure  of  30  in.  and  at  the  temperature  of  16°  C. 
weigh  31  grains ;  the  same  volume  of  carbonic  acid  gas  under 
the  same  circumstances  weighs  47*25  grains ;  100  cubic 
inches  of  hydrogen,  the  lightest  of  all  gases,  weigh  2-14 
grains  ;  and  100  cubic  inches  of  hydriodic  acid  gas  weigh 
146  grains. 

156.  Pressures  exerted  by  gases. — Gases  exert  on  their 
own  molecules,  and  on  the  sides  of  vessels  which  contain 
them,  pressures  which  may  be  regarded  from  two  points 
of  view.  First,  we  may  neglect  the  weight  of  the  gas ; 
secondly,  we  may  take  account  of  its  weight.  If  we  neglect 
the  weight  of  any  gaseous  mass  at  rest,  and  only  consider  its 
expansive  force,  it  will  be  seen  that  the  pressures  due  to  this 
force  act  with  the  same  strength  on  all  points,  both  of  the 
mass  itself  and  of  the  vessel  in  which  it  is  contained.  For 
it  is  a  necessary  consequence  of  the  elasticity  and  fluidity 
of  gases,  that  the  repulsive  force  between  the  molecules  is 
the  same  at  all  points,  and  acts  equally  in  all  directions. 
This  principle  of  the  equality  of  the  pressure  of  gases  in 
all  directions  may  be  shown  experimentally  by  means  of  an  apparatus 
resembling  that  by  which  the  same  principle  is  demonstrated  for  liquids 
(fig.  65). 

If  we  consider  the  weight  of  any  gas,  we  shall  see  that  it  gives  rise  to 
pressures  which  obey  the  same  laws  as  those  produced  by  the  weight  of 
liquids.  Let  us  imagine  a  cylinder,  with  its  axis  vertical,  several  miles  high, 
closed  at  both  ends  and  full  of  air.  Let  us  consider  any  small  portion  of 
the  air  enclosed  between  two  horizontal  planes.  This  portion  must  sustain 
the  weight  of  all  the  air  above  it,  and  transmit  that  weight  to  the  air  beneath 
it,  and  likewise  to  the  curved  surface  of  the  cylinder  which  contains  it,  and 
at  each  point  in  a  direction  at  right  angles  to  the  surface.  Thus  the  pressure 
increases  from  the  top  of  the  column  to  the  base  ;  at  any  given  layer  it 
acts  equally  on  equal  surfaces,  and  at  right  angles  to  them,  whether  they 
are  horizontal,  vertical,  or  inclined.  The  pressure  acts  on  the  sides  of 
the  vessel,  and  on  any  small  surface  it  is  equal  to  the  weight  of  a  column 
of  gas  whose  base  is  this  surface,  and  whose  height  its  distance  from  the 
summit  of  the  column.  The  pressure  is  also  independent  of  the  shape  and 
dimensions  of  the  supposed  cylinder,  provided  the  height  remains  the  same. 
For  a  small  quantity  of  gas  the  pressures  due  to  its  weight  are  quite  in- 
significant, and  may  be  neglected  ;  but  for  large  quantities,  like  the  atmo- 
sphere, the  pressures  are  considerable,  and  must  be  allowed  for. 

157-  The  atmosphere  :  its  composition. — The  atmosphere  is  the  layer 
of  air  which  surrounds  our  globe  in  every  part.     It  partakes  of  the  rotatory 


Fig.  125. 


-158]  Atmospheric  Pressure.  135 

motion  of  the  globe,  and  would  remain  fixed  relatively  to  terrestrial  objects 
but  for  local  circumstances,  which  produce  winds,  and  are  constantly  dis- 
turbing its  equilibrium. 

It  is  essentially  a  mixture  of  oxygen  and  nitrogen  gases  ;  its  average  com- 
position by  volume  being  as  follows  : — 

Nitrogen '  .  '    '.    "    '.  .  78-49 

Oxygen ,.  :..^  ,  ",...  .  20-63 

Aqueous  vapour        .         .     •    .         ....    ,,    ,    ..  *      .  .  o-g^ 

Carbonic  acid  ....         ..   ..    .       ...     .....  .  0-04 

100-00 

The  carbonic  acid  arises  from  the  respiration  of  animals,  from  the  pro- 
cesses of  combustion,  and  from  the  decomposition  of  organic  substances. 
Boussingault  estimated  that  in  Paris  the  following  quantities  of  carbonic 
acid  are  produced  every  24  hours  : — 

By  the  population  and  by  animals  .         .     11,895,000  cubic  feet 
By  processes  of  combustion   .         .         .     92,101,000       „ 

103,996,000      „ 

Notwithstanding  this  enormous  continual  production  of  carbonic  acid 
the  composition  of  the  atmosphere  does  not  vary ;  for  plants  in  the  process 
of  vegetation  decompose  the  carbonic  acid,  assimilating  the  carbon,  and 
restoring  to  the  atmosphere  the  oxygen,  which  is  being  continually  consumed 
in  the  processes  of  respiration  and  combustion. 

158.  Atmospheric  pressure. — If  we  neglect  the  perturbations  to  which 
the  atmosphere  is  subject,  as  being  inconsiderable,  we  may  consider  it 
as  a  fluid  sea  of  a  certain  depth,  surrounding  the  earth  on  all  sides,  and 
exercising  the  same  pressure  as  if  it  were  a  liquid  of  very  small  density. 
•Consequently  the  pressure  on  the  unit  of  area  is  constant  at  a  given  level, 
facing  equal  to  the  weight  of  the  column  of  atmosphere  above  that  level 
whose  horizontal  section  is  the  unit  of  area  (99).  It  will  act  at  right  angles 
to  the  surface,  whatever  be  its  position.  It  will  diminish  as  we  ascend,  and 
increase  as  we  descend  from  that  level.  Consequently,  at  the  same  height, 
the  atmospheric  pressures  on  unequal  plane  surfaces  will  be  proportional  to 
the  areas  of  those  surfaces,  provided  they  be  small  in  proportion  to  the 
height  of  the  atmosphere. 

In  virtue  of  the  expansive  force  of  the  air,  it  might  be  supposed  that  the 
molecules  would  expand  indefinitely  into  the  planetary  spaces.  But,  in  pro- 
portion as  the  air  expands,  its  expansive  force  decreases,  and  is  further 
weakened  by  the  low  temperature  of  the  upper  regions  of  the  atmosphere,  so 
that,  at  a  certain  height,  equilibrium  is  established  between  the  expansive 
force  which  separates  the  molecules,  and  the  action  of  gravity  which  draws 
them  towards  the  centre  of  the  earth.  It  is  therefore  concluded  that  the 
atmosphere  is  limited. 

From  the  weight  of  the  atmosphere,  and  its  increase  in  density,  and  from 
the  observation  of  certain  phenomena  of  twilight,  its  height  has  been  esti- 
mated at  from  30  to  40  miles.  Above  that  height  the  air  is  extremely  rarefied, 
and  at  a  height  of  60  miles  it  is  assumed  that  there  is  a  perfect  vacuum.  On 


136 


On  Gases. 


[158- 


the  other  hand,  meteorites  have  been  seen  at  a  height  of  200  miles,  and  as 
their  luminosity  is  undoubtedly  due  to  friction  against  air,  there  must  be  air  at 
such  a  height.  This  higher  estimate  is  supported  by  observations  made 
at  Rio  Janeiro  on  the  twilight  arc,  by  M.  Liais,  who  estimated  the 
height  of  the  atmosphere  at  between  198  and  212  miles.  The  question  as  to 
the  exact  height  of  the  atmosphere  must  therefore  be  considered  as  still 
awaiting  settlement. 

As  it  has  been  previously  stated  that  100  cubic  inches  of  air  weigh  31 
grains,  it  will  readily  be  conceived  that  the  whole  atmosphere  exercises  a 
considerable  pressure  on  the  surface  of  the  earth.  The  existence  of  this 
pressure  is  shown  by  the  following  experiments. 

1 59.  Crushing:  force  of  the  atmosphere. — On  one  end  of  a  stout  glass 
cylinder,  about  5  inches  high,  and  open  at  both  ends,  a  piece  of  bladder  is 
tied  quite  airtight.  The  other  end,  the  edge  of  which  is  ground  and  well 
greased,  is  pressed  on  the  plate  of  the  air-pump  (fig.  126).  As  soon  as  the 
air  in  the  vessel  is  rarefied  by  working  the  air-pump,  the  bladder  is  depressed 
by  the  weight  of  the  atmosphere  above  it,  and  finally  bursts  with  a  loud 
report  caused  by  the  sudden  entrance  of  the  air. 


Fig.  126. 


Fig.  127. 


Fig.  128. 


1 60.  Magdeburg  hemispheres. — The  preceding  experiment  only  serves 
to  illustrate  the  downward  pressure  of  the  atmosphere.  By  means  of  the 
Magdeburg  hemispheres  (figs.  127  and  128),  the  invention  of  which  is  due  to 
Otto  von  Guericke,  burgomaster  of  Magdeburg,  it  can  be  shown  that  the 
pressure  acts  in  all  directions.  This  apparatus  consists  of  two  hollow  brass 
hemispheres  of  4  to  4^  inches  diameter,  the  edges  of  which  are  made  to  fit 
tightly,  and  are  well  greased.  One  of  the  hemispheres  is  provided  with  a 
stop-cock,  by  which  it  can  be  screwed  onto  the  air-pump,  and  on  the  other  there 
is  a  handle.  As  long  as  the  hemispheres  contain  air  they  can  be  separated 


-162] 


Pascal's  Experiments. 


137 


without  any  difficulty,  for  the  external  pressure  of  the  atmosphere  is  counter- 
balanced by  the  elastic  force  of  the  air  in  the  interior.  But  when  the  air  in 
the  interior  is  pumped  out  by  means  of  the  air-pump,  the  hemispheres 
cannot  be  separated  without  a  powerful  effort  ;  and  as  this  is  the  case  in 
whatever  position  they  are  held,  it  follows  that  the  atmospheric  pressure  is 
transmitted  in  all  directions. 


DETERMINATION   OF  THE  ATMOSPHERIC  PRESSURE.      BAROMETERS, 
v/ 

'     161.  Torricelli's  experiment. — The  above  experiments  demonstrate  the 
existence  of  the  atmospheric  pressure,  but  they  give  no  precise  indication 
as  to  its  amount.     The  following  experiment,  which  was  first  made,  in  1643, 
by  Torricelli,  a  pupil  of  Galileo,  gives  an 
exact  measure  of  the  weight  of  the  atmo- 
sphere. 

A  glass  tube  is  taken,  about  a  yard 
long  and  a  quarter  of  an  inch  internal 
diameter  (fig.  129).  It  is  sealed  at  one 
end,  and  is  quite  filled  with  mercury. 
The  aperture  C  being  closed  by  the 
thumb,  the  tube  is  inverted,  the  open  end 
placed  in  a  small  mercury  trough,  and 
the  thumb  removed.  The  tube  being  in 
a  vertical  position,  the  column  of  mercury 
sinks,  and,  after  oscillating  some  time,  it 
finally  comes  to  rest  at  a  height  A,  which 
at  the  level  of  the  sea  is  about  30  inches 
above  the  mercury  in  the  trough.  The 
mercury  is  raised  in  the  tube  by  the 
pressure  of  the  atmosphere  on  the  mer- 
cury in  the  trough.  There  is  no  contrary 
pressure  on  the  mercury  in  the  tube, 
because  it  is  closed  ;  but  if  the  fend  of 
the  tube  be  opened,  the  atmosphere  will 
press  equally  inside  and  outside  the  tube, 
and  the  mercury  will  sink  to  the  level  of 
that  in  the  trough.  It  has  been  shown  in 
hydrostatics  (107)  that  '  the  heights  ^  of 
two  columns  of  liquid  in  communication 
with  each  other  are  inversely  as  their 
densities,  and  hence  it  follows  that  the 


Fig.  129. 


,      CUAU      ±JH~iJlv_\_      -it    .  j.vyj.Av-'  »•  , 

pressure  of  the  atmosphere  is  equal  to  that  of  a  column  of  mercury,  th 
height  of  which  is  30  inches.     If,  however,  the  weight  of  the  atmosphere 
diminishes,  the  height  of  the  column  which  it  can  sustain  must  also  diminish 

162.  Pascal's  experiments.-Pascal,  who  wished  to  ascertain  * 
?L  force  which  sustained  the  mercury  in  the  tube  was  really  the  pressu 
the  atmosphere,  made  the  following  experiments,     (i )   If  it  w         he  case 
the  column  of  mercury  ought  to  descend  m  proportion  as ,  *e ascend m 
the  atmosphere.     He  accordingly  requested  one  of  his  relatives  tc 


138  On  Gases.  [162- 

Torricelli's  experiment  on  the  summit  of  Puy  de  Dome  in  Auvergne. 
This  was  done,  and  it  was  found  that  the  mercurial  column  was  about  3 
inches  lower,  thus  proving  that  it  is  really  the  weight  of  the  atmosphere 
which  supports  the  mercury,  since,  when  this  weight  diminishes,  the  height 
of  the  column  also  diminishes,  (ii.)  Pascal  repeated  Torricelli's  experiment 
at  Rouen,  in  1646,  with  other  liquids.  He  took  a  tube  closed  at  one  end 
nearly  50  feet  long,  and,  having  filled  it  with  water,  placed  it  vertically  in  a 
vessel  of  water,  and  found  that  the  water  stood  in  the  tube  at  a  height  of 
34  feet  ;  that  is,  13-6  times  as  high  as  mercury.  But  since  the  mercury  is  13-6 
times  as  heavy  as  water,  the  height  of  the  column  of  water  was  exactly 
equalto  that  of  a  column  of  mercury  in  Torricelli's  experiment,  and  it  was 
consequently  the  same  force,  the  pressure  of  the  atmosphere,  which  succes- 
sively supported  the  two  liquids.  Pascal's  other  experiments  with  oil  and 
with  wine  gave  similar  results. 

y'""1  163.  Amount  of  the  atmospheric  pressure. — Let  us  assume  that  the 
tube  in  the  above  experiment  is  a  cylinder,  the  section  of  which  is  equal  to  a 
square  inch  ;  then,  since  the  height  of  the  mercurial  column  in  round  num- 
bers is  30  inches,  the  column  will  contain  30  cubic  inches  ;  and  as  a  cubic 
inch  of  mercury  weighs  3433*5  grains  =0-49  of  a  pound,  the  pressure  of  such 
a  column  on  a  square  inch  of  surface  is  equal  to  147  pounds.  In  round 
numbers  the  pressure  of  the  atmosphere  is  taken  at  1 5  pounds  on  the  square 
inch.  A  surface  of  a  foot  square  contains  144  square  inches,  and  therefore 
the  pressure  upon  it  is  equal  to  2,160  pounds,  or  nearly  a  ton.  Expressed 
in  the  metrical  system,  the  standard  atmospheric  pressure  at  o°  and  the  sea- 
level  is  760  millimetres,  which  is  equal  to  29-9217  inches  ;  and  a  calculation 
similar  to  the  above  shows  that  the  pressure  on  a  square  centimetre  is  = 
1*032896  kilogramme. 

A  gas  or  liquid  which  acts  in  such  a  manner  that  a  square  inch  of  surface 
is  exposed  to  a  pressure  of  1 5  pounds,  is  called  a  pressure  of  one  atmosphere. 
If,  for  instance,  the  elastic  force  of  the  steam  of  a  boiler  is  so  great  that  each 
square  inch  of  the  internal  surface  is  exposed  to  a  pressure  of  90  pounds 
(  =  6  x  15),  we  say  it  is  under  a  pressure  of  six  atmospheres. 

The  surface  of  the  body  of  a  man  of  middle  size  is  about  16  square  feet ; 
the  pressure,  therefore,  which  a  man  supports  on  the  surface  of  his  body  is 
35,560  pounds,  or  nearly  16  tons.  Such  an  enormous  pressure  might  seem 
impossible  to  be  borne  ;  but  it  must  be  remembered  that,  in  all  directions, 
there  are  equal  and  contrary  pressures  which  counterbalance  one  another. 
It  might  also  be  supposed  that  the  effect  of  this  force,  acting  in  all  directions, 
would  be  to  press  the  body  together  and  crush  it.  But  the  solid  parts  of  the 
skeleton  could  resist  a  far  greater  pressure  ;  and  as  to  the  air  and  liquids 
contained  in  the  organs  and  vessels,  the  air  has  the  same  density  as  the 
external  air,  and  cannot  be  further  compressed  by  the  atmospheric  pressure  ; 
.and  from  what  has  been  said  about  liquids  (97),  it  is  clear  that  they  are  vir- 
tually incompressible.  When  the  external  pressure  is  removed  from  any  part 
of  the  body,  either  by  means  of  a  cupping  vessel  or  by  the  air-pump,  the 

rssure  from  within  is  seen  by  the  distension  of  the  surface. 
164.  Different  kinds  of  barometers. — The  instruments  used  for  measur- 
ing the  atmospheric  pressure  are  called  barometers.     In  ordinary  barometers 
the  pressure  is  measured  by  the  height  of  a  column  of  mercury,  as  in  Torri- 


-165] 


Cistern  Barometer. 


139 


•celli's  experiment :  the  barometers  which  we  are  about  to  describe  are  of  this 
kind.  But  there  are  barometers  without  any  liquid,  one  of  which,  the  aneroid 
(187),  is  remarkable  for  its  simplicity  and  portability. 

\T  165.  Cistern  barometer. — The  cistern  barometer  consists  of  a  straight 
glass  tube  closed  at  one  end,  about  33  inches  long,  filled  with  mercury,  and 
•dipping  into  a  cistern  containing  the  same  metal.  In  order  to  render  the 
barometer  more  portable,  and  the  variations  of  the  level  in  the  cistern  less 
perceptible  when  the  mercury  rises  or  falls  in  the  tube,  several  different 


Fig.I3o. 


""rTefeTone  fault  to  which  this  barometer  is  liab.e,  in  common  with  all 


140  On  Gases.  [165— 

others  of  the  same  kind.  The  zero  of  the  scale  does  not  always  correspond 
to  the  level  of  the  mercury  in  the  cistern.  For,  as  the  atmospheric  pressure 
is  not  always  the  same,  the  height  of  the  mercurial  column  varies  ;  some- 
times mercury  is  forced  from  the  cistern  into  the  tube,  and  sometimes  from 
the  tube  into  the  cistern,  so  that  in  the  majority  of  cases,  the  graduation  of 
the  barometer  does  not  indicate  the  true  height.  If  the  diameter  of  the 
cistern  is  large,  relatively  to  that  of  the  tube,  the  error  from  this  source,  which 
is  known  as  the  error  of  capacity,  is  lessened. 

The  height  of  the  barometer  is  the  distance  between  the  levels  of  the 
mercury  in  the  tube  and  in  the  cistern.  Hence  the  barometer  should 
always  be  perfectly  vertical,  for  if  not,  the  tube  being  inclined,  the  column  of 
mercury  is  elongated  (fig.  131),  and  the  number  read  off  on  the  scale  is  too- 
great.  As  the  pressure  which  the  mercury  exerts  by  its  weight  at  the  base 
of  the  tube  is  independent  of  the  form  of  the  tube  and  of  its  diameter  (101), 
provided  it  is  not  capillary,  the  height  of  the  barometer  is  independent  of 
the  diameter  of  the  tube  and  of  its  shape,  but  is  inversely  as  the  density  of 
the  liquid.  With  mercury  the  mean  height  at  the  level  of  the  sea  is  29-92, 
or  in  round  numbers  30,  inches  ;  in  a  water  barometer  it  would  be  about  34 
feet,  or  10-33  metres. 

In  marine  barometers  the  error  of  capacity  is  got  rid  of  by  graduating  the 
scale  not  in  the  true  measurements,  but  by  an  empirical  correction  depending 
on  the  relative  diameters  of  the  tube  and  cistern.  Thus  if  arise  of  10  mm. 
in  the  tube  produced  a  fall  of  I  mm.  in  the  cistern,  the  true  change  would  not 
be  10  mm.  but  n  mm.  This  is  obviously  allowed  for  by  dividing  the  space 
of  10  mm.  on  the  scale  into  1 1  mm.  The  correctness  of  such  an  instrument 
depends  on  the  accuracy  with  which  the  scale  is  laid  off. 
^  1 66.  Fortin's  barometer. — Fortiris  barometer  differs  in  the  shape  of 
the  cistern  from  that  just  described.  The  base  of  the  cistern  is  made  of 
leather,  and  can  be  raised  or  lowered  by  means  of  a  screw  ;  this  has  the 
advantage  that  a  constant  level  can  be  obtained,  and  also  that  the  instru- 
ment is  made  more  portable.  For,  in  travelling,  it  is  only  necessary  to 
raise  the  leather  until  the  mercury,  which  rises  with  it,  quite  fills  the  cistern  ; 
the  barometer  may  then  be  inclined,  and  even  inverted,  without  any  fear 
that  a  bubble  of  air  may  enter,  or  that  the  shock  of  the  mercury  may  crack 
the  tube. 

Fig.  132  represents  the  arrangement  of  the  barometer,  the  tube  of  which 
is  placed  in  a  brass  case.  At  the  top  of  this  case  there  are  two  longitudinal 
apertures,  on  opposite  sides,  so  that  the  level  of  the  mercury,  B,  is  seen. 
The  scale  on  the  case  is  graduated  in  millimetres.  An  index  A,  moved  by  the 
hand,  gives,  by  means  of  a  vernier,  the  height  of  the  mercury  to  ~th  of  a  milli- 
metre. At  the  bottom  of  a  case  there  is  a  cistern  b,  containing  mercury  o. 

Fig.  133  shows  the  details  of  the  cistern  on  a  larger  scale.  It  consists  of 
a  glass  cylinder  b,  through  which  the  mercury  can  be  seen  ;  this  is  closed  at 
the  top  by  a  boxwood  disc  fitted  on  the  under  surface  of  the  brass  cover  M. 
Through  this  passes  the  barometer  tube  E,  which  is  drawn  out  at  the  end, 
and  dips  in  the  mercury  ;  the  cistern  and  the  tube  are  connected  by  a  piece 
of  buckskin  ce,  which  is  firmly  tied  at  c  to  a  contraction  in  the  tube,  and  at  e 
to  a  brass  tubulure  in  the  cover  of  the  cistern.  This  mode  of  closing 
prevents  the  mercury  from  escaping  when  the  barometer  is  inverted,  while 


-167]  Gay-Lussads  Syphon  Barometer.  141 

the  pores  of  the  leather  transmit  the  atmospheric  pressure.  The  bottom  of 
the  cylinder  b  is  cemented  on  a  boxwood  cylinder  zz,  on  a  contraction  in 
which,  z'z,  is  firmly  tied  the  buckskin  ;;/«,  which  forms  the  base  of  the  cistern. 
On  this  skin  is  fastened  a  wooden  button  x,  which  rests  against  the  end  of 
a  screw  C.  According  as  this  is  turned  in  one  direction  or  the  other,  the 
skin  mn  is  raised  or  lowered,  and  with  it  the  mercury.  In  using  this  baro- 
meter the  mercury  is  first  made  exactly  level  with  the  point  #,  which  is 
effected  by  turning  the  screw  C  either  in  one  direction  or  the  other.  The 
graduation  of  the  scale  is 
counted  from  this  point  a, 
and  thus  the  distance  of 
the  top  B  of  the  column  of 
mercury  from  a  gives  the 
height  of  the  barometer. 
The  bottom  of  the  cistern 
is  surrounded  by  a  brass 
case,  which  is  fastened  to 
the  cover  M  by  screws,  £, 
/&,  k.  We  have  already 
seen  (165)  the  importance 
of  having  the  barometer 
quite  vertical,  which  is 
effected  by  the  following 
plan,  known  as  Cardaris 
suspension. 

The  metal  case  contain- 
ing the  barometer  is  fixed 

In  a  copper  sheath  X  by 

two   screws   a  and    b  (fig. 

134).      This     is    provided 

with  two  axles  (only  one  of 

which,   0,    is   seen    in   the 

figure),  which  turn  freely  in 

two  holes  in  a  ring  Y.     In 

a  direction  at  right  angles 

to  that  of  the  axles,  00,  the 

ring  has  also  two  similar 

axles,  m  and  n,  resting  on 

a   support  Z.     By  means   of  this 

oscillate  freely  about  the  axes,  mn  and  oo,  in  two  directions  at  right  angle 

each  other.     But  as  care  is  taken  that  the  point  at  which  these  axes  cross 

corresponds  to  the  tube  itself,  the  centre  of  gravity  of  the  system,  whi 

must  always  be  lower  than  the  axis  of  suspension,  is  below  the  point  c 

section,  and  the  barometer  is  thus  perfectly  vertical. 

<   167.  Gay-Xmssac's    sypHon  barometer.-The  syphon  baromete 

bent  glass  tube,  one  of  the  branches  of  which  is  much  longer  than  the  other. 

The  longer  branch,  which  is  closed  at  the  top,  is  filled  with  mercury  as  in  the 

cistern   barometer,  while  the  shorter  branch,  which  - 

cistern.   The  difference  between  the  two  levels  is  the 


Fig.  133-  F'S-  '34- 

double  suspension   the  barometer  can 


142  On  Gases.  [167- 

Fig.  135  represents  the  syphon  barometer  as  modified  by  Gay-Lussac. 
In  order  to  render  it  more  available  for  travelling  by  preventing  the  entrance 
of  air,  he  joined  the  two  branches  by  a  capillary  tube  (fig.  136) ;  when  the 
instrument  is  inverted  (fig.  137)  the  tube  always  remains  full  in  virtue  of  its 
capillarity,  and  air  cannot  penetrate  into  the  longer  branch.  A  sudden 
shock,  however,  might  separate  the  mercury  and  admit  some  air.  To  avoid 
this,  Bunten  introduced  an  ingenious  modification  into  the  apparatus.  The 


Fig.  136. 


Fig.  137. 


Fig.  139- 


V 


longer  branch  is  drawn  out  to  a  fine  point,  and  is  joined  to  a  tube  B  of  the 
form  represented  in  fig.  138.  This  arrangement  forms  an  air-trap  ;  for  if  air 
passes  through  the  capillary  tube  it  cannot  penetrate  the  drawn-out  extremity 
of  the  longer  branch,  but  lodges  in  the  upper  part  of  the  enlargement  B. 
In  this  position  it  does  not  affect  the  observations,  since  the  vacuum  is 
always  at  the  upper  part  of  the  tube  ;  it  is,  moreover,  easily  removed. 

In  the  syphon   barometer  the  shorter  branch  is  closed,  but  there  is  a 


-169]  Correction  for  Capillarity. 

capillary  aperture  in  the  side  z,  through  which  the  atmospheric  pressure  is 
transmitted. 

The  barometric  height  is  determined  by  means  of  two  scales,  which  have 
a  common  zero  at  O,  towards  the  middle  of  the  longer  branch,  and  are  gra- 
duated in  contrary  directions,  the  one  from  O  to  E,  and  the  other  from  O  to 
B,  either  on  the  tube  itself,  or  on  brass  rules  fixed  parallel  to  the  tube.  Two 
sliding  verniers,  m  and  n,  indicate  tenths  of  a  millimetre.  The  total  height  of 
the  barometer,  AB,  is  the  sum  of  the  distances  from  O  to  A  and  from  O  to  B. 

Fig.  139  represents  a  very  convenient  mode  of  arranging  the  open  end  of 
a  syphon  barometer  for  transport.  The  quantity  of  mercury  is  so  arranged 
that  when  the  Torricellian  space  is  quite  filled  with  mercury,  by  inclining  the 
tube  the  enlargement  is  just  filled  to  d.  This  is  closed  by  a  carefully  fitted 
cork  fixed  on  the  end  of  a  glass  tube  about  a  millimetre  in  the  clear,  which 
allows  for  the  expansion  of  mercury  by  heat.  When  the  barometer  is  to  be 
us_ed,  the  cork  and  tube  are  raised. 

X  1 68.  Precautions  in  reference  to  barometers. — In  constructing  baro- 
meters mercury  is  chosen  in  preference  to  any  other  liquid,  for,  being  the 
densest  of  all  liquids,  it  stands  at  the  least  height.  When  the  mercurial 
barometer  stands  at  30  inches,  the  water  barometer  would  stand  at  about 
34  feet  (165).  It  also  deserves  preference  because  it  does  not  moisten  the 
glass.  It  is  necessary  that  the  mercury  be  pure  and  free  from  oxide,  other- 
wise it  adheres  to  the  glass  and  tarnishes  it.  Moreover,  if  it  is  impure  its 
density  is  changed,  and  the  height  of  the  barometer  is  too  great  or  too  small. 
Mercury  is  purified,  before  being  used  for  barometers,  by  treatment  with 
dilute  nitric  acid,  and  by  distillation. 

The  space  at  the  top  of  the  tube  (figs.  130  and  135),  which  is  called  the 
Torricellian  vacuum,  must  be  quite  free  from  air  and  from  aqueous  vapour, 
for  otherwise  either  would  depress  the  mercurial  column  by  its  elastic  force. 
To  obtain  this  result,  a  small  quantity  of  pure  mercury  is  placed  in  the  tube 
and  boiled  for  some  time.  It  is  then  allowed  to  cool,  and  a  further  quantity, 
previously  warmed,  added,  which  is  boiled,  and  so  on,  until  the  tube  is  quite 
full ;  in  this  manner  the  moisture  and  the  air  which  adhere  to  the  sides  of  the 
tube  (193)  pass  off  with  the  mercurial  vapour.  A  barometer  tube  should  not 
be  too  narrow,  for  otherwise  the  mercury  is  moved  with  difficulty ;  and  before 
reading  off,  the  barometer  should  be  tapped  so  as  to  get  rid  of  the  adhesion 
to  the  glass. 

A  barometer  is  free  from  air  and  moisture  if,  when  it  is  inclined,  the 
mercury  strikes  with  a  sharp  metallic  sound  against  the  top 
of  the  tube.     If  there  is  air  or  moisture  in  it,  the  sound  is 
deadened. 

\j  169.  Correction  for  capillarity.— In  cistern  barometers 
there  is  always  a  certain  depression  of  the  mercurial  column 
due  to  capillarity,  unless  the  internal  diameter  of  the  tube 
exceeds  0-8  inch.  To  make  the  correction  due  to  this 
depression,  it  is  not  enough  to  know  the  diameter  of  the 
tube  ;  we  must  also  know  the  height  of  the  meniscus  od  (fig. 
140),  which  varies  according  as  the  meniscus  has  been 
formed  during  an  ascending  or  descending  motion  of  the  mercury  i 
tube.  Consequently  the  height  of  the  meniscus  must  be  determined  by 


144 


On  Gases. 


[169- 


bringing  the  pointer  to  the  level  ab,  and  then  to  the  level  d,  when  the  differ- 
ence of  the  readings  will  give  the  height  od  required.  These  two  terms — 
namely,  the  internal  diameter  of  the  tube  and  the  height  of  the  meniscus — 
being  known,  the  resulting  correction  can  be  taken  out  of  the  following 
table  : 


Internal 

Height  of  sagitta  of  meniscus  in  inches 

in  inches 

O'OIO 

0*015 

O'O2O 

o'O25                o'o3O                0*035 

0*040 

0-157 

0-0293 

0-043I 

0^555 

I                        i 
0-0677         0-0780         0*0870 

0-0948 

0*236 

0-0119 

0-OI76 

0-023  l 

0-0294         0-0342    '     0-0398 

0*0432 

0-315 

0-0060 

0-0088 

O'OIlS 

0-0144    |     0-0175         0-OI96 

0*0221 

Q'394 

0-0039 

0*0048 

0-0063 

0*0078       0-0095       0*0110 

O'OI25 

0-472 

O'OO2O 

0-0029 

0-0036 

0*0045       0-0053       0-0063 

0-0073 

0-550 

O'OOIO 

0-0017 

O*OO24 

0*0029       0-0034       0*0039 

0*0044 

In  the  syphon  barometer  the  two  tubes  are  of  the  same  diameter,  so 
that  the  error  caused  by  the  depression  in  the  one  tube  very  nearly  corrects 
that  caused  by  the  depression  in  the  other.  As,  however,  the  meniscus  in 
the  one  tube  is  formed  by  a  column  of  mercury  with  an  ascending  motion, 
while  that  in  the  other  is  formed  by  a  column  with  a  descending  motion, 
their  heights  will  not  be  the  same,  and  the  reciprocal  correction  will  not  be 
quite  exact. 

170.  Correction  for  temperature. — In  all  observations  with  barometers, 
whatever  be  their  construction,  a  correction  must  be  made  for  temperature. 
Mercury  contracts    and   expands   with    different    temperatures,   hence    its 
density  changes,  and  consequently  the  barometric  height,  for  this  height  is 
inversely  as  the  density  of  the  mercury,  so  that  for  different  atmospheric 
pressures  the  mercurial  column  might  have  the  same  height.     Accordingly, 
in  each  observation  the  height  observed  must  be  reduced  to  a  determinate 
temperature.     The  choice  of  this  is  quite  arbitrary,  but  that  of  melting  ice  is 
always  adopted  in  practice.     It  will  be  seen,  in  the  Book  on  Heat,  how  this 
correction  is  made. 

171.  Variations  in  the  height  of  the  barometer. — When  the  barometer 
is  observed  for  several  days,  its  height  is  found  to  vary  in  the  same  place, 
not  only  from  one  day  to  another,  but  also  during  the  same  day. 

The  extent  of  these  variations — that  is,  the  difference  between  the  greatest 
and  the  least  height — is  different  in  different  places.  It  increases  from  the 
equator  towards  the  poles.  Except  under  extraordinary  circumstances,  the 
greatest  variations  do  not  exceed  six  millimetres  under  the  equator,  30  under 
the  tropic  of  Cancer,  40  in  France,  and  60  at  25  degrees  from  the  pole.  The 
greatest  variations  are  observed  in  winter. 

The  mean  daily  height  is  the  height  obtained  by  dividing  the  sum  of  24 
successive  hourly  observations  by  24.  In  our  latitudes  the  barometric  height 
at  noon  corresponds  to  the  mean  daily  height. 

The  mean  monthly  height  is  obtained  by  adding  together  the  mean  daily 
heights  for  a  month,  and  dividing  by  30.  The  mean  yearly  height  is  simi- 
larly obtained. 

Under  the  equator,  the  mean  annual  height  at  the  level  of  the  sea  is 


-173]        Relations  of  Barometric  Variations  to  Weather.          145 

0-758,  or  29-84  inches.     It  increases  from  the  equator,  and  between  the 
Etudes  30°  and  40'  it  attains  a  maximum  of  0-763,  or  30*04  inches      In 
lower  latitudes  it  decreases,  and  in  Paris  it  does  not  exceed  0-7568 
The  general  mean  at  the  level  of  the  sea  is  o™76i,  or  29-96  inches 
The  mean  monthly  height  is  greater  in  winter  than  in  summer,  in 'conse 
quence  of  the  cooler  atmosphere. 

Two  kinds  of  variations  are  observed  in  the  barometer  :— ist  the  acci 
dental  variations,  which  present  no  regularity  ;  they  depend  on  the  seasons 
the  direction  of  the  winds,  and  the  geographical  position,  and  are  common 
in  our  climates  ;  2nd,  the  daily  -variations,  which  are  produced  periodically 
at  certain  hours  of  the  day. 

At  the  equator,  and  between  the  tropics,  no  accidental  variations  are 
observed  ;  but  the  daily  variations  take  place  with  such  regularity  that  a 
barometer  may  serve  to  a  certain  extent  as  a  clock.  The  barometer  sinks 
from  midday  till  towards  four  o'clock;  it  then  rises,  and  reaches  its  maximum 
at  about  four  o'clock  in  the  evening.  It  then  again  sinks,  and  reaches  a 
second  minimum  towards  four  o'clock  in  the  morning,  and  a  second  maxi- 
mum at  ten  o'clock.  In  the  temperate  zones  there  are  also  daily  variations, 
but  they  are  detected  with  difficulty,  since  they  occur  in  conjunction  with 
accidental  variations. 

The  hours  of  the  maxima  and  minima  appear  to  be  the  same  in  all 
climates,  whatever  be  the  latitude  ;  they  merely  vary  a  little  with  the  seasons. 
172.  Causes  of  barometric  variations. — It  is  observed  that  the  course 
of  the  barometer  is  generally  in  the  opposite  direction  to  that  of  the  thermo- 
meter ;  that  is,  that  when  the  temperature  rises,  the  barometer  falls,  and  vice 
versa  ;  which  indicates  that  the  barometric  variations  at  any  given  place  are 
produced  by  the  expansion  or  contraction  of  the  air,  and  therefore  by  its 
change  in  density.  If  the  temperature  were  the  same  throughout  the  whole 
extent  of  the  atmosphere,  no  currents  would  be  produced,  and  at  the  same 
height,  atmospheric,  pressure  would  be  everywhere  the  same.  But  when 
any  portion  of  the  atmosphere  becomes  warmer  than  the  neighbouring  parts, 
its  specific  gravity  is  diminished,  and  it  rises  and  passes  away  through 
the  upper  regions  of  the  atmosphere,  whence  it  follows  that  the  pressure 
is  diminished,  and  the  barometer  falls.  If  any  portion  of  the  atmosphere 
retains  its  temperature,  while  the  neighbouring  parts  become  cooler,  the  same 
effect  is  produced  ;  for  in  this  case,  too,  the  density  of  the  first-mentioned 
portion  is  less  than  that  of  the  others.  Hence,  also,  it  usually  happens  that 
an  extraordinary  fall  of  the  barometer  at  one  place  is  counterbalanced  by  an 
extraordinary  rise  at  another  place.  The  daily  variations  appear  to  result 
from  the  expansions  and  contractions  which  are  periodically  produced  in 
the  atmosphere  by  the  heat  of  the  sun  during  the  rotation  of  the  earth. 

173.  Relation  of  barometric  variations  to  the  state  of  the  weather. — 
It  has  been  observed  that,  in  our  climate,  the  barometer  in  fine  weather  is 
generally  above  30  inches,  and  is  below  this  point  when  there  is  rain,  snow, 
wind,  or  storm  ;  and  also,  that  for  any  given  number  of  days  at  which  the 
barometer  stands  at  30  inches,  there  are  as  many  fine  as  rainy  days.  From 
this  coincidence  between  the  height  of  the  barometer  and  the  state  of  the 
weather,  the  following  indications  have  been  marked  on  the  barometer, 
counting  by  thirds  of  an  inch  above  and  below  30  inches  : — 

L 


146 


On  Gases. 


[173 


Height 

31  inches 


30  „ 

29§  „ 

295  „ 

29  „ 


State  of  the  weather 

Very  dry. 
Settled  weather. 
Fine  weather. 
Variable. 
Rain  or  wind. 
Much  rain. 
Tempest. 


In  using  the  barometer  as  an  indicator  of  the  state  of  the  weather,  we 
must  not  forget  that  it  really  only  serves  to  measure  the  weight  of  the  atmo- 
sphere, and  that  it  only  rises  or  falls  as  the  weight  increases  or  diminishes  ; 
and  although  a  change  of  weather  frequently  coincides  with  a  change  in  the 
pressure,  they  are  not  necessarily  connected.  This  coincidence  arises  from 
meteorological  conditions  peculiar  to  our  climate,  and  does  not  occur  every- 
where. That  a  fall  in  the  barometer  usually  precedes  rain  in  our  latitudes,  is 
caused  by  the  position  of  Europe.  The  prevailing  winds  here  are  the  south- 
west and  north-east.  The  former,  coming  to  us  from  the  equatorial  regions, 
are  warmer  and  lighter.  They  often,  therefore,  blow  for  hours  or  even  days 
in  the  higher  regions  of  the  atmosphere  before  manifesting  themselves  on  the 
surface  of  the  earth.  The  air  is  therefore  lighter,  and  the  pressure  lower. 
Hence  a  fall  of  the  barometer  is  a  probable  indication  of  the  south-west 
winds,  which  gradually  extend  downwards,  and  reaching  us,  after  having 
traversed  large  tracts  of  water,  are  charged  with  moisture,  and  bring  us  rain. 
The  north-east  blows  simultaneously  above  and  below,  but  the  hindrances 
to  the  motion  of  the  current  on  the  earth,  by  hills,  forests,  and  houses,  cause 
the  upper  current  to  be  somewhat  in  advance  of  the 
lower  ones,  though  not  so  much  so  as  the  south-west 
wind.  The  air  is  therefore  somewhat  heavier  even 
before  we  perceive  the  north-east,  and  a  rise  of  the 
barometer  affords  a  forecast  of  the  occurrence  of  this 
wind,  which,  as  it  reaches  us  after  having  passed  over 
the  immense  tracts  of  diy  land  in  Central  and  Northern 
Europe,  is  mostly  dry  and  fine. 

When  the  barometer  rises  or  sinks  slowly,  that  is, 
for  two  or  three  days,  towards  fine  weather  or  towards 
rain,  it  has  been  found  from  a  great  number  of  observa- 
tions that  the  indications  are  then  extremely  probable. 
Sudden  variations  in  either  direction  indicate  bad 
weather  or  wind. 

174.  Wheel  barometer. — The  wheel  barometer, 
which  was  invented  by  Hooke,  is  a  syphon  barometer, 
and  is  especially  intended  to  indicate  good  and  bad 
weather  (fig.  141).  In  the  shorter  leg  of  the  syphon 
there  is  a  float  which  rises  and  falls  with  the  mercury. 
A  string  attached  to  this  float  passes  round  a  pulley, 
and  at  the  other  end  there  is  a  weight,  somewhat  lighter 
than  the  float.  A  needle  fixed  to  the  pulley  moves 
round  a  graduated  circle,  on  which  is  marked  stormy,  ram,  set  fair,  &c. 
When  the  pressure  varies  the  float  sinks  or  rises,  and  moves  the  needle  round 
to  the  corresponding  points  on  the  scale. 


Fig.  141. 


-176] 


Glycerine  Barometer. 


'47 

The  barometers  ordinarily  met  with  in  houses,  and  which  are  called 
-weather-glasses,  are  of  this  kind.  They  are,  however,  of  little  use  for  two 
reasons.  The  first  is,  that  they  are  neither  very  delicate  nor  very 'accurate 
in  their  indications.  The  second,  which  applies  equally  to  all  barometers  is 
that  those  commonly  in  use  in  this  country  are  made  in  London,  and  the 
indications,  if  they  are  of  any  value,  are  only  so  for  a  place  of  the  same  level 
and  of  the  same  climatic  conditions  as  London.  Thus  a  barometer  standin" 
at  a  certain  height  in  London  would  indicate  a  certain  state  of  weather,  but 
if  removed  to  Shooter's  Hill  it  would  stand  half  an  inch  lower,  and  would 
indicate  a  different  state  of  weather.  As  the  pressure  differs  with  the  level 
and  with  geographical  conditions,  it  is  necessary  to  take  these  into  account 
if  exact  data  are  wanted. 

175.  Fixed  barometer. — For  accurate  observa- 
tions Regnault  uses  a  barometer  the  height  of  which 
he  measures  by  means  of  a  cathetometer  (88).  The 
cistern  (fig.  142)  is  of  cast  iron ;  against  the  frame  on 
which  it  is  supported  a  screw  is  fitted,  which  is  pointed 
at  both  ends,  and  the  length  of  which  has  been  deter- 
mined, once  for  all,  by  the  cathetometer.  To  mea- 
sure the  barometric  height,  the  screw  is  turned  until 
its  point  grazes  the  surface  of  the  mercury  in  the 
bath,  which  is  the  case  when  the  point  and  its  image 
are  in  contact.  The  distance  then  from  the  top  of 
the  point  to  the  level  of  the  mercury  in  the  tube  b  is 
measured  by  the  cathetometer,  and  this,  together  with 
the  length  of  the  screw,  gives  the  barometric  height 
with  great  accuracy.  This  barometer  has,  moreover, 
the  advantage  that,  as  a  tube  an  inch  in  diameter 
may  be  used,  the  influence  of  capillarity  becomes 
inappreciable.  Its  construction,  moreover,  is  very 
simple,  and  the  position  of  the  scale  leads  to  no  kind 
of  error,  since  this  is  transferred  to  the  cathetometer. 
Unfortunately  the  latter  instrument  requires  great 
accuracy  in  its  construction,  and  is  expensive. 

176.  Glycerine  barometer. — Jordan  has  recently 
constructed  a  barometer  in  which  the  liquid  used  is 
pure  glycerine.  This  has  the  specific  gravity  1-26, 
and  therefore  the  length  of  the  column  of  liquid  is 
rather  more  than  ten  times  that  of  mercury ;  hence 
small  alterations  in  the  atmospheric  pressure  produce 
considerable  oscillations  in  the  height  of  the  liquid. 
The  tube  consists  of  ordinary  composition  gas-tubing 
about  f  of  an  inch  in  diameter  and  28  feet  or  so  in 
length ;  the  lower  end  is  open  and  dips  in  the  cistern, 
which  may  be  placed  in  a  cellar  ;  the  top  is  sealed  to  Fig.  14?. 

a  closed  glass  tube  an  inch  in  diameter,  in  which  the 

fluctuations  of  the  column  are  observed.  This  may  be  arranged  in  an  upper 
storey,  and  the  tubing,  being  easily  bent,  lends  itself  to  any  adjustment 
which  the  locality  requires. 


u 


148 


On  Gases. 


[176- 


The  vapour  of  glycerine  has  very  low  tension  at  ordinary  temperatures, 
and  is  therefore  not  so  exposed  to  such  back  pressures,  varying  with  the 
temperature,  as  is  water.  On  the  other  hand,  it  readily  attracts  moisture 
from  the  air,  whereby  the  density  and  therewith  the  height  of  the  liquid 
column  vary.  This  is  prevented  by  covering  the  liquid  in  the  cistern  with  a 
layer  of  paraffine  oil. 

The  '  Philosophical  Magazine,'  vol.  xxx.  Fourth  series,  page  349,  contains 
a  detailed  account  of  a  method  of  constructing  a  water  barometer. 

177.  Huygliens'  barometer.  —  The  desire  to  amplify  the  small  variations 
which  take  place  in  the  barometer  has  led  to  a  number  of  contrivances,  one 
of  the  best  known  of  which  was  invented  by  Huyghens  (fig.  143). 

The  barometer  tube  a  is  wider  at  the  closed  end  £,  and  also  at  <:,  where  a 
liquid  of  smaller  specific  gravity  than  mercury,  such  as  coloured  water,  is 
poured  on  the  mercury  ;  it  fills  the  rest  of  the  tube  c  and  a  portion  of  d. 

Suppose  b  and  c  to  have  the  'same  diameter,  which  is  ;/  times  that  of  d. 
When  the  column  of  mercury  in  b  sinks  through  x  millimetres,  the  level  of 
the  mercury  in  c  rises  just  as  much,Swhile  the  coloured  liquid  rises  nx  milli- 
metres, and  therefore  its  level  is  (n  —  i}x  millimetres  higher.  A  column  of 
this  liquid  (n—  i)x  in  height  has  the  same  pressure  as  a  column  of  mercury 

llci  in  height,  where  s  is  the  number  expressing  the  ratio  of  the  specific 

gravities  of  mercury  and  the  liquid. 

Accordingly,  when  the  mercury  in  b  sinks  x  milli- 
metres, 


is  the  height  of  the  column  of  mercury,  which  corre- 
sponds to  the  decrease  of  atmospheric  pressure.  From 
this  we  have 


2  s  +  n  —  i 

Thus,  if  the  section  of  the  tubes  b  and  c  is  20  times 
that  of  d,  and  if  the  coloured  liquid  be  water,  we 
have 

i  T6y  1 3  6y 

_=±J  /  =  0-2947. 
27-2  +  20—1       46-2 

Accordingly,  when  an  ordinary  barometer  sinks 
through  7  millimetres,  the  mercury  in  b  sinks  0-2947 
millimetres,  while  the  coloured  liquid  rises  20  x  0-2947 
=  5*887.  Whenever,  that  is,  an  ordinary  barometer 
sinks  or  rises  i  millimetre,  the  coloured  liquid  rises  or 
sinks  5-98  millimetres,  or  nearly  six  times  as  much. 

Such  barometers  are  useful  in  cases  where  the 
variations  in  the  height  of  the  barometer,  rather  than 
its  actual  height,  are  to  be  observed.  The  scale 

should  be  placed  behind  the  tube  d,  and  two  points  fixed,  near  the  top  and 
bottom,  by  comparison  with  standard  barometers  ;  the  interval  between  the 
two  is  then  suitably  divided. 


-178]  Determination  of  Heights  by  the  Barometer.  149 

178.  Determination  of  heights  by  the  barometer.—  Since  the  atmo- 

spheric pressure  decreases  as  we  ascend,  it  is  obvious  that  the  barometer 
will  keep  on  falling  as  it  is  taken  to  a  greater  and  greater  height. 
On  this  depends  a  method  of  determining  the  difference  between       -rB 
the  heights   of  two  stations,  such  as  the  base  and  summit  of  a 
mountain.     The  method  may  be  explained  as  follows. 

According  to  Boyle's  law  (180),  if  the  temperature  of  an  'enclosed 
portion  of  air  continues  constant,  its  volume  will  vary  inversely  as 
the  pressure  ;  that  is  to  say,  if  we  double  the  pressure  we  shall  halve       4-Q 
the  volume.     But  if  we  halve  the  volume  we  manifestly  double  the       •  P 
quantity  of  air  in  each  cubic  inch  —  that  is  to  say,  we  double  the 
density  of  the  air  ;  and  so  on  in  any  proportion.     Consequently  the 
law  is  equivalent  to  this  :  —  That  for  a  constant  temperature  the 
density  of  air  is  proportional  to  the  pressure  which  it  sustains. 

Now  suppose  A.  and  B  (fig.  144)  to  represent  two  stations,  and 
that  it  is  required  to  determine  the  vertical  height  of  B  above  A,  it 
being  borne  in  mind  that  A  and  B  are  not  necessarily  in  the  same  ,,. 
vertical  line.  Take  P,  any  point  in  AB,  and  Q,  a  point  at  a  small 
distance  above  P.  Suppose  the  pressure  on  a  square  inch  of  the  atmosphere 
at  P  to  be  denoted  by/,  and  at  O  let  it  be  diminished  by  a  quantity  denoted 
by  dp.  It  is  clear  that  this  diminution  equals  the  weight  of  the  column  of 
air  between  P  and  Q,  whose  section  is  one  square  inch.  But,  since  the 
density  of  the  air  is  directly  proportional  to/,  the  weight  of  a  cubic  inch  of 
air  will  equal  kgp,  where  k  denotes  a  certain  quantity  to  be  determined 
presently,  and  g  the  accelerating  force  of  gravity  (79).  Hence,  if  we  denote 
PQ,  in  inches  by  dx^  the  pressure  will  be  diminished  by  kpg  .  dx,  and  we 
may  represent  this  algebraically  by  the  equation 

kpg  .  dx  =  dp. 
By  a  certain  algebraical  process  this  leads  to  the  conclusion  that 


where  X  denotes  the  height  of  AB,  and  P  and  P:  the  atmospheric  pressures 
at  A  and  B  respectively,  the  logarithms  being  what  are  called  '  Napierian 
logarithms.'  Now,  if  H  and  Hx  are  the  heights  of  the  barometer  at  A  and 
B  respectively,  the  temperature  of  the  mercury  being  the  same  at  both 
stations,  their  ratio  equals  that  of  P  to  P,,  and  therefore 


It  remains  to  determine  k  and  g. 

(i)  Since  the  force  of  gravity  is  different  for  places  in  different  latit 
g  will  depend  upon  the  latitude  (82).     It  is  found  that  \ig  is  the  accelerating 
force  of  gravity  in  latitude  <£,  and/that  force  in  latitude  45°,  then 

e-  f- 

6     i  +0-00256  cos  26 
where/  has  a  definite  numerical  value. 


1 50  On  Gases.  [178- 

(2)  If  o-  is  the  density  of  air  at  a  temperature  of  t°  C.,  under  O,  the  pres- 
sure exerted  by  29-92  inches  of  mercury,  we  shall  have 

*Q-/>- 

But  it  will  be  afterwards  shown  (332)  that  if  p0  is  the  density  of  air  under 
the  same  pressure  O  at  o°  C.,  we  shall  have 

P  =  -Po    , 
i  +at 

where  a  represents  the  coefficient  of  expansion  of  gases.     Therefore 

£Q=-P°    . 
^     \-rat 

Now  if  a-  is  the  density  of  mercury,  and  if  the  latitude  is  45°,  we  shall 
have 

0=29-92  .  of', 
and  therefore  •   ' 


o-     29-92  (i  +af) 

But  PQ-+-O-  is  the  ratio  which  the  density  of  dry  air  at  a  temperature  o°  C.,, 
in  latitude  45°,  under  a   pressure  of  29-92  inches  of  mercury,  bears  to  the 
density  of  mercury  at  o°  C.,  and  therefore  p0-^-o-  is  a  determinate  number. 
Substituting,  we  have 

a-  H 

P  =  29-92  in. (j  +  0-00256  cos  20)  (i+at]  log  jj-« 

Po  i 

The  value  of  a  is  0*003665,  which  is  nearly  equal  to  ^-.  If  we  substitute 
the  proper  values  for  o--f-/>0,  and  change  the  logarithms  into  common  loga- 
rithms, and  instead  of  /  use  the  mean  of  T  and  T15  the  temperatures  at  the 
upper  and  lower  stations,  it  will  be  found  that 

X  (in  feet)  -  60346  (i  +  0*00256  cos  20)  (i  +  -± Itj  log       , 

which  is  La  Place's  barometric  formula.  In  using  it,  we  must  remember 
that  T  and  Tl  are  temperatures  on  the  Centigrade  thermometer,  and  that  H 
and  H!  are  the  heights  of  the  barometer  reduced  to  o°  C.  Thus  if  //  is  the 
measured  height  of  the  barometer  at  the  lower  station  we  have 

~65c 

If  the  height  to  be  measured  is  not  great,  one  observer  is  enough.  For 
greater  heights  the  ascent  takes  some  time,  and  in  the  interval  the  pressure 
may  vary.  Consequently  in  this  case  there  must  be  two  observers,  one  at 
each  station,  who  make  simultaneous  observations. 

Let  us  take  the  following  example  of  the  above  formula  : — Suppose  that, 
in  latitude  65°  N.  at  the  lower  of  the  two  stations  the  height  of  the  barometer 
was  30-025  inches,  and  the  temperature  of  air  and  mercury  I7°'32  C.,  while 
at  the  upper  the  height  of  the  barometer  was  28-230  inches,  and  the  tempera- 
ture of  air  and  mercury  were  io°'55  C.  What  is  the  height  of  the  upper 
station  above  the  lower  ? 


179]  Ruhlmann'  s  Observations.  I5I 

(i)  Find  H  and  Hx  :  viz. 

-  H 


H,  =  28-301  _^55\     2g.l8 
V       65007 

TT 

Hence  log—  =  i  -4763243  -  i  -4500026  =  0-02632  1  7. 

(2)  Find  i  +  2(T  +  Ti)  viz.  i  -05574. 

1000 

(3)  Find  i  +  0-00256  cos  20. 

Since  0-00256  cos  130°=  -0-00256  cos  50°=  -0-001645, 

therefore  i  +0-00256  cos  2$  =  -0-998355. 

Hence  the  required  height  in  feet  equals 

60346  x  0-9983  c;  5  x  1-05574  x  0-0063217=  1674. 
If  H  and  H1  do  not  greatly  differ,  the  Napierian  logarithm  of 
H       H- 


If,  for  instance,  H=3o  and  H1  =  29  inches,  the  resulting  error  would  not 
exceed  the  -^  part  of  the  whole.  Accordingly  for  heights  not  exceeding 
2,000  ft.  we  may,  without  much  error,  use  the  formula 


179.  Ruhlmann's  observations.  —  The  results  obtained  for  the  difference 
in  height  of  places  by  using  che  above  formula  often  differ  from  the*  true 
heights  as  measured  trigonometrically,  to  an  extent  which  cannot  be  ascribed 
to  errors  in  observation.  The  numbers  thus  found  for  the  heights  of  places 
are  influenced  by  the  time  of  day,  and  also  by  the  season  of  year,  at  which 
they  are  made.  Ruhlmann  has  investigated  the  cause  of  this  discrepancy 
by  a  series  of  direct  barometric  and  thermometric  observations  made  at  two 
different  stations  in  Saxony,  and  also  by  a  comparison  of  the  continuous 
series  of  observations  made  at  Geneva  and  on  the  St.  Bernard. 

Ruhlmann  has  ascertained  thus  that  the  cause  of  the  discrepancy  is  to  be 
found  in  the  fact  that  the  mean  of  the  temperatures  indicated  by  the  ther- 
mometer at  the  two  stations  is  not  an  accurate  measure  of  the  actual  mean 
temperature  of  the  column  of  air  between  the  two  stations,  a  condition  which 
is  assumed  in  the  above  formula.  The  variations  in  the  temperature  of  the 
column  of  air  are  not  of  the  same  extent  as  those  indicated  by  the  thermo- 
meter, nor  do  they  follow  them  so  rapidly  ;  they  drag  after  them  as  it  were. 
If  the  mean  monthly  temperatures  at  the  two  fixed  stations  are  introduced 
into  the  formula,  they  give  in  winter  heights  which  are  somewhat  too  low, 
and  in  summer  such  as  are  too  high.  The  results  obtained  by  introducing 
the  mean  yearly  temperature  of  the  two  stations  are  very  near  the  true  ones. 

This  influence  of  temperature  is  most  perceptible  in  individual  observa- 
tions of  low  heights.  Thus,  using  the  observed  temperatures  in  the  barometric 


152  On  Gases.  [179- 

formula,  the  error  in  height  of  the  Uetliberg  above  Zurich  (about  1,700  feet) 
was  found  to  be  ^  of  the  total,  while  the  height  of  the  St.  Bernard  above 
Geneva  was  found  within  Tf  ¥  of  the  true  height. 

The  reason  why  the  thermometers  do  not  indicate  the  true  temperature 
of  the  air  is  undoubtedly  that  they  are  too  much  influenced  by  radiation 
from  the  earth  and  surrounding  bodies.  The  earth  is  highly  absorbent,  and 
becomes  rapidly  heated  under  the  influence  of  the  sun's  rays,  and  becomes 
as  rapidly  cooled  at  night ;  the  air,  as  a  very  diathermanous  body,  is  but 
little  heated  by  the  sun's  rays,  and  on  the  contrary  is  little  cooled  by  radia- 
tion during  the  night. 


-180]  Boyle's  Law.  153 


CHAPTER    II. 

MEASUREMENT   OF  THE  ELASTIC  FORCE   OF  GASES. 

Boyle's  law. — The  law  of  the  compressibility  of  gases  was  dis- 
covered by  Boyle  in  1662,  and  afterwards  independently  by  Mariotte  in  1679. 
It  is  in  England  commonly  called  'Boyle's  Law,'  and,  on  the  Continent, 
'  Mariotte's  law.'  It  is  as  follows  : — 

The  temperature  remaining  the  same,  the  volume  of  a  given  quantity  of 
gas  is  inversely  as  the  pressure  which  it  bears. 

This  law  may  be  verified  by  means  of  an  apparatus  devised  by  Boyle 
(fig.  145).  It  consists  of  a  long  glass  tube  fixed  to  a  vertical  support :  it  is 
open  at  the  upper  part,  and  the  other  end,  which  is  bent  into  a  short  vertical 
leg,  is  closed.  On  the  shorter  leg  there  is  a  scale,  which  indicates  equal 
capacities  ;  the  scale  against  the  long  leg  gives  the  heights.  The  zero  of 
both  scales  is  in  the  same  horizontal  line. 

A  small  quantity  of  mercury  is  poured  into  the  tube,  so  that  its  level  in 
both  branches  is  at  zero,  which  is  effected  without  much  difficulty  after  a  few 
trials  (fig.  145).  The  air  in  the  short  leg  is  thus  under  the  ordinary  atmo- 
spheric pressure  which  is  exerted  through  the  open  tube.  Mercury  is  then 
poured  into  the  longer  tube  until  the  volume  of  the  air  in  the  smaller  tube  is 
reduced  to  one-half;  that  is,  until  it  is  reduced  from  10  to  5,  as  shown  in 
fig.  146.  If  the  height  of  the  mercurial  column,  CA,  be  measured,  it  will  be 
found  exactly  equal  to  the  height  of  the  barometer  at  the  time  of  the  experi- 
ment. The  pressure  of  the  column  CA  is  therefore  equal  to  an  atmosphere 
which,  with  the  atmospheric  pressure  acting  on  the  surface  of  the  column  at 
C,  makes  two  atmospheres.  Accordingly,  by  doubling  the  pressure,  the 
volume  of  the  gas  has  been  diminished  to  one-half. 

If  mercury  be  poured  into  the  longer  branch  until  the  volume  of  the  air 
is  reduced  to  one-third,  it  will  be  found  that  the  distance  between  the  level 
of  the  two  tubes  is  equal  to  two  barometric  columns.  The  pressure  is  now 
three  atmospheres,  while  the  volume  is  reduced  to  one-third.  Dulong  and 
Petit  have  verified  the  law  for  air  up  to  27  atmospheres,  by  means  of  an 
apparatus  analogous  to  that  which  has  been  described. 

The  law  also  holds  good  in  the  case  of  pressures  of  less  than  one  atmo- 
sphere. To  establish  this,  mercury  is  poured  into  a  graduated  tube  until  it 
is  about  two-thirds  full,  the  rest  being  air.  It  is  then  inverted  in  a  deep 
trough  M  containing  mercury  (fig.  147),  and  lowered  until  the  levels  of  the 
mercury  inside  and  outside  the  tube  are  the  same,  and  the  volume  AB  noted. 
The  tube  is  then  raised,  as  represented  in  the  figure,  until  the  volume  of  air 
AC  is  double  that  of  AB  (fig.  148).  The  height  of  the  mercury  in  the  tube 


154 


On  Gases. 


[180- 


above  the  mercury  in  the  trough  CD  is  then  found  to  be  exactly  half  the 
height  of  the  barometric  column.  The  air  whose  volume  is  now  doubled  is 
now  only  under  the  pressure  of  half  an  atmosphere  ;  for  it  is  the  elastic  force 
of  this  air  which,  added  to  the  weight  of  the  column  CD,  is  equivalent  to  the 
atmospheric  pressure.  Hence  the  volume  is  inversely  as  the  pressure. 

In  the  experiment  with  Boyle's  tube,  as  the  quantity  of  air  remains  the 
same,  its  density  must  obviously  increase  as  its  volume  diminishes,  and  vice 
versa.  The  law  may  thus  be  enunciated  : — ^  For  the  same  temperature  the 


Fig.  145- 


Fig.  146. 


density  of  a  gas  is  proportional  to  its  pressure?  Hence,  as  water  is  773 
times  as  heavy  as  air,  under  a  pressure  of  773  atmospheres  air  would  be  as 
dense  as  water. 

Boyle's  law  must  not  be  unde:stood  to  mean  that  gases  of  equal  density 
have  equal  elastic  force  ;  different  gases  of  various  densities  have  the  same 
tension  when  they  are  under  the  same  pressure.  A  given  volume  of  hydrogen 
under  the  ordinary  atmospheric  pressure  has  the  same  elastic  force  as  the 
same  volume  of  air,  although  the  latter  is  14  times  as  heavy  as  the  former. 
Since,  for  the  same  volume,  there  are  the  same  number  of  atoms  in  all  gases, 


-181] 


Boyle's  Law. 


155 


the  lighter  atoms  must  possess  a  greater  velocity  in  order  to  exert  the  same 

pressure  as  the  same  number  of  atoms  of  greater  mass. 

y-i8i.  Boyle's  law  is  only  approximately  true.— Until  within  the  last 

few  years  Boyle's  law  was  supposed  to  be  absolutely  true  for  all  gases  at  all 

pressures,    but    Despretz 

obtained    results    incom- 
patible with  the  law.    He 

took  two  graduated  glass 

tubes  of  the  same  length, 

and   filled    one   with    air 

and   the   other   with    the 

gas      to     be     examined. 

These  tubes  were  placed 

in     the     same     mercury 

trough,    and    the    whole 

apparatus  immersed  in  a 

strong  glass  cylinder  filled 

with   water.      By  means 

of  a  piston  moved  by  a 

screw  which  worked  in  a 

cap  at  the  top  of  a  cylin- 
der, the  liquid  could  be 

subjected  to  an  increasing 

pressure,  and  it  could  be 

seen   whether    the    com- 
pression of  the   wo  gases 

was  the  same  or  not.    The 

apparatus  resembled  that 

used   for   examining    the 

compressibility  of  liquids 

(fig.  64).     In  this  manner 

Despretz  found  that  car- 
bonic  acid,   sulphuretted 

hydrogen,  ammonia,  and, 

cyanogen  are  more  com- 
pressible than  air :  hydro- 
gen, which  has  the  same 
compressibility  as  air  up  to  15  atmospheres,  is  then  less  compressible.    From 
these  experiments  it  was  concluded  that  the  law  of  Boyle  was  not  general. 

In  some  experiments  on  the  elastic  force  of  vapours,  Dulong  and  Arago 
had  occasion  to  test  the  accuracy  of  Boyle's  law.  The  method  adopted  was 
exactly  that  of  Boyle,  but  the  apparatus  had  gigantic  dimensions. 

The  gas  to  be  compressed  was  contained  in  a  strong  glass  tube,  GF  (fig. 
149),  about  six  feet  long  and  closed  at  the  top,  G.  The  pressure  was  pro- 
duced by  a  column  of  mercury,  which  could  be  increased  to  a  height  of  65 
feet,  contained  in  a  long  vertical  tube,  I£L,  formed  of  a  number  of  tubes 
firmly  joined  by  good  screws,  so  as  to  be  perfectly  tight. 

The  tubes  KL  and  GF  were  hermetically  fixed  in  a  horizontal  iron  pipe 
DE,  which  formed  part  of  a  mercuria1  reservoir,  A.  On  the  top  of  this 


Fig.  149- 


156  On  Gases.  [181- 

reservoir  there  was  a  force-pump,  BC,  by  which  mercury  could  be  forced 
into  the  apparatus. 

At  the  commencement  of  the  experiment  the  volume  of  the  air  in  the 
manometer  (183)  was  observed,  and  the  initial  pressure  determined,  by 
adding  to  the  pressure  of  the  atmosphere  the  height  of  the  mercury  in  K 
above  its  level  in  H.  If  the  level  of  the  mercury  in  the  manometer  had 
been  above  the  level  in  KL,  it  would  have  been  necessary  to  subtract  the 
difference. 

By  means  of  the  pump,  water  was  injected  into  A.  The  mercury  being 
then  pressed  by  the  water,  rose  in  the  tube  GF,  where  it  compressed  the 
air,  and  in  the  tube  KL,  where  it  rose  freely.  It  was  only  then  necessary 
to  measure  the  volume  of  the  air  in  GF  ;  the  height  of  the  mercury  in  KL 
above  the  level  in  GF,  together  with  the  pressure  of  the  atmosphere,  was 
the  total  pressure  to  which  the  gas  was  exposed.  These  were  all  the  elements 
necessary  for  comparing  different  volumes  and  the  corresponding  tempera- 
tures. The  tube  GF  was  kept  cold  during  the  experiment  by  a  stream  of 
cold  water. 

The  long  tube  was  attached  to  a  long  mast  by  means  of  staples.  The 
individual  tubes  were  supported  at  the  junction  by  cords,  which  passed 
round  pulleys  R  and  R',  and  were  kept  stretched  by  small  buckets,  P,  con- 
taining shot.  In  this  manner,  each  of  the  thirteen  tubes  having  been  sepa- 
rately counterpoised,  the  whole  column  was  perfectly  free  notwithstanding  its 
weight. 

Dulong  and  Arago  experimented  with  pressures  up  to  27  atmospheres, 
and  observed  that  the  volume  of  air  always  diminished  a  little  more  than  is 
required  by  Boyle's  law.  But  as  these  differences  were  very  small,  they 
attributed  them  to  errors  of  observation,  and  concluded  that  the  law  was 
perfectly  exact,  at  any  rate  up  to  27  atmospheres. 

Regnault  investigated  the  same  subject  with  an  apparatus  resembling 
that  of  Dulong  and  Arago,  but  in  which  all  the  sources  of  error  were  taken 
into  account,  and  the  observations  made  with  remarkable  precision.  He  found 
that  air  does  not  exactly  follow  Boyle's  law,  but  experiences  a  greater  com- 
pressibility, which  increases  with  the  pressure  ;  so  that  the  difference  between 
the  calculated  and  the  observed  diminution  of  volume  is  greater  in  proportion 
as  the  pressure  increases. 

Regnault  found  that  nitrogen  was  like  air,  but  is  less  compressible. 
Carbonic  acid  exhibits  considerable  deviation  from  Boyle's  law  even  under 
small  pressures.  Hydrogen  also  deviates  from  the  law,  but  its  compressi- 
bility is  less  with  increased  pressure. 

Cailletet  examined  the  compressibility  of  gases  by  a  special  method,  in 
which  the  pressure  could  be  carried  as  high  as  600  atmospheres.  His  results 
confirm  those  of  Regnault  as  regards  hydrogen  :  nitrogen  was  found  to 
present  the  curious  feature  that  towards  80  atmospheres  it  has  a  maximum 
relative  compressibility,  beyond  this  point  it  gradually  becomes  less  com- 
pressible, its  compressibility  diminishing  more  rapidly  than  that  of  hydrogen. 
Carbonic  acid  deviates  less  from  the  law  in  proportion  as  the  temperature 
is  higher.  This  is  also  the  case  with  other  gases.  Amagat  made  a  remark- 
able series  of  experiments  by  a  method  based  on  Boyle's  experiment.  The 
pressure  could  be  applied  directly  by  means  of  mercury  in  a  steel  tube  about 


-183]  Manometers.  157 

1,000  feet  in  length,  arranged  in  the  shaft  of  a  deep  coal  pit,  and  suitably 
connected  at  the  bottom  with  a  carefully  calibrated  glass  tube.  In  this  way 
pressures  of  as  much  as  400  atmospheres  could  be  applied,  and  the  tempera- 
tures remained  constant.  With  the  exception  of  hydrogen,  all  gases  showed  a 
minimum  of  compressibility,  that  of  nitrogen  and  carbonic  oxide  at  66  atmo- 
spheres ;  air  and  ethylene  at  85  ;  oxygen  at  130,  and  marsh  gas  at  160.  The 
deportment  of  ethylene  is  remarkable  ;  according  to  the  pressure  employed  it 
may  be  twice  or  one-third  as  compressible  as  is  required  by  the  law.  For 
gases  which  are  the  most  difficult  to  liquefy,  the  deviations  from  the  law  are 
inconsiderable,  and  may  be  quite  neglected  in  ordinary  physical  and 
chemical  experiments,  where  the  pressures  are  not  great. 
l/^i&2.  Applications  of  Boyle's  law. — Suppose  a  volume  of  gas  to 
measure  340  cubic  inches  under  a  .pressure  of  535  mm.,  what  will  be  its 
volume  at  the  standard  pressure,  760  mm.  ? 

We  have  V  =  34°  *  535  =  238  cubic  inches. 

760 

In  like  manner  let  it  be  asked,  if  D'  is  the  density  of  a  gas  when  the 
barometer  stands  at  H'  mm.,  what  will  be  its  density  D  at  the  same  tem- 
perature when  the  barometer  stands  at  H  mm.  ? 

Let  M  be  the  mass  of  the  gas,  V  its  volume  in  the  first  case,  V  its  volume 
in  the  second.  Therefore 

DV  =  M  =  D'V 

D    =  V  =  :P   =  H. 
D7  ~  V    ~  P'  ~  H' 

Thus,  if  H'  denote  760  mm.,  we  have 

TT 

Density  at  H'  =  (Density  at  standard  pressure)  _ 

^"183.  manometers. —  Manometers  are  instruments  for  measuring  the 
tension  of  gases  or  vapours.  In  all  such  instruments  the  unit  chosen  is  the 
pressure  of  one  atmosphere,  or  30  inches  of  mercury  at  the  standard  tem- 
perature, which,  as  we  have  seen,  is  nearly  1 5  Ibs.  to  the  square  inch. 

The  open-air  manometer  consists  of  a  bent  glass  tube  BD  (fig.  150), 
fastened  to  the  bottom  of  a  reservoir  AC,  of  the  same  material,  containing 
mercury,  which  is  connected  with  the  closed  recipient  containing  the  gas  or 
vapour  the  pressure  of  which  is  to  be  measured.  The  whole  is  fixed  on  a 
long  plank  kept  in  a  vertical  position. 

In  graduating  this  manometer  C  is  left  open,  and  the  number  I  marked 
at  the  level  of  the  mercury,  for  this  represents  one  atmosphere.     From  this 
point  the  numbers  2,  3,  4,  5,  6,  are  marked  at  each  30  inches,  indicating  so 
many  atmospheres,  since  a  column  of  mercury  30  inches  represents  a  pre 
sure  of  one  atmosphere.   The  intervals,  from  I  to  2,  and  from  2  to  3,  &c.,  are 
divided  into  tenths.     C  being  then  placed  in  connection  with  a  boiler,  for 
example,  the  mercury  rises  in  the  tube  BD  to  a  height  which  measures  the 
tension  of  the  vapour.     In  the  figure  the  manometer  marks  2  atmospheres 
which  represents  a  height  of  30  inches,  plus  the  atmospheric  pressure  exeri 
at  the  top  of  the  column  through  the  aperture  D. 


T58 


On  Gases. 


[183- 


16 


This  manometer  is  only  used  when  the  pressures  do  not  exceed  5  to  6 
atmospheres.  Beyond  this,  the  length  of  tube  necessary  makes  it  very  in- 
•convenient,  and  the  following  apparatus  is  commonly  used. 

184.  Manometer  with  compressed  air. — The  manometer  ivith  com- 
pressed air  is  founded  on  Boyle's  law  :  one  form  is  repre- 
sented in  fig.  151,  which  may  be  screwed  into  a  boiler  or 
steam-pipe  where  pressure  is  to  be  measured.  The  pres- 
sure is  transmitted  through  the  opening  «,  into  the  closed 
space  b.  In  this  is  an  iron  vessel  containing  mercury,  in 
which  dips  the  open  end  of  the  manometer  tube,  which  is 
screwed  airtight  in  the  tubulure. 

In  the  graduation  of  this  manometer,  the  quantity  of 
air  contained  in  the  tube  is  such  that  when  the  aperture 
A  communicates  freely  with  the  atmosphere,  the  level 
of  the  mercury  is  the  same  in  the  tube  and  in  the  tubu- 
lure. Consequently,  at  this  level,  the 
number  I  is  marked  on  the  scale  to 
which  the  tube  is  affixed.  As  the  pres- 
sure acting  through  the  tubulure  A  in- 
creases, the  mercury  rises  in  the  tube, 
until  its  weight,  added  to  the  tension  of 
the  compressed  air,  is  equal  to  the  ex- 
ternal pressure.  It  would  consequently 
be  incorrect  to  mark  two  atmospheres  in 
the  middle  of  the  tube  ;  for  since  the 
volume  of  the  air  is  reduced  to  one-half, 
its  tension  is  equal  to  two  atmospheres, 
and,  together  with  the  weight  of  the  mer- 
cury raised  in  the  tube,  is  therefore  more 
than  two  atmospheres.  The  position  of 
the  number  is  at  such  a  height  that  the 
elastic  force  of  the  compressed  air,  to- 
gether with  the  weight  of  the  column  of 
mercury  in  the  tube,  is  equal  to  two 
atmospheres.  The  exact  position  of  the 
numbers  2,  3,  4,  &c.,  on  the  manometer 
scale  can  only  be  determined  by  calcula- 
tion. Sometimes  this  manometer  is  made 
of  one  glass  tube  ;  the  principle  is  obvi- 
ously the  same. 


r/n- 

D 

Jj 

. 

3 

m 

BR- 

'fl- 

,4 

N 
M 

2 

C" 

50 

40- 
50- 

.1. 

1  2 

'o  -: 

/f 

|{ 

^fir 
ir 

Fig.  150. 


185.  Volumometer. — An  interesting  application  of  Boyle's  law  is  met 
•with  in  the  volumometer,  which  is  used  in  determinations  of  the  specific 
gravity  of  solids  which  cannot  be  brought  in  contact  with  water.  A  simple 
form  consists  of  a  glass  tube  with  a  cylinder  G  at  the  top  (fig.  152),  the  edges 
of  which  are  carefully  ground,  and  which  can  be  closed  hermetically  by  means 
of  a  ground-glass  plate  D.  The  top  being  open,  the  tube  is  immersed  until 
the  level  of  the  mercury  inside  and  outside  is  the  same  ;  this  is  represented 
by  the  mark  Z.  The  apparatus  is  then  closed  airtight  by  the  plate,  and  is 
raised  until  the  mercury  stands  at  a  height  /i,  above  the  level  Q  in  the  bath. 


-187] 


Aneroid  Barometer. 


159 


The  original  volume  of  the  enclosed  air  V,  which  was  under  the  pressure  of 
the  atmosphere,  is  now  increased  to  V  +  v,  since  the  pressure 
has  diminished  by  the  height  of  the  column  of  mercury  h. 
Calling  the  pressure  of  the  atmosphere  at  the  time  of  obser- 
vation b,  we  shall  have  V  :  V  +  ?/  =  £  —  h  :  b, 

Placing  now  in  the  cylinder  a  body  K,  whose  volume  x  is 
unknown,  the  same  operations  are  repeated,  the  tube  is  raised 
until  the  mercury  again  stands  at  the  same  mark  as  before,  but 
its  height  above  the  bath  is  now  different ;  a  second  reading 
7/j,  is  obtained,  and  we  have  (V  —  x)  :  (V-.r)  +  v  =  b-hl\b. 

Combining  and  reducing,  we  get  x  =  (V  +  v)    ( i  -  i).        The 

volume  V  +  v  is  constant,  and  is  determined  numerically, 
once  for  all,  by  making  the  experiment  with  a  substance  of 
known  volume,  such  as  a  glass  bulb. 

This  apparatus,  which  is  also  known  as  the  sterometer,  is 
of  great  value  in  determining  the  gravimetrical  density  of 
gunpowder  ;  this  averages  from  i  -67  to  i  -84,  and  is  thus 
materially  different  from  its  apparent  density,  or  the  weight 
of  a  given  volume  compared  with  that  of  an  equal  volume  of 
water,  which  is  from  0-89  to  0-94. 

1 86.  Regrnault's  barometric  manometer. — For  measuring  pressures  of 
less  than  one  atmosphere,  Regnault  devised  the  following  arrangement, 
which  is  a  modification  of  his  fixed  barometer  (fig.  141).  In  the  same  cistern 
dips  a  second  tube  «,  of  the  same  diameter,  open  at  both  ends,  and  provided 
at  the  top  with  a  three-way  cock,  one  of  which  is  connected  with  an  air-pump 
and  the  other  with  the  space  to  be  exhausted.  The  further  the  exhaustion 
is  carried  the  higher  the  mercury  rises  in  the  tube  a.  The  differences 
of  level  in  the  tubes  b  and  a  give  the  pressures.  Hence,  by  measuring  the 
height  ab,  by  means  of  the  cathetometer,  the  pressure  in  the  space  that  is 
being  exhausted  is  accurately  given.  This  apparatus  is  also  called  the 
differential  barometer. 

7.  Aneroid  barometer. — This  instrument  derives  its  name  from  the 
circumstance  that  no  liquid  is  used  in  its  construction  (a,  without ;  vrjpbs, 
moist).  Fig.  1 53  represents  one  of  the  forms  of  these  instruments,  constructed 
by  Casella  ;  it  consists  of  a  cylindrical  metal  box,  exhausted  of  air,  the  top 
of  which  is  made  of  thin  corrugated  metal,  so  elastic  that  it  readily  yields  to 
alterations  in  the  pressure  of  the  atmosphere. 

When  the  pressure  increases,  the  top  is  pressed  inwards  ;  when,  on  the 
contrary,  it  decreases,  the  elasticity  of  the  lid,  aided  by  a  spring,  tends  to 
move  it  in  the  opposite  direction.  These  motions  are  transmitted  by  delicate 
multiplying  levers  to  an  index  which  moves  on  a  scale.  The  instrument  is 
graduated  empirically  by  comparing  its  indications,  under  different  pressures, 
with  those  of  an  ordinary  mercurial  barometer. 

The  aneroid  has  the  advantage  of  being  portable,  and  can  be  constructed 
of  such  delicacy  as  to  indicate  the  difference  in  pressure  between  the  height 
of  an  ordinary  table  and  the  ground.  It  is  hence  much  used  in  determining 
heights  in  mountain  ascents.  But  it  is  somewhat  liable  to  get  out  of  order, 
•  especially  when  it  has  been  subjected  to  great  variations  of  pressure  ;  and 


160  On  Gases.  [187— 

its  indications  must  from  time  to  time  be  compared  with  those  of  a  standard 
barometer. 

The  errors  arising  from  the  use  of  the  aneroid  are  mainly  due  to  the 
transmission  of  the  motion  of  the  lid  by  the  multiplying  arrangement.  Gold- 
schmid  of  Zurich  devised  a  form  in  which  the  motion  of  the  lid  is  directly 
observed. 

Like  that  of  other  aneroids,  the  lid  of  a  box  a  (fig.  154),  in  which  the 
alterations  of  pressure  are  determined,  is  of  fine  corrugated  sheet  metal.  To 
this  is  fixed  a  horizontal  metal  strip  b,  on  the  front  end  of  which  is  a  small 
square  <?,  acting  as  index.  This  rises  and  falls  with  the  movement  of  the  lid, 
and  indicates  on  a  scale  f  f,  on  the  sides  of  the  slit  d  d',  alterations  in 
pressure  of  centimetres.  To  this  strip  a  second  and  more  delicate  one,  c,  is 
fixed,  on  the  front  end  of  which  is  also  fixed  an  index  e'.  Before  making  an 
observation,  the  horizontal  line  of  this  index  is  made  to  coincide  with  that  of 


Fig.  153- 


Fie. 


e  ;  this  is  effected  by  means  of  a  micrometer  screw  »/,  which  is  raised  _or 
lowered  by  the  movable  ring  h  :  on  the  corresponding  scale  millimetres  and 
tenths  of  a  millimetre  are  read  off.  To  do  this  the  instrument  is  provided 
with  a  lens,  not  represented  in  the  figure.  There  is  aiso  a  small  thermo- 
meter / ;  from  its  indications  a  correction  is  made  for  temperature  according 
X:o  an  empirical  scale  specially  constructed  for  each  instrument. 
V  1 88.  Laws  of  the  mixture  of  gases. — If  a  communication  is  opened 
between  two  closed  vessels  containing  gases,  they  at  once  begin  to  mix, 
whatever  be  their  density,  and  in  a  longer  or  shorter  time  the  mixture  is 
complete,  and  will  continue  so,  unless  chemical  action  is  set  up.  The  laws 
which  govern  the  mixture  of  gases  may  be  thus  stated  : — 

I.  The  mixture  takes  place  rapidly  and  is   homogeneous;  that  zs,  each 
portion  of  the  mixture  contains  the  two  gases  in  the  same  proportion. 

II.  If  the  gases  severally  and  the  mixture  have  the  same  temperature,  ant 


-189]  Absorption  of  Gases  by  Liquids.  l6l 

V^^ySK  ^^K£S^  "  "^  **  * 

Pressures  on  the  unit  of  area  exerted  by  the  ^l^slvemlly.  '^  ***  """*  ^ 

second  law  a  very  convenient  formula  can  be  easily  deduced. 
*    *    /"          3  '  '  '  '  volumes  of  several  gases  under   pressure  of 

A,  A,  A-  •  -  -  respectively.     Suppose  these  gases  when  mi^H It    T 
volume  V,  under  a  pressure  P,  the  temperature!  haV6  a 

being  the  same.  By  Boyle's  law  we  know  that 
z/x  will  occupy  a  volume  V  under  a  pressure  i>  ' 
provided  that 

YA' =  viPi  ;  similarly,  V//  =  v^p^ 
and  so  on.     But  from  the  above  law 

therefore        VP  =  ^iA +  /Z/2A +  Z/3A + 
It  obviously  follows  that  if  the  pressures  are  all 
the  same,  the  volume  of  the  mixture  equals  the 
sum  of  the  separate  volumes. 

The  first  law  was  shown  experimentally  by 
Berthollet,  by  means  of  an  apparatus  repre- 
sented in  fig.  155.  It  consists  of  two  glass 
globes  provided  with  stopcocks,  which  can  be 
screwed  one  on  the  other.  The  upper  globe 
was  filled  with  hydrogen,  and  the  lower  one 
with  carbonic  acid,  which  has  22  times  the  Fi 

density  of  hydrogen.     The  globes  having  been 

fixed  together  were  placed  in  the  cellars  of  the  Paris  Observatory  and  the 
stopcocks  then  opened,  the  globe  containing  hydrogen  being  uppermost. 
Berthollet  found  after  some  time  that  the  pressure  had  not  changed,  and 
that,  in  spite  of  the  difference  in  density,  the  two  gases  had  become  uniformly 
mixed  in  the  two  globes.  Experiments  made  in  the  same  manner  with 
other  gases  gave  the  same  results,  and  it  was  found  that  the  diffusion  was 
more  rapid  in  proportion  as  the  difference  between  the  densities  was 
greater. 

The  second  law  may  be  demonstrated  by  passing  into  a  graduated  tube, 
over  mercury,  known  volumes  of  gas  at  known  pressures.  The  pressure  and 
volume  of  the  whole  mixture  are  then  measured,  and  found  to  be  in  accord- 
ance with  the  law. 

Gaseous  mixtures  follow  Boyle's  law,  like  simple  gases,  as  has  been 
proved  for  air  (180),  which  is  a  mixture  of  nitrogen  and  oxygen. 

189.  Absorption  of  gases  by  liquids. — Water  and  many  liquids  possess 
the  property  of  absorbing  gases.  Under  the  same  conditions  of  pressure  and 
temperature  a  liquid  does  not  absorb  equal  quantities  of  different  gases. 
At  the  temperature  o°  C.  and  pressure  760  mm.,  one  volume  of  water  dissolves 
the  following  volumes  of  gas  : — 

Nitrogen  .  .  0*020  Sulphuretted  hydrogen  .  4-37 
Oxygen  .  .  0-041  Sulphurous  acid  .  .  .  7979 
Carbonic  acid  .  1-79  Ammonia  ....  1046-63 

M 


162 


On  Gases. 


[189 


From  the  very  great  condensation,  to  which  the  latter  correspond,  it  may  be 
inferred  that  the  gases  are  in  the  liquid  state. 

Gases  are  more  soluble  in  alcohol  ;  thus  at  o°  C.  alcohol  dissolves  4-33 
volumes  of  carbonic  acid  gas. 

The  whole  subject  of  gas  absorption  has  been  investigated  by  Bunsen. 
The  general  laws  are  the  following  : — 

I.  For  the  same  gas,   the  same  liquid,  and  the  same  temperature,  the 
weight  of  gas  absorbed  is  proportional  to  the  pressure.     This  may  also  be 
expressed  by  saying  that  at  all  pressures  the  volume  dissolved  is  the  same  ; 
or  that  the  density  of  the  gas  absorbed  is  in  a  constant  relation  with  that  ot 
the  external  gas  which  is  not  absorbed. 

Accordingly,  when  the  pressure  diminishes,  the  quantity  of  dissolved 
gas  decreases.  If  a  solution  of  gas  be  placed  under  the  air-pump  and 
a  vacuum  created,  the  gas  obeys  its  expansive  force,  and  escapes  with 
effervescence. 

II.  The  quantity  of  gas  absorbed  decreases  with  the  temperature  \  that  is 
to  say,  when  the  elastic  force  of  the  gas  is  greater.     Thus  at  1 5°  water  only 
absorbs  i  -oo  of  carbonic  acid. 

III.  The  quantity  of  gas  which  a  liquid  can  dissolve  is  independent  of 
the  nature  and  of  the  quantity  of  other  gases  which  it  may  already  hold  in 
solution. 

In  every  gaseous  mixture  each  gas  exercises  the  same  pressure  as  it 
would  if  its  volume  occupied  the  whole  space  ;  and  the  total  pressure  is 
equal  to  the  sum  of  the  individual  pressures.  When  a  liquid  is  in  contact 
with  a  gaseous  mixture,  it  absorbs  a  certain  part  of  each  gas,  but  less  than 
it  would  if  the  whole  space  were  occupied  by  each  gas.  The  quantity  of 
each  gas  dissolved  is  proportional  to  the  pressure  which  the  unabsorbed 
gas  exercises  alone.  For  instance,  oxygen  forms  only  about  \  the  quantity 
of  air  ;  and  water,  under  ordinary  conditions,  absorbs  exactly  the  same 
quantity  of  oxygen  as  it  would  if  the  atmosphere  were  entirely  formed  of  this 
gas  under  a  pressure  equal  to  f  that  of  the  atmosphere. 


Fig.  156. 


Fig.  i£7- 


Fig.  158. 


\    -   190.  Diffusion  of  gases. — Phenomena  analogous  to  those  of  endosmose 
(139)  are  seen  in  a  high  degree  in  the  case  of  gases.     When  two  different 


190] 


Diffusion  of  Gases. 


163 


gases  are  separated  by  a  porous  diaphragm,  an  interchange  takes  place 
between  them,  and  ultimately  the  composition  of  the  gas  on  both  sides  of 
the  diaphragm  is  the  same  ;  but  the  rapidity  with  which  different  gases 
diffuse  into  each  other  under  these  circumstances  varies  considerably. 
There  is,  however,  an  essential  difference  between  the  phenomena  of 
endosmose  and  those  of  diffusion  ;  for  while  the  inequality  in  the  currents 
in  the  former  case  is  due  to  the  different  attraction  of  the  materials  of  the 
diaphragm  for  the  constituents,  in  the  diffusion  of  gases  this  nature  has  no 
influence ;  from  the  smallness  of  the  pores  the  actions  are  molecular,  and  not 
molar,  and  the  rate  of  interchange  depends  only  on  the  size  of  the  molecules, 
that  is,  on  the  specific  gravities  of  the  gases.  The  laws  of  the  diffusion  of 
gases  were  investigated  by  Graham.  Nume- 
rous experiments  illustrate  it,  some  of  the  most 
interesting  of  which  are  the  following  : — 

A  glass  cylinder  closed  at  one  end  is  filled 
with  carbonic  acid  gas,  its  open  end  tied  over 
with  a  bladder,  and  the  whole  placed  under  a 
jar  of  hydrogen.  Diffusion  takes  place  between 
them  through  the  porous  diaphragm,  and  after 
the  lapse  of  a  certain  time  hydrogen  has  passed 
through  the  bladder  into  the  cylindrical  vessel 
in  much  greater  quantity  than  the  carbonic  acid 
which  has  passed  out,  so  that  the  bladder  be- 
comes very  much  distended  outwards  (fig.  156). 
If  the  cylinder  be  filled  with  hydrogen  and  the 
bell-jar  with  carbonic  acid,  the  reverse  pheno- 
menon will  be  produced — the  bladder  will  be 
distended  inwards  (fig.  157). 

A  tube  about  12  inches  long,  closed  at  one 
end  by  a  plug  of  dry  plaster  of  Paris,  is  filled 
with  dry  hydrogen,  and  its  open  end  then  im- 
mersed in  a  mercury  bath.  Diffusion  of  the 
hydrogen  towards  the  air  takes  place  so  rapidly 
that  a  partial  vacuum  is  produced,  and  mercury 
rises  in  the  tube  to  a  height  of  several  inches 
(fig.  158).  If  several  such  tubes  are  filled  with 
different  gases,  and  allowed  to  diffuse  into  the 
air  in  a  similar  manner,  in  the  same  time, 
different  quantities  of  the  various  gases  will 
diffuse  ;  and  Graham  found  that  the  law  regu- 
lating these  diffusions  is  that  the  force  of  diffu- 
sion is  inversely  as  the  square  roots  of  the  densities  of  gases.  Thus,  if 
two  vessels  of  equal  capacity,  containing  oxygen  and  hydrogen,  be  separated 
by  a  porous  plug,  diffusion  takes  place  ;  and  after  the  lapse  of  some  time, 
for  every  one  part  of  oxygen  which  has  passed  into  the  hydrogen,  four  parts 
of  hydrogen  have  passed  into  the  oxygen.  Now  the  density  of  hydrogen 
being  I,  that  of  oxygen  is  16,  hence  the  force  of  diffusion  is  inversely  as  the 
square  roots  of  these  numbers.  It  is  four  times  as  great  in  the  one  which 
has  T\  the  density  of  the  other. 

M  2 


.Fig.  159. 


1 64 


On  Gases, 


[190- 


Let  the  stem  of  an  ordinary  tobacco  pipe  be  cemented,  so  that  its  ends 
project,  in  an  outer  glass  tube,  which  can  be  connected  with  an  air-pump 
and  thus  exhausted.  On  allowing  then  a  slow  current  of  air  to  enter  one 
end  of  the  pipe,  its  nitrogen  diffuses  more  rapidly  on  its  way  through  the 
porous  pipe  than  the  heavier  oxygen,  so  that  the  gas  which  emerges  at  the 
other  end  of  the  porous  pipe,  and  which  can  be  collected,  is  richer  in  oxygen, 
and  by  repeating  the  operation  on  the  gas  which  has  passed  through,  the 
proportion  of  oxygen  is  so  much  increased  that  the  gas  can  relight  a  semi- 
extinguished  taper.  To  this  process,  in  which  one  gas  can  be  separated  from 
another  by  diffusion,  the  term  atmolysis  is  given. 

Fig.  159  is  an  excellent  illustration  of  the 
action  of  diffusion.  A  porous  pot,  A,  such  as  is 
used  for  batteries,  is  fixed  by  means  of  a  cork 
to  the  glass  tube,  which  contains  water  up  to 
the  bulb  C,  the  upper  part  containing  air.  When 
a  beaker  containing  hydrogen,  B,  is  placed  over 
the  pot,  the  diffusion  of  the  hydrogen  into  it 
is  so  rapid  that  the  water  is  at  once  driven  down 
and  jets  out.  When  the  beaker  is  removed, 
the  gas  inside  the  pot  being  richer  in  hydrogen 
now  diffuses  out  with  great  rapidity,  and  the 
water  rises  in  the  tube  beyond  its  original 
level. 

V  191.  Effusion  of  gases. — A  gas  can  only 
flow  from  one  space  to  another  space  occupied 
by  the  same  gas  when  the  pressure  in  the  one 
is  greater  than  in  the  other.  Effusion  is  the 
term  applied  to  the  phenomenon  of  the  passage 
of  gases  into  vacuum,  through  a  minute  aper- 
ture not  much  more  or  less  than  0-013  milli- 
metre in  diameter,  in  a  thin  plate  of  metal  or 
of  glass  ;  for  in  a  tube  we  are  dealing  with 
masses  of  gases,  and  friction  comes  into  play ; 
and  in  a  larger  aperture  the  particles  would 
strike  against  one  another,  and  form  eddies  and 
whirlpools.  The  velocity  of  ^he  efflux  is  mea- 
sured by  the  formula  v  =  \figh,  in  which  h  re- 
presents the  pressure  under  which  the  gas 
flows,  expressed  in  terms  of  the  height  of  a 
column  of  the  gas  which  would  exert  the  same 
pressure  as  that  of  the  effluent  gas.  Thus  for 
air  under  the  ordinary  pressure  flowing  into  a  vacuum,  the  pressure  is 
equivalent  to  a  column  of  mercury  76  centimetres  high  ;  and  as  mercury 
is  approximately  10,500  times  as  dense  as  air,  the  equivalent  column  of  air 
will  be  76  x  1 0,500  =  7,980  metres.  Hence  the  velocity  of  efflux  of  air  into 
vacuum  is  =  ^2  x  9-8  x  7,980  =  395-5  metres.  This  velocity  into  vacuum 
only  holds,  however,  for  the  first  moment,  for  the  space  contains  a  con- 
tinually increasing  quantity  of  air,  so  that  the  velocity  becomes  continually 
smaller,  and  is  null  when  the  pressure  on  each  side  is  the  same.  If  the 


Fig.  1 60. 


-193]  Absorption  of  Gases  by  Solids.  165 

height  of  the  column  of  air  M15  corresponding  to  the  external  pressure,  is 
known,  the  velocity  may  be  calculated  by  the  formula  v  =  ^/2g  (h-h^). 

For  gases  lighter  than  air  a  greater  height  must  be  inserted  in  the 
formula,  and  for  heavier  gases  a  lower  height ;  and  this  change  must  be 
inversely  as  the  change  of  density.  Hence  the  velocities  of  efflux  of 
various  gases  must  be  inversely  as  the  sqtiare  roots  of  their  densities. 
A  simple  inversion  of  this  statement  is  that  the  densities  of  two  gases  are 
inversely  as  the  squares  of  their  velocities  of  effusion.  On  this  law  Bunsen 
has  based  an  interesting  method  of  determining  the  densities  of  gases  and 
vapours,  which  is  of  great  service  where  only  small  quantities  of  the  sub- 
stances are  available. 

The  gas  in  question  is  contained  (fig.  160)  in  a  glass  tube  A,  closed  at  the 
top  with  a  stopper  S,  in  the  neck  B.  In  a  little  enlargement  here  a  platinum 
plate  v  is  fixed,  in  which  is  a  fine  capillary  aperture.  The  tube  is  inserted 
in  a  deep  mercury  trough,  CC,  so  that  the  top  r  of  a  glass  swimmer  D  is  level 
with  the  mercury.  The  stopper  S  having  been 
removed,  the  gas  issues  through  the  capillary  aper- 
ture, and  the  time  is  noted  which  elapses  until  a 
mark  /  in  the  swimmer  is  level  with  the  mercury. 
Working  in  this  way  with  different  gases,  it  is  found 
that  the  ratios  of  the  times  of  effusion  are  directly 
as  the  squares  of  the  densities,  which  is  another 
form  of  the  above  statement. 

\f  192.  Transpiration  of  gases. — If  gases  issue 
through  long,  fine  capillary  tubes  into  a  vacuum,  the 
phenomenon  is  called  transpiration  ;  and  the  rate 
of  efflux,  or  the  velocity  of  transpiration,  is  indepen- 
dent of  the  rate  of  diffusion. 

i.  For  the  same  gas,  the  rate  of  transpiration 
increases,  other  things  being  equal,  directly  as  the 
pressure  ;  that  is,  equal  volumes  of  air  of  different 
densities  require  times  inversely  proportional  to 
their  densities. 

ii.  With  tubes  of  eqtial  diameters,  the  volume  transpired  in  equal  times 
is  inversely  as  the  length  of  the  tube. 

iii.  As  the  temperature  rises  the  transpiration  becomes  slower. 

iv.   The  rate  of  transpiration  is  independent  of  the  material  of  the  tube. 

1 93.  Absorption  of  gases  by  solids. — The  surfaces  of  all  solid  bodies 
exert  an  attraction  on  the  molecules  of  gases  with  which  they  are  in  contact, 
of  such  a  nature  that  they  become  covered  with  a  more  or  less  thick  layer 
of  condensed  gas.  When  a  porous  body  such  as  a  piece  of  charcoal,  which 
consequently  presents  an  immensely  increased  surface  in  proportion  to  its 
size,  is  placed  in  a  vessel  of  ammonia  gas  over  mercury  (fig.  161),  the  great 
diminution  of  volume  which  ensues  indicates  that  considerable  quantities  of 
gas  are  absorbed. 

Now,  although    there   is   no  absorption  such  as   arises  from  che 
combination  between  the  solid  and  the  gas  (as  with  phosphorus  and  oxygen), 
still  the  quantity  of  gas  absorbed  is  not  entirely  dependent  on  the  phy- 
sical conditions  of  the  solid  body  ;  it  is  influenced  in  some  measure  by  the 


1 56  On  Gases.  [193- 

chem  cal  nature  both  of  the  solid  and  the  gas.  Boxwood  charcoal  has 
very  great  absorptive  power.  The  following  table  gives  the  volumes  of  gas, 
under  standard  conditions  of  temperature  and  pressure,  absorbed  by  one 
volume  of  boxwood  charcoal  and  of  meerschaum  respectively  :— 

Charcoal          Meerschaum 

Ammonia 90  15 

Hydrochloric  acid 85 

Sulphurous  acid          ......  65 

Sulphuretted  hydrogen 55  n 

Carbonic  acid    .        '.'•'.     *'  ,  '    "'.         .         .  35  5'3 

Carbonic  oxide  .         .    .    .      _»  •  9'4  1*2 

Oxygen      ...  .  9-2  1-5 

Nitrogen    .         .         .     "   .        ....  7-5  r6 

Hydrogen.         .         .       '.'       .         .         .         .  175  0-5 

The  absorption  of  gases  is  in  general  greatest  in  the  case  of  those  which  are 
most  easily  liquefied. 

Cocoa-nut  charcoal  is  even  more  highly  absorbent;  it  absorbs  171  of 
ammonia,  73  of  carbonic  acid,  and  108  of  cyanogen  at  the  ordinary  pressure  ; 
the  amount  of  absorption  increases  with  the  pressure.  The  absorptive 
power  of  pine  charcoal  is  about  half  as  much  as  that  of  boxwood.  The 
charcoal  made  from  corkwood,  which  is  very  porous,  is  not  absorbent, 
neither  is  graphite.  Platinum,  in  the  finely  divided  form  known  as  platinum 
sponge,  is  said  to  absorb  250  times  its  volume  of  oxygen  gas.  Many  other 
porous  substances,  such  as  meerschaum,  gypsum,  silk,  &c.,  are  also  highly 
absorbent. 

If  a  coin  be  laid  on  a  plate  of  glass  or  of  metal,  after  some  time,  when 
the  plate  is  breathed  on,  an  image  of  the  coin  appears.  If  a  figure  is  traced 
on  a  glass  plate  with  the  finger,  nothing  appears  until  the  plate  is  breathed 
on,  when  the  figure  is  at  once  seen.  Indeed,  the  traces  of  an  engraving 
which  has  long  laid  on  a  glass  plate  may  be  produced  in  this  way. 

These'  phenomena  are  known  as  Moser^s  images,  for  he  first  investigated 
them,  although  he  explained  them  erroneously.  The  correct  explanation 
was  given  by  Waidele,  who  ascribed  them  to  alterations  in  the  layer  of  gas, 
vapour,  and  fine  dust  which  is  condensed  on  the  surface  of  all  solids.  If 
this  layer  is  removed  by  wiping,  on  afterwards  breathing  against  the  surface 
more  vapour  is  condensed  on  the  marks  in  question,  which  then  present  a 
different  appearance  from  the  rest. 

If  a  die  or  a  stamp  is  laid  on  a  freshly  polished  metal  plate,  and  one 
therefore  which  has  been  deprived  of  its  atmosphere,  the  layer  of  vapour 
from  the  coin  will  diffuse  on  to  the  metal  plate,  which  thereby  becomes 
altered  ;  so  that  when  this  is  breathed  on  an  impression  is  seen. 

Conversely,  if  a  coin  be  polished  and  placed  on  an  ordinary  glass  plate, 
it  will  partially  remove  the  layer  of  gas  from  the  parts  in  contact,  so  that  on 
breathing  on  the  plate  the  image  is  visible. 

194.  Occlusion  of  gases. — Graham  found  that  at  a  high  temperature 
platinum  and  iron  allow  hydrogen  to  traverse  them  even  more  readily  than 
does  caoutchouc  in  the  cold.  Thus  while  a  square  metre  of  caoutchouc  0^014 
millimetre  in  thickness  allowed  129  cubic  centimetres  of  hydrogen  at  20°  to 


-194]  Occlusion  of  Gases.  167 

traverse  it  in  a  minute,  a  platinum  tube  ri  millimetre  in  thickness  and  of  the 
same  surface  allowed  489  cubic  centimetres  to  traverse  it  at  a  bright  red  heat. 

This  is  probably  connected  with  the  property  which  some  metals,  though 
destitute  of  physical  pores,  possess  of  absorbing  gases  either  on  their  surface 
or  in  their  mass,  and  to  which  Graham  has  applied  the  term  occlusion.  It 
is  best  observed  by  allowing  the  heated  metal  to  cool  in  contact  with  the 
gas.  The  gas  cannot  then  be  extracted  by  the  air-pump,  but  is  disengaged 
on  heating.  In  this  way  Graham  found  that  platinum  occluded  four  times 
its  volume  of  hydrogen  ;  iron  wire  0-44  its  volume  of  hydrogen,  and  4-15 
volumes  of  carbonic  oxide  ;  silver,  reduced  from  the  oxide,  absorbed  about 
seven  volumes  of  oxygen,  and  nearly  one  volume  of  hydrogen  when  heated 
to  dull  redness  in  these  gases.  This  property  is  most  remarkable  in  palla- 
dium, which  absorbs  hydrogen,  not  only  in  cooling  after  being  heated,  but 
also  in  the  cold.  When,  for  instance,  a  palladium  electrode  is  used  in  the 
decomposition  of  water,  one  volume  of  the  metal  can  absorb  980  times  its 
volume  of  the  gas.  This  gas  is  again  driven  out  on  being  heated,  in  which 
respect  there  is  a  resemblance  to  the  solution  of  gases  in  liquids.  By  the 
occlusion  of  hydrogen  the  volume  of  palladium  is  increased  by  0*09827  of 
its  original  amount,  from  which  it  follows  that  the  hydrogen,  which  under 
ordinary  circumstances  has  a  density  O'Oooo89546  that  of  water,  has  here  a 
density  nearly  9,868  times  as  great,  or  about  0-88  that  of  water.  Hence  the 
hydrogen  must  be  in  the  liquid  or  even  solid  state  ;  it  probably  forms  thus 
an  alloy  with  palladium,  like  a  true  metal — a  view  of  this  gas  which  is 
strongly  supported  by  independent  chemical  considerations.  The  physical 
properties  too,  in  so  far  as  they  have  been  examined,  support  this  view  of  its 
being  an  alloy. 

The  phenomenon  of  occlusion  may  be  illustrated  by  the  following  experi- 
ment (fig.  162).  A  platinum  wire  be  is  stretched  between  supports  on  a 
glass  plate ;  one  end  of  a  palladium 

wire  fg  is  also  fixed,  of  which  the  other                             r*  Jg 

end  is  attached  to  the  short  arm  of  a  light 
lever  movable  about  <?,  the  long  arm  of  •• 


which  is  loaded  with  a  weight  not  repre- 
sented in  the  figure,  to  keep  the  wire  tight. 
The  platinum  wire  is  connected  with  the 
positive  pole  a  and  the  palladium  with  the 
negative  pole  d  of  a  voltaic  battery,  and 
the  apparatus  is  partially  immersed  in 
acidulated  water  ;  the  water  is  thereby 
decomposed  into  its  constituent  gases  ; 
oxygen  is  liberated  in  bubbles  from  the 

platinum  wire,  but  there  is  no  visible  dis-  [__ 

engagement  at  the  palladium.    It  becomes  Fig.  162. 

longer,  however,  as  is  seen  by  the  lever 

moving  downwards.    If  the  current  is  reversed,  the  wire  again  contracts,  and 
the  lever  resumes  its  original  position. 


168 


On  Gases. 


[195- 


CHAPTER  III. 

PRESSURE  OF   BODIES   IN   AIR.      BALLOONS. 

/^ 

195.  Archimedes'  principle  applied  to  gases. — The  pressure  exerted 
by  gases,  on  bodies  immersed  in  them,  is  transmitted  equally  in  all  directions, 

as  has  been  shown  by  the  experiment 
with  the  Magdeburg  hemispheres.  It 
therefore  follows  that  all  which  has 
been  said  about  the  equilibrium  of 
bodies  in  liquids  applies  to  bodies  in 
air  ;  they  lose  a  part  of  their  weight 
equal  to  that  of  the  air  which  they  dis- 
place. 

The  loss  of  weight  in  air  is  demon- 
strated by  means  of  the  baroscope, 
which  consists  of  a  scalebeam,  at  one 
of  whose  extremities  a  small  leaden 
weight  is  supported,  and  at  the  other 
there  is  a  hollow  copper  sphere  (fig. 
163).  In  the  air  they  exactly  balance 
one  another  ;  but  when  they  are  placed 
under  the  receiver  of  an  air-pump, 
and  a  vacuum  is  produced,  the  sphere 
sinks,  thereby  showing  that  in  reality 
it  is  heavier  than  the  small  leaden 
weight.  Before  the  air  is  exhausted,  each  body  is  buoyed  up  by  the  weight 
of  the  air  which  it  displaces.  But  as  the  sphere  is  much  the  larger  of  the 
two,  its  weight  undergoes  most  apparent  diminution,  and  thus,  though  in 
reality  the  heavier  body,  it  is  balanced  by  the  small  leaden  weight.  It  may 
be  proved  by  means  of  the  same  apparatus  that  this  loss  is  equal  to  the 
weight  of  the  displaced  air.  Suppose  the  volume  of  the  sphere  is  10  cubic 
inches.  The  weight  of  this  volume  of  air  is  3-1  grains.  If  now  this  weight 
be  added  to  the  leaden  weight,  it  will  overbalance  the  sphere  in  air,  but  will 
exactly  balance  it  in  vacuo. 

The  principle  of  Archimedes  is  true  for  bodies  in  air  ;  all  that  has  been 
said  about  bodies  immersed  in  liquids  applies  to  them  ;  that  is,  that  when  a 
body  is  heavier  than  air,  it  will  sink,  owing  to  the  excess  of  its  weight  over 
the  buoyancy.  If  it  is  as  heavy  as  air,  its  weight  will  exactly  counterbalance 
the  buoyancy,  and  the  body  will  float  in  the  atmosphere.  If  the  body  is 
lighter  than  air,  the  buoyancy  of  the  air  will  prevail,  and  the  body  will  rise 
in  the  atmosphere  until  it  reaches  a  layer  of  the  same  density  as  its  own. 


Fig.  163. 


-197]  Construction  and  Management  of  Balloons.  169 

The  force  of  the  ascent  is  equal  to  the  excess  of  the  buoyancy  over  the  weight 
or  the  body.  This  is  the  reason  why  smoke,  vapours,  clouds,  and  air-balloons 
rise  in  the  air. 

AIR-BALLOONS. 

v  196.  Air-balloons. — Air-balloons  are  hollow  spheres  made  of  some  light 
impermeable  material,  which,  when  filled  with  heated  air,  with  hydrogen 
gas,  or  with  coal  gas,  rise  in  the  air  by  virtue  of  their  relative  lightness. 

They  were  invented  by  the  brothers  Montgolfier  of  Annonay,'  and  the 
first  experiment  was  made  at  that  place  in  June  1783.  Their  balloon  was  a 
sphere  of  forty  yards  in  circumference,  and  weighed  500  pounds.  At  the 
lower  part  there  was  an  aperture,  and  a  sort  of  boat  was  suspended,  in  which 
fire  was  lighted  to  heat  the  internal  air.  The  balloon  rose  to  a  height  of 
2,200  yards,  and  then  descended  without  any  accident. 

Charles,  a  professor  of  physics  in  Paris,  substituted  hydrogen  for  hot  air. 
He  himself  ascended  in  a  balloon  of  this  kind  in  December  1783.  The  use 
of  hot-air  balloons  was  entirely  given  up  in  consequence  of  the  serious 
accidents  to  which  they  were  liable. 

Since  then  the  art  of  ballooning  has  been  greatly  extended,  and  many 
ascents  have  been  made.  That  which  Gay-Lussac  made  in  1804  was  the 
most  remarkable  for  the  facts  with  which  it  has  enriched  science,  and  for  the 
height  which  he  attained — 23,000  feet  above  the  sea-level.  At  this  height 
the  barometer  sunk  to  12 -6  inches,  and  the  thermometer,  which  was  31°  C. 
on  the  ground,  was  9  degrees  below  zero. 

In  these  high  regions  the  dryness  was  such  on  the  day  of  Gay-Lussac's 
ascent,  that  hygrometric  substances,  such  as  paper,  parchment,  £c.,  became 
dried  and  crumpled  as  if  they  had  been  placed  near  the  fire.  The  respira- 
tion and  circulation  of  the  blood  were  accelerated  in  consequence  of  the 
great  rarefaction  of  the  air.  Gay-Lussac's  pulse  made  120  pulsations  in  a 
minute  instead  of  66,  the  normal  number.  At  this  great  height  the  sky  had 
a  very  dark  blue  tint,  and  an  absolute  silence  prevailed. 

One  of  the  most  remarkable  of  ascents  was  made  by  Mr.  Glaisher  and 
Mr.  Coxwell,  in  a  large  balloon  belonging  to  the  latter.  This  was  filled  with 
90,000  cubic  feet  of  coal  gas  (sp.  gr.  0-37  to  0-33) ;  the  weight  of  the  load 
was  600  pounds.  The  ascent  took  place  at  I  P.M.  on  September  5,  1861 ;  at 
1.28  they  had  reached  a  height  of  15,750  feet,  and  in  eleven  minutes  after  a 
height  of  21,000  feet,  the  temperature  being  -10-4°;  at  1.50  they  were  at 
26,200  feet,  with  the  thermometer  at  -15-2°.  At  1.52  the  height  attained 
was  29,000  feet,  and  the  temperature  -  16°  C.  At  this  height  the  rarefaction 
of  the  air  was  so  great,  and  the  cold  so  intense,  that  Mr.  Glaisher  fainted, 
and  could  no  longer  observe.  According  to  an  approximate  estimation  the 
lowest  barometric  height  they  attained  was  7  inches,  which  would  correspond 
to  an  elevation  of  from  36,000  to  37,000  feet. 

197.  Construction  and  management  of  balloons.— A  balloon  (fig.  104) 
is  made  of  long  bands  of  silk  sewed  together  and  covered  with  caoutchouc 
varnish,  which  renders  it  airtight.     At  the  top  there  is  a  safety-valve  clo 
by  a  spring,  which  the  aeronaut  can  open  at  pleasure  by  means  of  a  cord. 
A  light  wickerwork  boat  is  suspended  by  means  of  cords  to  a  network  whi 
entirely  covers  the  balloon. 


On  Gases. 


[197- 


about 


A  balloon  of  the  ordinary  dimensions,  which  can  carry  three  persons,  i 
mt  1 6  yards  high,  12  yards  in  diameter,  and  its  volume,  when  it  is  quit 


quite 


full,  is  about  680  cubic  yards.  The  bal- 
loon itself  weighs  200  pounds  ;  the  ac- 
cessories, such  as  the  rope  and  boat,  100 
pounds. 

The  balloon  is  filled  either  with  hy- 
drogen or  with  coal  gas.  Although  the 
latter  is  heavier  than  the  former,  it  is 
generally  preferred,  because  it  is  cheaper 
and  more  easily  obtained.  It  is  passed 
into  the  balloon  from  the  gas  reservoir 
by  means  of  a  flexible  tube.  It  is  im- 
portant not  to  fill  the  balloon  quite 
full,  for  the  atmospheric  pressure  dimin- 
ishes as  it  rises,  and  the  gas  inside, 
expanding  in  consequence  of  its  elastic 
force,  tends  to  burst  it.  It  is  suffi- 
cient for  the  ascent  if  the  weight  of 
the  displaced  air  exceeds  that  of  the 
balloon  by  8  or  10  pounds.  And  this 
force  remains  constant  so  long  as  the 
balloon  is  not  quite  distended  by  the 
dilatation  of  the  air  in  the  interior.  If 
the  atmospheric  pressure,  for  example, 
has  diminished  to  one-half,  the  gas  in  the 
balloon,  according1  to  Boyle's  law,  has 
doubled  its  volume.  The  volume  of  the 
air  displaced  is  therefore  twice  as  great  ; 
but  since  its  density  has  become  only 
one-half,  the  weight  and  consequently 
the  upward  buoyancy  are  the  same. 
When  once  the  balloon  is  completely 
dilated,  if  it  continues  to  rise,  the  force  of 
the  ascent  decreases,  for  the  volume  of 
the  displaced  air  remains  the  same,  but 
its  density  diminishes,  and  a  time  arrives 
at  which  the  buoyancy  is  equal  to  the 
weight  of  the  balloon.  The  balloon  can  now  only  take  a  horizontal  direction, 
carried  by  the  currents  of  air  which  prevail  in  the  atmosphere.  The  aero- 
naut knows  by  the  barometer  whether  he  is  ascending  or  descending,  and 
by  the  same  means  he  determines  the  height  which  he  has  reached.  A  long 
flag  fixed  to  the  boat  would  indicate,  by  the  position  it  takes  either  above  or 
below,  whether  the  balloon  is  descending  or  ascending. 

When  the  aeronaut  wishes  to  descend,  he  opens  the  valve  at  the  top  of 
the  balloon  by  means  of  the  cord,  which  allows  gas  to  escape,  and  the 
balloon  sinks.  If  he  wants  to  descend  more  slowly,  or  to  rise  again,  he 
empties  out  bags  of  sand,  of  which  there  is  an  ample  supply  in  the  car.  The 
descent  is  facilitated  by  means  of  a  grappling  iron  fixed  to  the  boat.  When 


Fig.  164. 


-198] 


ParacJiute. 


171 


once  this  is  fixed  to  any   obstacle,  the  balloon  is  lowered  by  pulling  the 
cord. 

The  only  practical  applications  which  air-balloons  have  hitherto  had 
have  been  in  military  reconnoitring.  At  the  battle  of  Fleurus,  in  1794,  a 
captive  balloon — that  is,  one  held  by  a  rope — was  used,  in  which  there  was 
an  observer  who  reported  the  movements  of  the  enemy  by  means  of  signals. 
At  the  battle  of  Solferino  the  movements  and  dispositions  of  the  Austrian 
troops  were  watched  by  a  captive  balloon  ;  and  in  the  war  in  America 
balloons  were  frequently  used,  while  their  importance  during  the  siege  of 
Paris  is  fresh  in  all  memories.  The  whole  subject  of  military  ballooning 
was  treated  in  two  papers  by  Col.  Grover  and  by  Col.  Beaumont,  in  a 
volume  of  the  Professional  Papers  of  the  Royal  Engineers  ;  and  experiments 
are  in  progress,  at  Woolwich  and  at  Aldershot,  with  a  view  of  ascertain- 
ing the  most  practicable  means  of  inflating  balloons,  and  the  best  form  and 
equipment  for  service  in  the  field.  It  has  been  proposed  to  use  captive 
balloons  for  observations  on  the  changes  of  temperature  in  the  air,  &c.  Air- 
balloons  can  only  be  truly  useful  when  they  can  be  guided,  and  as  yet  all 
attempts  made  with  this  view  have  completely  failed.  There  is  no  other 
course  at  present  than  to  rise  in  the  air  until  there  is  a  current  which  has 
more  or  less  the  desired  direc- 
tion. Unfortunately  the  currents 
in  the  higher  regions  of  the 
atmosphere  are  variable  and 
irregular. 

198.  Parachute. — The  ob- 
ject of  the  parachute  is  to  allow 
the  aeronaut  to  leave  the  bal- 
loon, by  giving  him  the  means 
of  lessening  the  rapidity  of  his 
descent.  It  consists  of  a  large 
circular  piece  of  cloth  (fig.  165), 
about  1 6  feet  in  diameter,  and 
which  by  the  resistance  of  the 
air  spreads  out  like  a  gigantic 
umbrella.  In  the  centre  there 
is  an  aperture,  through  which 
the  air.  compressed  by  the 
rapidity  of  the  descent  makes 
its  escape ;  for  otherwise  os- 
cillations might  be  produced, 
which,  when  communicated  to 
the  boat,  would  be  dangerous. 

In  fig.  164  there  is  a  para- 
chute attached  to  the  network 
of  the  balloon  by  means  of  a 
cord  which  passes  round  a 

pulley,  and  is  fixed  at  the  other  end  to  the  boat.     When  the  cord  is  cut 
the  parachute  sinks,  at  first  very  rapidly,  but  more  slowly  as  it  b 
tended,  as  represented  in  the  figure. 


Fig.  165. 


172  On  Gases.  [199- 

199.  Calculation    of  the    weight   which    a   balloon    can    raise.  —  To 

calculate  the  weight  which  can  be  raised  by  a  balloon  of  given  dimensions 
let  us  suppose  it  perfectly  spherical,  and  premise  that  the  formulas  which 

express  the  volume  and  the  superficies  in  terms  of  the  radius  are  V  =  .     _ 

S  =  47rR2  ;  TT  being  the  ratio  of  the  circumference  to  the  diameter.  The 
radius  R  being  measured  in  feet,  let  p  be,  in  pounds,  the  weight  of  a 
square  foot  of  the  material  of  which  the  balloon  is  constructed  ;  let  P 
be  the  weight  of  the  car  and  the  accessories,  a  the  weight  in  pounds  of 
a  cubic  foot  of  air  at  zero,  and  under  the  pressure  076™,  and  a'  the  weight 
of  the  same  volume,  under  the  same  conditions,  of  the  gas  with  which 
the  balloon  is  inflated  (155).  Then  the  total  weight  of  the  envelope  in 
pounds  will  be  47rR2^  ;  that  of  the  gas  will  be  ^R3^  and  that  of  the  dis_ 

placed  air  ^  —  -.  If  X  be  the  weight  which  the  balloon  can  support,  we 
have 


x  =  -  -  47rR2/  _  P. 

3  3 

Whence 


X  =    7r  _  ^  _  47J.R2^  _  p 

But,  as  we  have  before  seen  (197),  in  order  that  the  balloon  may  rise,  the 
weights  must  be  less  by  8  or  10  pounds  than  that  given  by  this  equation. 


200] 


Air-pump. 


173 


CHAPTER    IV. 

APPARATUS   WHICH  DEPEND   ON   THE  PROPERTIES   OF  AIR. 


f 


200.  Air-pump. — The  air-pump  is  an  instrument  by  which  a  vacuum  can 
be  produced  in  a  given  space,  or  rather  by  which  air  can  be  greatly  rarefied, 
for  an  absolute  vacuum  cannot  be  produced  by  its  means.  It  was  invented 


Fig.  166. 


by  Otto  von  Guericke  in  1650,  a  few  years  after  the  invention  of  the  baro- 
meter. 

The  air-pump,  as  now  usually  constructed,  may  be  described  as  follows. 
Fig.  1 66  represents  a  general  view  ;  fig.  167  a  section,  and  figs.  168-173 
various  parts ;  the  letters  in  all  the  figures  having  everywhere  the  same 
meaning. 

The  base  V  G  L  is  of  stout  metal,  and  is  firmly  fixed  on  a  table.  At  one 
end  two  glass  cylinders  or  barrels  are  firmly  cemented,  and  the  two  leather 


174 


On  Gases. 


[200- 


pistons  P  and  P'  work  airtight  in  them.  To  these  pistons  are  attached 
racks  H,  K,  and  by  means  of  a  handle  M  N  working  about  a  pinion  X,  the 
pistons  P  and  P'  are  moved  alternately  up  and  down.  On  the  plate  V  is 
fitted  a  thick  glass  plate  with  a  very  true  surface.  In  its  centre  is  a  screw 
tubulure  #,  fixed  into  a  conduit  nc  in  the  base  of  the  pump,  and  which  con- 
nects the  receiver  and  the  barrels. 

Fig.  1 68  gives  a  vertical  section  of  one  of  the  pistons  on  a  larger  scale. 
It  consists  of  two  brass  discs,  A  and  B,  the  latter  of  which  is  provided  with 
a  tubulure  in  which  is  a  screw  D  \  this  presses  together  a  number  of  leather 
washers,  very  slightly  larger  than  the  disc.  The  leather  is  thoroughly 


M 


Fig.  167. 

soaked  with  oil,  and  slides  airtight  in  the  barrels,  but  with  slight  friction.  D 
is  pierced  by  a  channel  which  connects  it  with  the  outer  air.  In  the  centre 
of  the  disc  B  is  a  hole  z,  closed  by  a  metal  valve  Z,  which  is  'shod  with  cork, 
and  by  means  of  a  rod  e  is  kept  in  position  in  the  channel. 

A  valve  s  opens  and  closes  the  orifice  of  the  channel  c,  whjch  is  in  con- 
nection with  the  receiver.  It  is  fixed  to  the  end  of  a  rod  a,  which  moves,  but 
with  friction,  through  the  piston.  Then  when  the  piston  sinks  it  carries  with 
it  the  rod  a,  and  closes  the  orifice.  As  the  piston  rises  it  lifts  the  rod,  but 
only  for  a  small  distance,  for  the  rod  strikes  against  the  top  of  the  barrel,  and 
the  piston,  continuing  its  upward  motion,  slides  along  the  rod. 

The  stopcock  T  connects  the  receiver  R  with  the  air-pump  gauge  E  (201), 
while  S  connects  the  receiver  with  the  barrels.  When  the  receiver  has  been 
exhausted,  S  is  turned  through  a  quarter,  and  the  vacuum  is  thus  preserved. 


-201] 


Air-pump  Gauge. 


175 


Air  can  be  admitted  by  opening  a  screw  r,  at  the  top  of  a  channel  in  the 
stopcock  itself. 

The  piston  P'  being  at  the  bottom  of  the  barrel  (figs.  168  and  169),  as  the 
handle  is  worked,  the  piston  rises,  and  with  it  the  rod  a  and  the  valve  s 
while  Z  is  closed  by  its  own  weight  and  the  pressure  of  the  air  A  partial 
vacuum  is  created  under  the  piston,  but  the  valve  s,  having  opened  up  con- 
nection with  the  receiver  R,  the  air  in  this  expands  and  fills  both  the  receiver 
and  the  barrel.  When  P'  begins  to  descend,  the  valve  s  is  closed  by  the 
descent  of  the  rod  a,  the  rarefied  air  in  the  barrel  can  no  longer  return  to 
the  receiver,  it  gets  more  and  more  condensed,  and  its  elastic  force  is  ulti- 
mately so  great  as  to  open  the  valve  Z,  and  the  air  under  the  piston  escapes 
by  the  channel  D  into  the  outer  air,  and  thus  the  rarefaction  produced 


Fig.  i 68. 


Fig.  169. 


in  the  receiver  is  permanent.  At  the  second  stroke  of  the  piston  the 
same  phenomenon  is  repeated,  until  a  limit  is  reached  at  which,  although 
there  is  air  in  the  receiver,  its  elastic  force  is  insufficient  to  raise  the 
valve  Z. 

It  is  clear  that  when  the  rarefaction  has  proceeded  to  a  considerable 
extent,  the  atmospheric  pressure  on  the  top  of  P  will  be  very  great,  but  it  will 
be  very  nearly  balanced  by  the  atmospheric  pressure  on  the  top  of  the  other 
piston.  Consequently  the  experimenter  will  have  to  overcome  only  the 
difference  of  the  two  pressures.  This  is  the  reason  why  two  barrels  are 
employed,  a  plan  first  adopted  by  Hawksbee. 

^  201.  Air-pump  gauge. — When  the  pump  has  been  worked  some  time, 
the  pressure  in  the  receiver  is  indicated  by  the  difference  of  level  of  the 
mercury  in  the  two  legs  of  a  glass  tube  bent  like  a  syphon,  one  of  which  is 


176  On  Gases.  [201- 

opened,  and  the  other  closed  like  the  barometer.  This  little  apparatus, 
which  is  called  the  gauge,  is  fixed  to  an  upright  scale,  and  placed  under  a 
small  bell-jar,  which  communicates  with  the  receiver  E  by  a  stopcock  A, 
inserted  in  the  tube  leading  from  the  orifice  C  to  the  cylinders,  fig.  167. 

Before  commencing  to  exhaust  the  air  in  the  receiver,  its  elastic  force 
exceeds  the  weight  of  the  column  of  mercury  which  is  in  the  closed  branch, 
and  which  consequently  remains  full.  But  as  the  pump  is  worked,  the 
elastic  force  soon  diminishes,  and  is  unable  to  support  the  weight  of  the 
mercury,  which  sinks  and  tends  to  stand  at  the  same  level  in  both  legs.  If 
an  absolute  vacuum  could  be  produced,  they  would  be  exactly  on  the  same 
level,  for  there  would  be  no  pressure  either  on  the  one  side  or  the  other.  But 
with  the  very  best  machines  the  level  is  always  about  a  thirtieth  of  an  inch 
higher  in  the  closed  branch,  which  indicates  that  the  vacuum  is  not  absolute 
for  the  elastic  force  of  the  residue  is  equal  to  the  pressure  of  a  column  of 
mercury  of  that  height. 

Theoretically  an  absolute  vacuum  is  impossible  ;  for,  since  the  volume 
of  each  cylinder  is,  say,  ^  that  of  the  receiver,  only  ^  of  the  air  in  the 
receiver  is  extracted  at  each  stroke  of  the  piston,  and  consequently  it  is  im- 
possible to  exhaust  all  the  air  which  it  contains.  The  theoretical  degree  of 
exhaustion  after  a  given  number  of  strokes  is  easily  calculated  as  follows  :  — 
Let  a  denote  the  volume  of  the  receiver,  including  in  that  term  the  pipe  ; 
b  the  volume  of  the  cylinder  between  the  highest  and  lowest  positions  of 
the  piston  ;  and  assume,  for  the  sake  of  distinctness,  that  there  is  only  one 
cylinder  :  then  the  air  which  occupied  a  before  the  piston  is  lifted  occupies 
a  +  b  after  it  is  lifted  ;  and  consequently  if  d^  is  the  density  at  the  end  of  the 
first  stroke,  and  d  the  original  density,  we  must  have 


If  d^  is  the  density  at  the  end  of  the  second  stroke,  we  have 


Now  this  reasoning  will  apply  to  n  strokes  ; 
consequently  d"  =  /rf_JL_  j 

If  there  are  two  equal  cylinders,  the  same  formula  holds  ;  but  in  this 
case,  in  counting  n,  upstrokes  and  downstrokes  equally  reckon  as  one. 

It  is  obvious  that  the  exhaustion  is  never  complete,  since  d  can  be  zero 
only  when  n  is  infinite.  However,  no  very  great  number  of  strokes  is  re- 
quired to  render  the  exhaustion  virtually  complete,  even  if  a  is  several  times 
greater  than  b.  Thus  if  a=  lod  a  hundred  strokes  will  reduce  the  density 
from  d?  to  o'ooo4</  ;  that  is,  if  the  initial  pressure  is  30  inches,  the  pressure  at 
the  end  of  100  strokes  is  0-012  of  an  inch. 

Practically,  however,  a  limit  is  placed  on  the  rarefaction  that  can  be  pro- 
duced by  any  given  air-pump  ;  for,  as  we  have  seen,  the  air  becomes  ulti- 
mately so  rarefied  that,  when  the  pistons  are  at  the  bottom  of  the  cylinder, 
its  elastic  force  cannot  overcome  the  pressure  in  the  valves  on  the  inside  of 


Double-exhaustion  Stopcock. 

do  not  open,  and  there  is  no  further  action  of  the 

202.  Double-exhaustion  stopcock.-By  means  of  this  device  the  ex- 
haustion of  the  air  can  be  carried  to  a  very  high  degree.  Fig.  170  gives  a 
horizontal  section  of  the  stopcock  Q,  which  by  means  of  a  central  channel 
and  wo  lateral  ones  forms  a  communication  with  the  receiver  and  the 
barrels.  When  the  working  ceases,  that  is  when  Z  no  longer  rises,  a  quarter- 
turn  is  given  to  Q,  fig.  172.  The  connections  are  now  altered,  as  is  seen  from 
.the  horizontal  sections  in  figs.  170  and  172,  and  the  vertical  sections  in  figs 
171  and  173-  The  new  channels  correspond  now  with  those  of  the  base  and 
the  right  barrel  is  alone  connected  with  the  receiver  by  the  channel  nmc 


Fig.  17 


Fig.  172. 


Fig.  171. 


Fig.  173- 


while  the  left  is  connected  by  an  oblique  channel  in  the  stopcock  with  a 
central  aperture  s  in  the  base  of  the  right  barrel. 

The  right  piston  as  it  rises  exhausts  air  from  the  receiver  ;  but  when  it 
sinks  the  exhausting  air  is  drawn  into  the  left  barrel  by  the  apertures  o  and 
d,  this  latter  being  always  open,  for  the  corresponding  conical  valve  is  raised. 
When  the  right  piston  rises,  that  of  the  left  sinks ;  but  the  air  below  does 
not  return  to  the  right  barrel,  for  the  orifice  is  now  closed  by  the  conical 
valve.  As  the  right  cylinder  continues  to  exhaust  the  air  in  the  receiver, 
and  to  force  it  into  the  left  cylinder,  the  air  accumulates  here  and  ultimately 
acquires  sufficient  pressure  to  raise  the  valve  of  the  piston  Q,  which  was 
impossible  before  the  stopcock  was  turned,  for  it  is  only  when  the  valves  in 

N 


On  Gases. 


[202- 


the  piston  no  longer  open,  that  a  quarter  of  a  turn  is  given  to  the  stopcock. 
In  this  way  a  rarefaction  of  half  a  millimetre  has  been  attained. 

203.  Bianchi's  air-pump. — Bianchi  invented  an   air-pump  which   has 
several  advantages.  It  is  made  entirely  of  iron,  and  it  has  only  one  cylinder, 


Fig.  174. 

which  oscillates  on  a  horizontal  axis  fixed  at  its  base,  as  seen  in  fig.  174. 
A  horizontal  shaft,  with  heavy  fly-wheel,  V,  works  in  a  frame,  and  is  turned 
by  a  handle,  M.  A  crank,  ;/z,  which  is  joined  to  the  top  of  the  piston-rod,  is 
fixed  to  the  same  shaft,  and  consequently  at  every  revolution  of  the  wheel 
the  cylinder  makes  two  oscillations. 

In  some  cases,  as  in  that  shown  in  the  figure,  the  crank  and  the  fly-wheel 
are  on  parallel  axes  connected  by  a  pair  of  cog-wheels.  The  modification 
in  the  action  produced  by  this  arrangement  is  as  follows  : — If  the  cog- 


204] 


DeleuiPs  Air-Pump. 


an   advantage 


179 

wheel  on  the  former  axis  has  twice  as  many  teeth  as  that   on  the  latter 

axis,    the    pressure   which   raises   the   piston    is    doubled 

which   is    counterbalanced   by   the 

inconvenience  that  now  the  piston 

will  make  one  oscillation  for  one 

revolution  of  the  fly-wheel. 

The  machine  is  double-acting  ; 
that  is,  the  piston  PP  (fig.  175)  pro- 
duces a  vacuum,  both  in  ascending 
and  descending.  This  is  effected 
by  the  following  arrangements  : — 
In  the  piston  there  is  a  valve,  b, 
opening  upwards  as  in  the  ordinary 
machine.  The  piston  rod  AA  is 
hollow,  and  in  the  inside  there  is  a 
copper  tube,  X,  by  which  the  air 
makes  its  escape  through  the  valve 
b.  At  the  top  of  the  cylinder  there 
is  a  second  valve,  a,  opening  up- 
wards. An  iron  rod,  D,  works  with 
gentle  friction  in  the  piston,  and 
terminates  at  its  ends  in  two  conical 
valves,  s  and  s',  which  fit  into  the 
openings  of  the  tube  BB  leading  to 
the  receiver. 

Let  us  suppose  the  piston  de- 
scends. The  valve  s'  is  then  closed, 
and,  the  valve  s  being  open,  the  air 
of  the  receiver  passes  into  the  space 
above  the  piston,  while  the  air  in 
the  space  below  the  piston  under- 
goes compression,  and,  raising  the 
valve,  escapes  by  the  tube  X,  which 
communicates  with  the  atmosphere. 

When  the  piston  ascends,  the  exhaustion  takes  place  through  s',  and  the 
valve  s  being  closed,  the  compressed  air  escapes  by  the  valve  a. 

The  machine  has  a  stopcock  for  double  exhaustion,  similar  to  that 
already  described  (202).  It  is  also  oiled  in  an  ingenious  manner.  A  cup,  E, 
round  the  rod  is  filled  with  oil,  which  passes  into  the  annular  space  between 
the  rod  AA  and  the  tube  X  ;  it  passes  then  into  a  tube  oo  in  the  piston,  and, 
forced  by  the  atmospheric  pressure,  is  uniformly  distributed  on  the  surface 
of  the  piston. 

The  apparatus,  being  of  iron,  may  be  made  of  much  greater  dimensions 
than  the  ordinary  air-pump.  A  vacuum  can  also  be  produced  with  it  in  far 
less  time  and  in  apparatus  of  greater  size  than  usual. 

204.  Deleuii's  air-pump.— In  this  air-pump  the  main  peculiarity  is  its 
piston,  which  is  of  considerable  length,  and  consists  of  a  series  of  accurately 
constructed  metal  discs  bolted  together.  This  works  easily  and  smoothly  in 
the  barrel,  and  no  packing  or  lubricator  is  used  ;  or  rather,  the  lubricator 

N  2 


1 8o 


On  Gases. 


[204- 


is  the  air  in  the  space  between  the  piston  and  the  barrel.  The  internal 
friction  of  the  air  in  this  narrow  space  is  so  great  that  the  rate  at  which  it 
leaks  into  the  barrel  is  far  inferior  to  the  rate  at  which  the  pump  is  exhaust- 
ing air  from  the  receiver.  And  Maxwell  showed  that  the  internal  friction 
is  not  diminished  even  when  its  density  is  greatly  reduced.  Hence  the 

pump  works  very  satisfactorily  up  to  a 
considerable  degree  of  exhaustion— to 
a  millimetre  of  mercury,  for  instance. 
\J  205.  Sprengel's  air  -  pump.  — 
&prengel  has  devised  a  form  of  air- 
pump  which  depends  on  the  principle 
of  converting  the  space  to  be  exhausted 
into  a  Torricellian  vacuum. 

If  an  aperture  be  made  in  the  top 
of  a  barometer  tube,  the  mercury  sinks 
and  draws  in  air  ;  if  the  experiment 
be  so  arranged  as  to  allow  air  to  enter 
along  with  mercury,  and  if  the  supply 
of  air  be  limited  while  that  of  mercury 
is  unlimited,  the  air  will  be  carried 
away  and  a  vacuum  produced.  The 
following  is  the  simplest  form  of  the 
apparatus  in  which  this  action  is  real- 
ised. In  fig.  176,  cd  is  a  glass  tube 
longer  than  a  barometer,  open  at  both 
ends,  and  connected,  by  means  of  india- 
rubber  tubing,  with  a  funnel,  A,  filled 
with  mercury  and  supported  by  a  stand. 
Mercury  is  allowed  to  fall  in  this  tube 
at  a  rate  regulated  by  a  clamp  at  c ; 
the  lower  end  of  the  tube  cd  fits  in  the 
flask  B,  which  has  a  spout  at  the  side 
a  little  higher  than  the  lower  end  of 
cd  ;  the  upper  part  has  a  branch  at  .r> 
to  which  a  receiver  R  can  be  tightly 
fixed.  When  the  clamp  at  c  is  opened, 
the  first  portions  of  mercury  which 
run  out,  close  the  tube  and  prevent  air 
from  entering  below.  As  the  mercury  is  allowed  to  run  down,  the  ex- 
haustion begins,  and  the  whole  length  of  the  tube  from  x  to  d  is  filled  with 
cylinders  of  air  and  mercury  having  a  downward  motion.  Air  and  mercury 
escape  through  the  spout  of  the  flask  B  which  is  above  the  basin  H,  where 
the  mercury  is  collected.  It  is  poured  back  from  time  to  time  into  the  funnel 
A,  to  be  repassed  through  the  tube  until  the  exhaustion  is  complete.  As  this 
point  is  approached,  the  enclosed  air  between  the  mercury  cylinders  is  seen 
to  diminish,  until  the  lower  part  of  cd  forms  a  continuous  column  of  mercury 
about  30  inches  high.  Towards  this  stage  of  the  process  a  noise  is  heard 
like  that  of  a  water-hammer  when  shaken  ;  the  operation  is  completed  when 
the  column  of  mercury  encloses  no  air,  and  a  drop  of  mercury  falls  on  the 


Fig.  176. 


-206]  Bunseris  Sprengel  Pump.  181 

top  of  the  column  without  enclosing  the  slightest  air-bubble.  The  height  of 
the  column  then  represents  the  height  of  the  column  of  mercury  in  the 
barometer  ;  in  other  words,  it  is  a  barometer  whose  Torricellian  vacuum 
is  the  receiver  R.  This  apparatus  has  been  used  with  great  success  in 
experiments  in  which  a  very  complete  exhaustion  is  required,  as  in  the 
preparation  of  Geissler's  tubes  and  in  incandescent  electrical  lamps.  It 
may  be  advantageously  combined  with  an  exhausting  syringe,  which  first 
removes  the  greater  part  of  the  air,  the  exhaustion  being  then  completed  as 
above. 

The  most  perfect  vacua  are  obtained  by  absorbing  the  residual  gas,  after 
the  exhaustion  has  been  pushed  as  far  as  possible,  either  mechanically  or 
by  some  substance  with  which 
it  combines  chemically.  Thus 
Dewar  has  produced  a  vacuum, 
which  he  estimates  at  3^  of  a 
millimetre,  by  heating  charcoal 
to  redness,  in  a  vessel  from 
which  air  had  been  exhausted 
by  the  Sprengel  pump,  and  then 
allowing  it  to  cool.  Finkener 
filled  a  vessel  with  oxygen,  then 
exhausted  as  far  as  possible, 
and  finally  heated  to  redness 
some  copper  contained  in  the 
vessel.  This  absorbed  the 
minute  quantity  of  gas  left,  with 
the  formation  of  cupric  oxide. 
In  some  of  his  experiments 
Crookes  obtained  by  chemical 
means  a  vacuum  of  geibs  °f  a 
millimetre.  In  these  highly 
rarefied  gases  the  pressure  is  so 
low  that  it  is  very  difficult  to 
measure  minute  differences. 
For  such  cases  McLeod  has 
devised  a  very  valuable  gauge, 
the  principle  of  which  is  to  con- 
dense a  measured  volume  of 


Fig.  177. 


the  highly  rarefied  gas  to  a  much  smaller  volume,  and  then  to  measure  its 
pressure  under  the  new  conditions. 

206.  Bunsen's  Sprengel  pump.— This  is  a  very  convenient  arrangement 
for  producing  a  vacuum  in  cases  where  a  good  supply  of  water  is  available, 
.as  in  laboratories.  A  composition  tube  a  (fig.  177)1  connected  with  the  ser- 
vice-pipe of  a  water-supply,  is  joined  by  means  of  a  caoutchouc  tube  to  a 
glass  tube,  cdfi  to  which  is  attached  at/a  leaden  tube  about  10  to  12  yards 
long.  The  tube  sr  is  connected  with  the  space  to  be  exhausted.  The  wat 
enters  by  a,  and  in  falling  down  the  tube  carries  with  it  air  from  the  space 
to  be  exhausted.  The  supply  of  water,  and  therewith  the  rate  of  exhaustion, 
can  be  regulated  by  the  stopcock  b  ;  the  bent  tube/?,  which  contains  mer- 


182 


On  Gases. 


[206- 


cury,  measures  the  degree  of  exhaustion,  which  may  be  reduced  to  a 
pressure  of  10  to  15  millimetres. 

207.  Aspirating  action  of  currents  of  air. — When  a  jet  of  liquid  or  of 
a  gas  passes  through  air,  it  carries  the  surrounding  air  along  with  it,  fresh 
air  rushes  in  to  supply  its  place,  comes  also  in  contact  with  the  jet,  and  is  in 
like  manner  carried  away.  Thus,  then,  there  is  a  continual  rarefaction  of  the 
air  round  the  jet,  in  consequence  of  which  it  exerts  an  aspiratory  action. 

This  phenomenon  may  be  well  illustrated  by  means  of  an  apparatus  re- 
presented in  fig.  178,  the  analogy  of  which  to  the  experiment  described  (146) 
will  be  at  once  evident.  It  consists  of  a  wide  glass  tube,  in  the  two  ends  of 
which  are  fitted  two  small  tubes,  nd  and  B  ;  in  the  bottom  is  a  manometer 
tube  containing  a  coloured  liquid.  On  blowing  through  the  narrow  tube  the 
liquid  at  o  is  seen  to  rise.  If,  on  the  contrary,  the  wide  tube  is  blown  into, 
a  depression  is  produced  at  o. 


Fig.  178. 


Fig.  179. 


To  this  class  of  phenomena  belongs  the  following  experiment,  which  is  a 
simple  modification  of  one  originally  described  by  Clement  and  Desormes. 
A  tube  is  fixed  in  a  metal  disc  (fig.  179),  its  end  being  flush  with  the  surface. 
A  light  disc  is  held  at  a  little  distance  by  means  of  three  metal  studs. 
Holding  the  tube  vertically  with  th'e  discs  downwards,  and  blowing  into  it, 
the  movable  disc  is  seen  to  rise  until  it  comes  in  contact  with  the  upper  one. 
The  current  of  air  spreads  out  from  the  centre  of  the  plate  towards  the 
circumference,  and  in  doing  so  it  is  rarefied  ;  in  consequence  of  this  lessened 
pressure  in  the  space,  the  lower  disc  is  lifted  by  the  external  pressure  against 
the  upper  one,  where  it  remains  as  long  as  the  blowing  continues.  The 
simplest  plan  of  making  this  experiment  was  devised  by  Faraday.  Holding 
one  hand  horizontal,  the  palm  downwards  and  the  fingers  clpsed,  the  space 
between  the  index  and  middle  finger  is  blown  through.  If  a  piece  of  light 
paper,  of  2  or  3  square  inches,  is  held  against  the  aperture,  it  does  not  fall 
as  long  as  the  blowing  continues. 

The  old  ivatcr-belloius,  still  used  in  mountainous  places  where  there  is  a 
continuous  fall,  is  a  further  application  of  the  principle.  Water  falling  from 
a  reservoir  down  a  narrow  tube  divides  and  carries  air  along  with  it ;  and  if 
there  are  apertures  in  the  side  through  which  air  can  enter,  this  also  is 


-208] 


Morren's  Mercury  Pump. 


183 


carried  along,  and  becomes  accumulated  in  a  reservoir  placed  below,  from 
which  by  means  of  a  lateral  tube  it  can  be  directed  into  the  hearth  of  a 
forge. 

By  the  locomotive  steam-pipe  a  jet  of  steam  entering  the  chimney  of  the 
locomotive  carries  the  air  away,  so  that  fresh  air  must  arrive  through  the 
fire,  and  thus  the  draught  be  kept  up.  In  GiffarcCs  injector  water  is  pumped 
by  means  of  a  jet  of  steam  into  the  boiler  of  a  steam-engine. 


Fig. 


Fig.  181. 


/208.  IKorren's  mercury  pump. -Figs.  1 80  and  181  represent  a  mercu- 
rial air-pump,  constructed  by  Alvergniat.     It  consists  of  two  reservoirs,  A 
and  B,  connected"  by  a  barometer  tube  T,  and  a  long  caoutchouc  tube  L. 
The  reservoir  B  and  the  tube  T  are  fixed  to  a  vertical  support  A,  whicl 
movable  and  open,  and  can  be  alternately  raised  and  lowered  thro 
distance  of  nearly  4  feet.     This  is  effected  by  means  of  a  long  wire  re 
which  is  fixed  at  one  end  to  the  reservoir  A,  and  passes  over  two  pulleys,  a 


1 84 


On  Gases, 


[208 


and  b,  the  latter  of  which  is  turned  by  a  handle.  Above  the  reservoir  B  is  a 
three-way  cock  n  ;  to  this  is  attached  a  tube  d,  for  exhaustion,  and  on  the 
left  is  an  ordinary  stopcock  ?#,  which  communicates  with  a  reservoir  of 
mercury  v,  and  with  the  air.  The  exhausting  tube  d  is  not  in  direct  com- 
munication with  the  receiver  to  be  exhausted  ;  it  is  first  connected  with  a 
reservoir  0,  partially  filled  with  sulphuric  acid,  and  designed  to  dry  the  gases 
which  enter  the  apparatus.  A  caoutchouc  tube,  <r,  makes  communication 
with  the  receiver  which  is  to  be  exhausted.  On  the  reservoir  o  is  a  small 
mercury  manometer^. 

These  details  being  understood,  suppose  the  reservoir  A  at  the  top  of  its 
course  (fig.  180),  the  stopcock  m  open,  and  the  stopcock  n  turned  as  seen  in 
Z ;  the  caoutchouc  tube  C,  the  tube  T,  the  reservoir  B,  and  the  tube  above 
are  filled  with  mercury  as  far  as  v ;  closing  then  the  stopcock  ;/z,  and  lower- 
ing the  reservoir  A  (fig.  181),  the  mercury  sinks  in  the  reservoir  B,  and  in 
the  tube  T,  until  the  difference  of  levels  in  the  two  tubes  is  equal  to  the  baro- 
metric height,  and  there  is  a  vacuum  in  the  reservoir  B.  Turning  now  the 

stopcock  «,  as  shown  in  fig.  X,  the  gas 
from  the  space  to  be  exhausted  passes 
into  the  barometric  chamber  B  by  the 
tubes  c  and  d^  and  the  level  again  sinks 
in  the  tube  T.  The  stopcocks  are  now 
replaced  in  the  first  position  (fig.  Z),  and 
the  reservoir  A  is  again  lifted,  the  excess 
of  pressure  of  mercury  in  the  caoutchouc 
tube  expels,  through  the  stopcocks  n  and 
;;z,  the  gas  which  had  passed  into  the 
chamber  B,  and  if  a  few  droplets  of  mer- 
cury are  carried  along  with  them,  they 
are  collected  in  the  vessel  -z/.  The  pro- 
cess is  repeated  until  the  mercury  is  vir- 
tually at  the  same  level  in  both  legs. 

Like  Sprengel's  pump,  this  is  very 
slow  in  its  working,  and,  like  it,  is  best 
employed  in  completing  the  exhaustion 
of  a  space  which  has  already  been  par- 
tially rarefied  ;  for  a  vacuum  of  ^  of  a 
millimetre  may  be  obtained  by  its  means. 
209.  Condensing:  pump. — The  con- 
densing pump  is  an  apparatus  for  com- 
pressing air,  or  any  other  gas.  The  form 
usually  adopted  is  the  following  : — In  a 
Fig<  l83'  cylinder,  A,  of  small  diameter  (fig.  183), 

there  is  a  solid  piston,  the  rod  of  which  is  moved  by  the  hand.  The  cylinder 
is  provided  with  a  screw  which  fits  into  the  receiver  K.  Fig.  182  shows  the 
arrangement  of  the  valves,  which  are  so  constructed  that  the  lateral  valve  o 
opens  from  the  outside,  and  the  lower  valve  s  from  the  inside. 

When  the  piston  descends,  the  valve  o  closes,  and  the  elastic  force  of  the 
compressed  air  opens  the  valve  s,  which  thus  allows  the  compressed  air  to 
pass  into  the  receiver.  When  the  piston  ascends,  s  closes  and  o  opens,  and 


-210] 


Uses  of  the  Air-pump. 


185 


permits  the  entrance  of  fresh  air,  which  in  turn  becomes  compressed  by  the 
descent  of  the  piston,  and  so  on.  This  apparatus  is  chiefly  used  for  charg- 
ing liquids  with  gases.  For  this  purpose  the  stopcock  B  is  connected  with 
a  reservoir  of  the  gas  by  means  of  the  tube  D.  The  pump  exhausts  this 
gas,  and  forces  it  into  the  vessel  K,  in  which  the  liquid  is  contained.  The 
artificial  gaseous  waters  are  made  by  means  of  analogous  apparatus. 

The  principle  of  the  condensing,  pump  has  many  applications,  such  as  in 
the  small  pump  used  by  plumbers  for  testing  and  for  clearing  gas-pipes,  in 
ventilating  mines,  in  supplying  air  to  blast-furnaces,  in  the  air-brakes  used 
in  railway  trains,  and  so  forth. 

210.  TJses  of  the  air-pump. — A  great  many  experiments  with  the  air- 
pump  have  been  already  described.  Such  are  the  mercurial  rain  (13),  the 
fall  of  bodies  in  vacuo  (76),  the  bladder  (153), 
the  bursting  of  a  bladder  (159),  the  Magde- 
burg hemispheres  (160),  and  the  baroscope 

(195). 

The  fountain  in  vacuo  (fig.  184)  is  an  ex- 
periment made  with  the  air-pump,  and  shows 
the  elastic  force  of  the  air.  It  consists  of  a 
glass  vessel,  A,  provided  at  the  bottom  with 
a  stopcock,  and  a  tubulure  which  projects 
into  the  interior.  Having  screwed  this 
apparatus  to  the  air-pump  it  is  exhausted, 
and,  the  stopcock  being  closed,  it  is  placed 
in  a  vessel  of  water,  R.  Opening  then  the 
stopcock,  the  atmospheric  pressure  upon  the 
water  in  the  vessel  makes  it  jet  through  the 
tubulure  into  the  interior  of  the  vessel,  as 
shown  in  the  drawing. 

Fig.  185  represents  an  experiment  illus- 
trating the  effect  of  atmospheric  pressure  on 
the  human  body.  A  glass  vessel,  open  at 
both  ends,  being  placed  on  the  plate  of  the 
machine,  the  upper  end  of  the  cylinder  is 
closed  by  the  hand,  and  a  vacuum  is  made. 
The  hand  then  becomes  pressed  by  the 
weight  of  the  atmosphere,  and  can  only 
be  taken  away  by  a  great  effort.  And  as  the  elasticity  of  the  fluids  con- 
tained in  the  organs  is  not  counterbalanced  by  the  weight  of  the  atmo- 
sphere, the  palm  of  the  hand  swells,  and  blood  tends  to  escape  from  the 
pores. 

By  means  of  the  air-pump  it  may  be  shown  that  air,  by  reason  of  the 
oxygen  it  contains,   is  necessary  for  the  support  of  combustion  and  of  1 
For  if  we  place  a  lighted  taper  under  the  receiver,  and  begin  to  exhaust  the 
air  the  flame  becomes  weaker  as  rarefaction  proceeds,  and  is  finally  extin- 
guished.    Similarly  an  animal  faints  and  dies  if  a  vacuum  is  formed 
receiver  under  which  it  is  placed.     Mammalia  and  birds ,  soon  die  in  vacuo. 
Fish  and  reptiles  support  the  loss  of  air  for  a  much  longer  time.     Inse< 
can  live  several  days  in  vacuo. 


Fig.  184. 


i86 


On  Gases.  [210- 

Substances  liable  to  ferment  may  be 
kept  in  vacuo  for  a  long  time  without 
alteration,  as  they  are  not  in  contact  with 
oxygen,  which  is  necessary  for  fermenta- 
tion. Food  kept  in  airtight  cases,  from 
which  the  air  had  been  exhausted,  have 
been  found  as  fresh  after  years  as  on  the 
first  day. 

211.  Hero's  fountain.- — Hero's  fountain, 
which  derives  its  name  from  its  inventor, 
Hero,  who  lived  at  Alexandria,  120  B.C., 
depends  on  the  elasticity  of  the  air.  It 
consists  of  a  brass  dish,  D  (fig.  186),  and  of 
two  glass  globes,  M  and  N.  The  dish  com- 
municates with  the  lower  part  of  the  globe  N 
by  a  long  tube,  B  ;  and  another  tube,  A, 
connects  the  two  globes.  A  third  tube 
passes  through  the  dish  D  to  the  lower  part 
of  the  globe  M.  This  tube  having  been 

taken  out,  the  globe  M  is  partially  filled  with  water  ;  the  tube  is  then  replaced, 
and  water  is  poured  into  the  dish.     The  water  flows  through  the  tube  B  into 

the  lower  globe,  and  expels  the  air,  which  is 
forced  into  the  upper  globe  ;  the  air,  thus 
compressed,  acts  upon  the  water,  and  makes  it 
jet  out  as  represented  in  the  figure.  If  it 
were  not  for  the  resistance  of  the  atmosphere 
and  friction,  the  liquid  would  rise  to  a  height 
above  the  water  in  the  dish  equal  to  the 
difference  of  the  level  in  the  two  globes. 

212.  Intermittent  fountain. — The  in- 
termittent fountain  depends  partly  on  the 
elastic  force  of  the  air,  and  partly  on  the 
atmospheric  pressure.  It  consists  of  a 
stoppered  glass  globe  (C,  fig.  187),  provided 
with  two  or  three  capillary  tubulures,  D. 
A  glass  tube  open  at  both  ends  reaches  at 
one  end  to  the  upper  part  of  the  globe  C  ; 
the  other  end  terminates  just  above  a  little 
aperture  in  the  dish  B,  which  supports  the 
whole  apparatus. 

The  water  with  which  the  globe  C  is 
nearly  two-thirds  filled,  runs  out  by  the  tubes 
U,  as  shown  in  the  figure,  the  internal  pres- 
sure at  D  being  equal  to  the  atmospheric 
pressure,  together  with  the  weight  of  the 
column  of  water  CD,  while  the  external 
pressure  at  that"  point  is  only  that  of  the 
atmosphere.  These  conditions  prevail  so 
F;g  l86  long  as  the  lower  end  of  the  glass  tube  is  open  ; 


-213] 


The  Syphon. 


that  is,  so  long  as  air  can  enter  C  and  keep  the  air  in  G  at  the  same  density 
as  the  external  air  ;  but  the  apparatus  is  arranged  so  that  the  orifice  in  the 
dish  B  does  not  allow  so  much  water  to 
flow  out  as  it  receives  from  the  tubes 
D,  in  consequence  of  which  the  level 
gradually  rises  in  the  dish,  and  closes 
the  lower  end  of  the  glass  tube.  As 
the  external  air  cannot  now  enter  the 
globe  C,  the  air  becomes  rarefied  in  pro- 
portion as  the  flow  continues,  until 
the  pressure  of  the  column  of  water  CD, 
together  with  the  tension  of  the  air  con- 
tained in  the  globe,  is  equal  to  this  external 
pressure  at  D  ;  the  flow  consequently  stops. 
But  as  water  continues  to  flow  out  of  the 
dish  B,  the  tubes  D  become  open  again,  air 
enters,  and  the  flow  recommences,  and  so 
on,  as  long  as  there  is  water  in  the  globe  C. 
^213.  Tlie  Syphon.-T-The  syphon  is 
a  bent  tube  open  at  both  ends,  and 
with  unequal  legs  (fig.  188).  It  is  used 
in  transferring  liquids  in  the  following 
manner  : — The  syphon  is  filled  with  some 
liquid,  and,  the  two  ends  being  closed, 
the  snorter  leg  is  dipped  in  the  liquid, 
as  represented  in  fig.  188  ;  or,  the 
shorter  leg  having  been  dipped  in  the 
liquid,  the  air  is  exhausted  by  applying 
the  mouth  at  B.  A  vacuum  is  thus  produced,  the  liquid  in  C  rises  and  fills 
the  tube  in  consequence  of  the  atmospheric  pressure.  It  will  then  run  out 
through  the  syphon  as  long  as  the  shorter 
end  dips  in  the  liquid. 

To  explain  this  flow  of  water  from  the 
syphon,  let  us  suppose  it  filled  and  the 
short  leg  immersed  in  the  liquid.  The 
pressure  then  acting  on  C,  and  tending  to 
raise  the  liquid  in  the  tube,  is  the  atmo- 
spheric pressure  minus  the  height  of  the 
column  of  liquid  DC.  In  like  manner, 
the  pressure  on  the  end  of  the  tube  B  is 
the  weight  of  the  atmosphere  less  the 
pressure  of  the  column  of  liquid  AB.  But 
as  this  latter  column  is  longer  than  CD, 
the  force  acting  at  B  is  less  than  the  force 
acting  at  C,  and  consequently  a  flow  takes 
place  proportional  to  the  difference  be- 
tween these  two  forces.  The  flow  will 
therefore  be  more  rapid  in  proportion  as  the  difference  of  level 
aperture  B  and  the  surface  of  the  liquid  in  C  is  greater. 


Fig.  187. 


Fig.  188. 


1 88  On  Gases.  [213- 

It  follows  from  the  theory  of  the  syphon  that  it  would  not  work  in  vacuo. 
nor  if  the  height  CD  were  greater  than  that  of  a  column  of  liquid  which 
counterbalances  the  atmospheric  pressure. 

214.  The  intermittent  syphon. — In  the  intermittent  syphon  the  flow  is 
not  continuous.     It  is  arranged  in  a  vessel,  so  that  the  shorter  leg  is  near  the 

bottom  of  the  vessel,  while  the  longer  leg  passes 
through  it  (fig.  189).  Being  fed  by  a  constant 
supply  of  water,  the  level  gradually  rises  both 
in  the  vessel,  and  in  the  tube  to  the  top  of  the 
syphon,  which  it  fills,  and  water  begins  to  flow 
out.  But  the  apparatus  is  arranged  so  that  the 
flow  of  the  syphon  is  more  rapid  than  that  of  the 
tube  which  supplies  the  vessel,  and  consequently 
the  level  sinks  in  the  vessel  until  the  shorter 
branch  no  longer  dips  in  the  liquid  ;  the  syphon 
is  then  empty,  and  the  flow  ceases.  But  as  the 
vessel  is  continually  fed  from  the  same  source 
the  level  again  rises,  and  the  same  series  of  phenomena  is  reproduced. 

The  theory  of  the  intermittent  syphon  explains  the  natural  intermittent 
springs  which  are  found  in  many  countries,  and  of  which  there  is  an  excel- 
lent example  near  Giggleswick  in  Yorkshire.  Many  of  these  springs  fur- 
nish water  for  several  days  or  months,  and  then,  after  stopping  for  a  certain 
interval,  again  recommence.  In  others  the  flow  stops  and  recommences 
several  times  in  an  hour. 

These  phenomena  are  explained  by  assuming  that  there  are  subterranean 
fountains,  which  are  more  or  less  slowly  filled  by  springs,  and  which  are  then 
emptied  by  fissures  so  occurring  in  the  ground  as  to  form  an  intermittent 
syphon. 

215.  Different  kinds  of  pumps. — Pumps  are  machines  which  serve  to 
raise  water  either  by  suction,  by  pressure,  or  by  both  efforts  combined  ;  they 
are  consequently  divided  into  suction  or  lif t  pumps,  for ce-ptimps,  and  suction 
and  forcing  pumps. 

The  various  parts  entering  into  the  construction  of  a  pump  are  the  barrel, 
the  piston,  the  valves,  and  the  pipes.  The  barrel  is  a  cylinder  of  metal  or 

of  wood,  in  which  is  the  pis- 
ton. The  latter  is  a  metal 
or  wooden  cylinder  wrapped 
with  tow,  and  working  with 
gentle  friction  the  whole 
length  of  the  barrel. 

The   valves   are  discs  of 
metal  or  leather,  which  alter- 


Fig.  190. 


Fig.  191. 

nately  close  the  apertures  which  connect  the  barrel  with  the  pipes.  The 
most  usual  valves  are  the  clack  valve  (fig.  190)  and  the  conical  valve  (fig. 
191).  The  first  is  a  metal  disc  fixed  to  a  hinge  on  the  edge  of  the  orifice  to 
be  closed.  In  order  more  effectually  to  close  it,  the  lower  part  of  the  disc 
is  covered  with  thick  leather.  Sometimes  the  valve  consists  merely  of  a 
leather  disc,  of  larger  diameter  than  the  orifice,  nailed  on  the  edge  of  the 
orifice.  Its  flexibility  enables  it  to  act  as  a  hinge. 


-216] 


Suction-pump. 


The  conical  valve  consists  of  a  metal  cone  fitting  in  an  aperture  of  the 
same  shape.  Below  this  is  an  iron  hoop,  through  which  passes  a  bolt-head 
fixed  to  the  valve.  The  object  of  this  is  to  limit  the  play  of  the  valve  when 
it  isXaised  by  the  water,  and  to  prevent  its  removal. 

Y2i6.  Suction-pump. — Fig.  192  represents  a  model  of  a  suction-pump 
such  as  is  used  in  lectures,  but  which  has  the  same  arrangement  as  the 
pumps  in  common  use.  It  consists,  ist,  of  a.  glass  cylinder,  B,  at  the  bottom 
of  which  there  is  a  valve,  S,  opening  upwards  ;  2nd,  of  a  suction-tube,  A, 
which  dips  into  the  reservoir  from  which  water  is  to  be  raised  ;  3rd,  of  a 
piston,  which  is  moved  up  and  down  by  a  rod  worked  by  a  handle,  P.  The 
piston  is  perforated  by  a  hole  ;  the  upper  aperture  is  closed  by  a  valve,  O, 
opening  upwards. 

When  the  piston  rises  from  the  bottom  of  the  cylinder  B,  a  vacuum  is 
produced  below,  and  the  valve  O  is  kept  closed  by  the  atmospheric  pres- 
sure, while  the  air  in  the  pipe  A,  in 
consequence  of  its  elasticity,  raises  the 
valve  S,  and  partially  passes  into  the 
cylinder.  The  air  being  thus  rarefied, 
water  rises  in  the  pipe  until  the  pres- 
sure of  the  liquid  column,  together 
with  the  tension  of  the  rarefied  air 
which  remains  in  the  tube,  counter- 
balances the  pressure  of  the  atmo- 
sphere on  the  water  of  the  reservoir. 

When   the    piston    descends,   the 
valve  S  closes  by  its  own  weight,  and 
prevents  the  return  of  the  air  from  the 
cylinder   into   the  tube  A.      The  air 
compressed  by  the  piston  opens  the 
valve  O,  and  escapes  into  the  atmo- 
sphere by  the  pipe  C.     With  a  second 
stroke  of  the  piston  the  same  series  of 
phenomena  is  produced,  and  after  a 
few   strokes   the    water   reaches    the 
cylinder.     The  effect  is  now  somewhat 
modified  ;  during  the   descent  of  the 
piston   the   valve   S  closes,   and  the 
water  raises  the  valve  O,  and  passes 
above  the  piston  by  which  it  is  lifted 
into  the  upper  reservoir  D.     There  is 
now  no  more  air  in  the  pump,  and  the 
water  forced  by  the  atmospheric  pres- 
sure rises  with  the   piston,  provided 
that  when  it  is  at  the  summit  of  its  course,  it  is  not  more  than  34  feet  abo 
the  level  of  the  water  in  which  the  tube  A  dips,  for  we  have  seen  (163)  that 
a  column  of  water  of  this  height  is  equal  to  the  pressure  of  the  atmosphere. 
In  practice  the  height  of  the  tube  A  does  not  exceed  26  to  28  feet,  fo 
although  the  atmospheric  pressure  can  support  a  higher  column,  the  vacuum 
produced  in  the  barrel  is  not  perfect,  owing  to  the  fact  that  the  piston  does 


Fig.  192. 


190  '  .          On  Gases.  [216- 

not  fit  exactly  on  the  bottom  of  the  barrel.  But  when  the  water  has  passed  the 
piston,  it  is  the  ascending  force  of  the  latter  which  raises  it,  and  the  height 
to  which  it  can  be  brought  depends  on  the  power  which  works  the  piston. 

217.  Suction  and  force  pump. — The  action  of  this  pump,  a  model  of 
which  is  represented  in  fig.  193,  depends  both  on  exhaustion  and  on  pres- 
sure.    At  the  base  of  the  barrel,  where  it  is  connected  with  the  tube  A,  there 
is  a  valve,  S,  which  opens  upwards.     Another  valve,  O,  opening  in  the  same 
direction,  closes  the  aperture  of  a  conduit,  which  passes  from  a  hole  o,  near 
the  valve  S,  into  a  vessel  M,  which  is  called  the  air-chamber.     From  this 
chamber  there  is  another  tube,  D,  up  which  the  water  is  forced. 

At  each  ascent  of  the 
piston  B,  which  is  solid, 
the  water  rises  through 
the  tube  A  into  the  barrel. 
When  the  piston  sinks, 
the  valve  S  closes,  and 
the  water  is  forced  through 
the  valve  O  into  the  reser- 
voir M,  and  thence  into 
the  tube  D.  The  height 
to  which  it  can  be  raised 
in  this  tube  depends 
solely  on  the  motive  force 
which  works  the  pump. 

If  the  tube  D  were  a 
prolongation  of  the  tube 
}ao,  the  flow  would  be  in- 
termittent ;  it  would  take 
place  when  the  piston  de- 
scended, and  would  cease 
as  soon  as  it  ascended. 
But  between  these  tubes 
there  is  an  interval, 
which,  by  means  of  the 
air  in  the  reservoir  M, 
ensures  a  continuous  flow. 
The  water  forced  into  the 
reservoir  M  divides  into 
two  parts,  one  of  which,  rising  in  D,  presses  on  the  water  in  the  reservoir  by 
its  weight ;  while  the  other,  in  virtue  of  this  pressure,  rises  in  the  reservoir, 
above  the  lower  orifice  of  the  tube  D,  compressing  the  air  above.  Conse- 
quently, when  the  piston  ascends,  and  no  longer  forces  the  water  into  M,  the 
air  of  the  reservoir,  by  the  pressure  it  has  received,  reacts  on  the  liquid,  and 
raises  it  in  the  tube  D,  until  the  piston  again  descends,  so  that  the  jet  is 
cont'inuous. 

218.  Load  which  the  piston  supports. — In  the  suction-pump,  when 
once  the  water  fills  the  pipe,  and  the  barrel,  as  far  as  the  spout,  the  effort 
necessary  to  raise  the  piston  is  equal  to  the  weight  of  a  column  of  water, 
the  base  of  which  is  this  piston,  and  the  height  the  vertical  distance  of  the 


-219] 


Fire-engine, 


191 


spout  from  the  level  of  the  water  in  the  reservoir;  that  is,  the  height  to 
which  the  water  is  raised.  For  if  H  is  the  atmospheric  pressure,  h  the 
height  of  the  water  above  the  piston,  and  h'  the  height  of  the  column 
which  fills  the  suction-tube  A  (fig.  191),  and  the  lower  part  of  the  barrel,  the 
pressure  above  the  piston  is  obviously  H  +  //,  and  that  below  is  H  -  h',  since 
the  weight  of  the  column  h'  tends  to  counterbalance  the  atmospheric  pressure. 
But  as  the  pressure  H  -  h'  tends  to  raise  the  piston,  the  effective  resistance 
is  equal  to  the  excess  of  H  +  h  over  H  -  /*',  that  is  to  say,  to  h  +  h'. 

In  the  suction  and  force  pump  it  is  readily  seen  that  the  pressure  which 
the  piston  supports  is  also  equal  to  the  weight  of  a  column  of  water  the  base 
of  which  is  the  section  of  the  piston,  and  the  height  that  to  which  the  water 
is  raised. 

219.  Fire-engine. — The  fire-engine  is  a  force-pump  in  which  a  steady  jet 
is  obtained  by  the  aid  of  an  air-chamber,  and  also  by  two  pumps  working 


Fig.  194. 

alternately  (fig.  194).  The  two  pumps  m  and  n,  worked  by  the  same  lever 
PQ,  are  immersed  in  a  tank,  which  is  kept  filled  with  water  as  long  as  the 
pump  works.  From  the  arrangement  of  the  valves  it  will  be  seen  that  when 
one  pump,  »,  draws  water  from  the  tank,  the  other,  m,  forces  it  into  the  air- 
chamber  R  ;  whence,  by  an  orifice  Z,  it  passes  into  the  delivery  tube,  by 
which  it  can  be  sent  in  any  direction. 

Without  the  air-chamber  the  jet  would  be  intermittent.  But  as  the  velo- 
city of  the  water  on  entering  the  reservoir  is  less  than  on  emerging,  the  level 
of  the  water  rises  above  the  orifice  Z,  compressing  the  air  which  fills  the 
reservoir.  Hence,  whenever  the  piston  stops,  the  air  thus  compressed,  re- 
acting on  the  liquid,  forces  it  out  during  its  momentary  stoppage,  and  thus 
keeps  up  a  constant  flow. 


192  On  Sound.  [220- 


BOOK   V. 

ON     SOUND. 


CHAPTER    I. 

PRODUCTION,   PROPAGATION,   AND   REFLECTION   OF   SOUND. 

220.  Province  of  acoustics. — The    study  of  sounds,   and   that  of  the 
vibrations  of  elastic  bodies,  form  the  province  of  the  science  of  sounds,  or 
acoustics. 

Music  considers  sounds  with  reference  to  the  pleasurable  feelings  they  are 
calculated  to  excite.  Acoustics  is  concerned  with  the  questions  of  the  pro- 
duction, transmission,  and  comparison  of  sounds  ;  to  which  may  be  added 
the  physiological  question  of  the  perception  of  sounds. 

221.  Sound  and  noise. — Sound  is  a  peculiar  sensation  excited  in  the 
organ  of  hearing  by  the  vibratory  motion   of  bodies,  when  this   motion  is 
transmitted  to  the  ear  through  an  elastic  medium. 

All  sounds  are  not  identical ;  they  present  differences  by  which  they  may 
be  distinguished,  compared,  and  their  relations  determined. 

Sounds  are  distinguished  from  noises.  Sound  properly  so  called,  or 
musical  sound,  is  that  which  produces  a  continuous  sensation,  and  the 
musical  value  of  which  can  be  estimated  ;  while  noise  is  either  a  sound 
of  too  short  a  duration  to  be  determined,  like  the  report  of  a  cannon  ;  or 
else  it  is  a  confused  mixture  of  many  discordant  sounds  like  the  rolling 
of  thunder  or  the  noise  of  the  waves.  Nevertheless  the  difference  between 
sound  and  noise  is  by  no  means  precise  :  Savart  showed  that  there  are 
relations  of  height  in  the  case  of  noise,  as  well  as  in  that  of  sound ;  and 
there  are  said  to  be  certain  ears  sufficiently  well  organised  to  determine 
the  musical  value  of  the  sound  produced  by  a  carriage  rolling  on  the 
pavement. 

222.  Cause  of  sound. — Sound  is  always  the  result  of  rapid  oscillations 
imparted  to  the  molecules  of  elastic  bodies,  when  the  state  of  equilibrium  of 
these  bodies  has  been  disturbed  either  by  a  shock  or  by  friction.  Such  bodies 
tend  to  regain  their  first  position  of  equilibrium,  but  only  reach  it  after  per- 
forming, on  each  side  of  that  position,  very  rapid  vibratory  movements,  the 
amplitude  of  which  quickly  decreases.     A  body  which  produces  a  sound  is 
called  a  sonorous  or  sounding  body. 


Fig.  195. 


-224]  Sound  is  Propagated  in  all  Elastic  Bodies.  1 93 

As  understood  in  England  and  Germany,  a  vibration  comprises  a  motion 

to  and  to  ;  m  France,  on  the  contrary,  a  vibration  means  a  movement  to  or 

fro      The  French  vibrations  are  with  us  semi-vibrations,  an  oscillation  or 

vibration  is  the  movement  of  the  vibrating  molecule  in  only  one  direction  • 

a  double  or  complete  vibration  comprises  the  oscillation  both  backwards  and 

forwards.     Vibrations  of  sounding  bodies  are  very  readily  observed      If 

light  powder  is  sprinkled  on  a  body  which  is  in  the  act  of  yielding  a  musical 

sound,  a  rapid  motion  is  imparted 

to  the  powder,  which  renders  visible 

the  vibrations  of  the  body  ;  and  in 

the  same   manner,  if  a   stretched 

cord  be  smartly  pulled  and  let  go, 

its  vibrations  are  apparent  to  the 

eye. 

A  bell-jar  is  held  horizontally 

in   one  hand  (fig.   195),  and  made 

to  vibrate  by  being  struck  with  the 

other  ;  if  then  a  piece  of  metal  is  placed  in  it,  it  is    rapidly  raised  by  the 

vibrations  of  the"  side  ;  touching  the  bell-jar  with  the  hand,  the  sound  ceases, 

.and  with  it  the  motion  of  the  metal. 

223.  Sounds  not  propagated  in  vacuo. — The  vibrations  of  elastic  bodies 
can  only  produce  the  sensation  of  sound  in  us   by  the  intervention  of  a 
medium  interposed  between  the  ear  and  the 

sonorous  body  and  vibrating  with  it.  This 
medium  is  usually  the  air,  but  all  gases, 
vapours,  liquids,  and  solids  also  transmit 
sounds. 

The  following  experiment  shows  that  the 
presence  of  a  ponderable  medium  is  neces- 
sary for  the  propagation  of  sound.  A  small 
metal  bell,  which  is  continually  struck  by  a 
small  hammer  by  means  of  clockwork,  or 
else  an  ordinary  musical  box,  is  placed  under 
the  receiver  of  an  air-pump  (fig.  196).  As 
long  as  the  f  receiver  is  full  of  air  at  the  ordi- 
nary pressure  the  sound  is  transmitted,  but 
in  proportion  as  the  air  is  exhausted  the 
sound  becomes  feebler,  and  is  imperceptible 
in  a  vacuum. 

To  ensure  the  success  of  the  experiment, 
the  bellwork  or  the  musical  box  must  be 
placed  on  wadding  ;  for  otherwise  the  vibra- 
tions would  be  transmitted  to  the  air  through 
the  plate  of  the  pump. 

224.  Sound  is   propagated  in   all  elastic  bodies. —  If,  in  the  above 
experiment,  any  vapour  or  gas  be  admitted  after  the  vacuum  has  been  made, 
the  sound  of  the  bell  will  be  heard,  showing  that  sound  is  propagated  in  this 
medium  as  in  air. 

Sound  is  also  propagated  in  liquids.     When  two  bodies  strike  against 

o 


Fig.  196. 


194  On  Sound.  [224- 

each  other  under  water  the  shock  is  distinctly  heard.     And  a  diver  at  the 
bottom  of  the  water  can  hear  the  sound  of  voices  on  the  bank. 

The  conductibility  of  solids  is  such  that  the  faint  scratching  of  a  pen  at 
the  end  of  a  long  piece  of  wood  is  heard  at  the  other  end.  The  earth  con- 
ducts sound  so  well  that  at  night,  when  the  ear  is  applied  to  the  ground,  the 
stepping  of  horses,  or  any  other  noise  at  a  great  distance,  is  heard. 

225.  Propagation  of  sound  in  the  air. — In  order  to  simplify  the  theory 
of  the  propagation  of  sound  in  the  air,  we  shall  first  consider  the  case  in 
which  it  is  propagated  in  a  cylindrical  tube  of  indefinite  length.  Let  MN,. 
fig.  197,  be  a  tube  filled  with  air  at  a  constant  pressure  and  temperature,  and 
let  P  be  a  piston  oscillating  rapidly  from  A  to  a.  When  the  piston  passes 
from  A  to  a  it  compresses  the  air  in  the  tube.  But  in  consequence  of  the 
great  compressibility,  the  condensation  of  the  air  does  not  take  place  at  once 
throughout  the  whole  length  of  the  tube,  but  solely  within  a  certain  length, 
#H,  which  is  called  the  condensed  wave. 

If  the  tube  MN  be  supposed  to  be  divided  into  lengths  equal  to  <;zH,  and 
each  of  these  lengths  divided  into  layers  parallel  to  the  piston,  it  may  be 
shown  by  calculation,  that  when  the  first  layer  of  the  wave  aH  comes  to  rest, 
the  motion  is  communicated  to  the  first  layer  of  the  second  wave  HH',  and 
so  on  from  layer  to  layer  in  all  parts  of  H'H",  H^H"".  The  condensed  wave 


M  i 


Fig.  197. 

advances  in  the  tube,  each  of  its  parts  having  successively  the  same  degree 
of  velocity  and  condensation. 

When  the  piston  returns  in  the  direction  aA  a  vacuum  is  produced 
behind  it,  which  causes  an  expansion  of  the  air  in  contact  with  its  posterior 
face.  The  next  layer  expanding  in  turn  brings  the  first  to  its  original  state 
of  condensation,  and  so  on  from  layer  to  layer.  Thus  when  the  piston  has 
returned  to  A,  an  expanded  wave  is  produced  of  the  same  length  as  the  con- 
densed wave,  and  directly  following  it  in  the  tube  where  they  are  propagated 
together,  the  corresponding  layers  of  the  two  waves  possessing  equal  and 
contrary  velocities. 

The  whole  of  a  condensed  and  expanded  wave  forms  an  undulation  ; 
that  is,  an  undulation  comprehends  that  part  of  the  column  of  air  affected 
during  the  backward  and  forward  motion  of  the  piston.  The  length  of  an 
undulation  is  the  space  which  sound  traverses  during  a  complete  vibration 
of  the  body  which  produces  it.  This  length  is  less  in  proportion  as  the 
vibrations  are  more  rapid. 

It  is  important  to  remark  that  if  we  consider  a  single  row  of  particles, 
which  when  at  rest  occupy  a  line  parallel  to  the  axis  of  the  cylinder,  for 
instance,  those  along  AH"  (fig.  197),  we  shall  find  they  will  have  respectively 
at  the  same  instant,  all  the  various  velocities  which  the  piston  has  had  suc- 
cessively while  oscillating  from  A  to  a  and  back  to  A.  So  that  if  in  fig.  37 


-226]        Causes  which  Influence  the  Intensity  of  Sound.  195 

AH'  represents  the  length  of  one  undulation,  the  curved  line  H'PQA  will 
represent  the  various  velocities  which  all  the  points  in  the  line  AH'  have 
simultaneously :  for  instance,  at  the  instant  the  piston  has  returned  to  A, 
the  particle  at  M  will  be  moving  to  the  right  with  a  velocity  represented  by 
QM,  the  particle  at  N  will  be  moving  to  the  left  with  a  velocity  represented 
by  PN,  and  so  on  of  the  other  particles. 

When  an  undulatory  motion  is  transmitted  through  a  medium,  the 
motions  of  any  two  particles  are  said  to  be  in  the  same  phase  when  those 
particles  move  with  equal  velocities  in  the  same  direction  ;  the  motions  are 
said  to  be  in  opposite  phases  when  the  particles  move  with  the  same  velocities 
in  opposite  directions.  It  is  plain  from  an  inspection  of  fig.  37  that  when 
any  two  particles  are  separated  by  a  distance  equal  to  half  an  undulation, 
their  motions  are  always  in  opposite  phases,  but  if  their  distance  equals  the 
length  of  a  complete  undulation  their  motions  are  in  the  same  phase.  A 
little  consideration  will  show  that  in  the  condensed  wave  the  condensation 
will  be  greatest  at  the  middle  of  the  wave,  and  likewise  that  the  expanded 
wave  will  be  most  rarefied  at  its  middle. 

It  is  an  easy  transition  from  the  explanation  of  the  motion  of  sound- 
waves in  a  cylinder  to  that  of  their  motion  in  an  unenclosed  medium.  It  is 
simply  necessary  to  apply  in  all  directions,  to  each  molecule  of  the  vibrating 
body,  what  has  been  said  about  a  piston  movable  in  a  tube.  A  series  of 
spherical  waves  alternately  condensed  and  rarefied  is  produced  around  each 
centre  of  disturbance.  As  these  waves  are  contained  within  two  concentrical 
spherical  surfaces,  whose  radii  gradually  increase,  while  the  length  of  the 
undulation  remains  the  same,  their  mass  increases  with  the  distance  from 
the  centre  of  disturbance,  so  that  the  amplitude  of  the  vibration  of  the  mole- 
cules gradually  lessens,  and  the  intensity  of  the  sound  diminishes. 

It  is  these  spherical  waves,  alternately  condensed  and  expanded, 
which  in  being  propagated  transmit  sound.  If  many  points  are  disturbed  at 
the  same  time,  a  system  of  waves  is  produced  around  each  point.  But  all 
these  waves  are  transmitted  one  through  the  other  without  modifying  either 
their  lengths  or  their  velocities.  Sometimes  condensed  or  expanded  waves 
coincide  with  others  of  the  same  nature  to  produce  an  effect  equal  to  their 
sum  ;  sometimes  they  meet  and  produce  an  effect  equal  to  their  difference. 
If  the  surface  of  still  water  is  disturbed  at  two  or  more  points,  the  co-exist- 
ence of  waves  becomes  sensible  to  the  eye. 

226.  Causes  which  influence  the  intensity  of  sound. — Many  causes 
modify  the  force  or  the  intensity  of  sound.  These  are  the  distance  of  the 
sounding  body,  the  amplitude  of  the  vibrations,  the  density  of  the  air  at  the 
place  where  the  sound  is  produced,  the  direction  of  the  currents  of  air,  and, 
lastly,  the  neighbourhood  of  other  sounding  bodies. 

i.  The  intensity  of  sound  is  inversely  as  the  square  of  the  distance  of  the 
sonorous  body  from  the  ear.  This  law  has  been  deduced  by  calculation,  but 
it  may  be  also  demonstrated  experimentally.  Let  us  suppose  several  sounds 
of  equal  intensity — for  instance,  bells  of  the  same  kind,  struck  by  hammers 
of  the  same  weight,  falling  from  equal  heights.  If  four  of  these  bells  are 
placed  at  a  distance  of  20  yards  from  the  ear,  and  one  at  a  distance  of  10 
yards,  it  is  found  that  the  single  bell  produces  a  sound  of  the  same  intensity 

O  2 


196  On  Sound.  [226- 

as  the  four  bells  struck  simultaneously.  Consequently,  for  double  the  dis- 
tance the  intensity  of  the  sound  is  only  one-fourth.  A  method  of  com- 
paring the  intensities  of  different  sounds  will  be  described  afterwards  (289). 

The  distance  at  which  sounds  can  be  heard  depends  on  their  intensity. 
The  report  of  a  volcano  at  St.  Vincent  was  heard  at  Demerara,  300  miles 
off,  and  the  firing  at  Waterloo  was  heard  at  Dover. 

ii.  The  intensity  of  the  sound  increases  with  the  amplitude  of  the  vibrations 
of  the  sonorous  body.  The  connection  between  the  intensity  of  the  sound 
and  the  amplitude  of  the  vibrations  is  readily  observed  by  means  of  vibrating 
cords.  For  if  the  cords  are  somewhat  long,  the  oscillations  are  perceptible 
to  the  eye,  and  it  is  seen  that  the  sound  is  feebler  in  proportion  as  the  am- 
plitude of  the  oscillations  decreases. 

iii.  The  intensity  of  sound  depends  on  the  density  of  the  air  in  the  place  in 
which  it  is  produced.  As  we  have  already  seen  (222),  when  an  alarum  moved 
by  clockwork  is  placed  under  the  bell-jar  of  an  air-pump,  the  sound  becomes 
weaker  in  proportion  as  the  air  is  rarefied. 

In  hydrogen,  which  is  about  ^  the  density  of  air,  sounds  are  much 
feebler,  although  the  pressure  is  the  same.  In  carbonic  acid,  on  the  con- 
trary, whose  density  is  1*529,  sounds  are  more  intense.  On  high  mountains, 
where  the  air  is  much  rarefied,  it  is  necessary  to  speak  with  some  effort  in 
order  to  be  heard,  and  the  discharge  of  a  gun  produces  only  a  feeble  sound. 
The  ticking  of  a  watch  is  heard  in  water  at  a  distance  of  23  feet,  in  oil  of  i6£, 
in  alcohol  of  13,  and  in  air  of  only  10  feet. 

iv.  The  intensity  of  sound  is  modified  by  the  motion  of  the  atmosphere, 
and  the  direction  of  the  wind.  In  calm  weather  sound  is  always  better 
propagated  than  when  there  is  wind  ;  in  the  latter  case,  for  an  equal  distance, 
sound  is  more  intense  in  the  direction  of  the  wind  than  in  the  contrary 
direction. 

v.  Lastly,  sound  is  strengthened  by  the  neighbourhood  of  a  sonorous  body. 
A  string  made  to  vibrate  in  free  air  has  but  a  very  feeble  sound  ;  but  when  it 
vibrates  above  a  sounding-box,  as  in  the  case  of  the  violin,  guitar,  or  violon- 
cello, its  sound  is  much  stronger.  This  arises  from  the  fact  that  the  box  and 
the  air  which  it  contains  vibrate  in  unison  with  the  string.  Hence  the  use  of 
sounding-boxes  in  stringed  instruments. 

Attempts  have  been  made  to  get  a  measure  of  the  loudness  of  sound 
which  should  serve  as  a  standard,  by  allowing  leaden  pellets  to  fall  from 
various  heights  on  an  iron  plate  of  same  size.  It  appears  that  within 
certain  limits  the  loudness  is  nearly  proportional  to  the  square  root  of  the 
height  from  which  the  pellet  falls,  and  not  to  the  height  itself.  It  thus 
appears  that  only  a  portion  of  the  energy  of  the  falling  body  is  expended  in 
producing  vibrations  of  the  plate. 

227.  Apparatus  to  strengthen  sound. — The  apparatus  represented  in 
fig.  198  was  used  by  Savart  to  show  the  influence  of  boxes  in  strengthening 
sound.  It  consists  of  a  hemispherical  brass  vessel,  A,  which  is  set  in  vibra- 
tion by  means  of  a  violin  bow.  Near  it  there  is  a  hollow  cardboard  cylinder, 
B,  closed  at  the  further  end.  By  means  of  a  handle  this  cylinder  can  be  turned 
on  its  support,  so  as  to  be  inclined  at  any  given  degree  towards  the  vessel. 
The  cylinder  is  fixed  on  a  slide,  C,  by  which  means  it  can  be  placed  at  any 


Fig.  198. 


Regnautfs  Experiments.  igj 

distance  from  A.  When  the  vessel  is  made  to  vibrate,  the  strengthening  of 
the  sound  is  very  remarkable.  But  the  sound  loses  almost  all  its  intensity  if 
the  cylinder  is  turned 
away,  and  it  becomes 
gradually  weaker  when 
the  cylinder  is  removed  to 
a  greater  distance,  show- 
ing that  the  strengthen- 
ing is  due  to  the  vi- 
bration of  the  air  in  the 
cylinder. 

The  cylinder  B  is 
made  to  vibrate  in  unison 
with  the  brass  vessel  by 
adjusting  it  to  a  certain 
depth,  which  is  effected 
by  making  one  part  slide 
into  the  other. 

Vitruvius  states  that, 
in  the  theatres  of  the 
ancients,  resonant  brass 
vessels  were  placed  to 
strengthen  the  voices  of  the  actors. 

228.  Influence    of  tubes  on  the  transmission    of  sound.— The    law 
that  the  intensity  of  sound  decreases  in  proportion  to  the  square  of  the 
distance  does  not  apply  to  the  case  of  tubes,  especially  if  they  are  straight 
and  cylindrical.     The  sound  waves  in  that  case  are  not  propagated  in  the 
form  of  increasing  concentrical  spheres,  and  sound  can  be  transmitted  to  a 
great  distance  without  any  perceptible  alteration.     Biot  found  that  in  one 
of  the  Paris  water-pipes,  1,040  yards  long,  the  voice  lost  so  little  of  its  inten- 
sity, that  a  conversation  could  be  kept  up  at  the  ends  of  a  tube  in  a  very  low 
tone.     The  weakening  of  sound  becomes,  however,  perceptible  in  tubes  of 
large  diameter,  or  where  the  sides  are  rough.     This  property  of  transmitting 
sounds  was  first  used  in  England  for  speaking  tubes.     They  consist  of  caout- 
chouc or  metal  tubes  of  small  diameter  passing  from  one  room  to  another. 
If  a  person  speaks  at  one  end  of  the  tube,  he  is  distinctly  heard  by  a  person 
with  his  ear  at  the  other  end. 

From  Biot's  experiments  it  is  evident  that  a  communication  might  be 
made  between  two  towns  by  means  of  speaking  tubes.  The  velocity  of 
sound  is  1,125  feet  in  a  second  at  i6°-6  C.,  so  that  a  distance  of  50  miles 
would  be  traversed  in  four  minutes. 

229.  Regnault's  experiments. — Theoretically,  a  sound-wave  should  be 
propagated  in  a  straight  cylindrical  tube  with  a  constant  intensity.     Regnault 
found,  however,  that  in  these  circumstances  the  intensity  of  sound  gradually 
diminishes  with  the  distance,  and  that  the  distance  at  which  it  ceases  to  be 
audible  is  nearly  proportional  to  the  diameter  of  the  tube. 

He  produced  sound-waves  of  equal  strength  by  means  of  a  small  pistol 
charged  with  a  gramme  of  powder,  and  fired  at  the  open  ends  of  tubes  of 
various  diameters  ;  and  he  then  ascertained  the  distance  at  which  the  sound 


198  On  Sound.  [229- 

could  no  longer  be  heard,  or  at  which  it  ceased  to  act  on  what  he  calls  a 
sensitive  membrane.  This  was  a  very  flexible  membrane  which  could  be 
fixed  across  the  tube  at  various  distances,  and  was  provided  with  a  small 
metal  disc  in  its  centre.  When  the  membrane  began  to  vibrate,  this  disc 
struck  against  a  metallic  contact,  and  thereby  closed  a  voltaic  circuit,  which 
traced  on  a  chronograph  the  exact  moment  at  which  the  membrane  received 
the  sound-wave. 

Experimenting  in  this  manner,  Regnault  found  that  the  report  of  a  pistol 
charged  as  stated  is  no  longer  audible  at  a  distance  of 

1,159  metres  in  a  tube  of om-i 08  diameter. 

3»8io         „  „  oro-3oo        „ 

9.540         „  „  im-ioo 

The  sound-wave,  of  which  these  numbers  represent  the  limit  of  distance  at 
which  it  is  no  longer  heard,  still  acts  on  the  membrane  at  the  distances  ot 
4,156,  11,430,  and  19,851  metres  respectively. 

According  to  Regnault  the  principal  cause  of  this  diminution  of  intensity 
is  the  loss  of  vis  viva  against  the  sides  of  the  tube  :  he  found  also  that  sounds 
of  high  pitch  are  propagated  in  tubes  less  easily  than  those  of  low  ones  ;  a 
bass  would  be  heard  at  a  greater  distance  than  a  treble  voice. 

230.  Velocity  of  sound  in  air. — Since  the  propagation  of  sound-waves 
is  gradual,  sound  requires  a  certain  time  for  its  transmission  from  one  place 
to  another,  as  is  seen  in  numerous  phenomena.  For  example,  the  sound 
of  thunder  is  only  heard  some  time  after  the  flash  of  lightning  has  been  seen, 
although  both  the  sound  and  the  light  are  produced  simultaneously  ;  and  in 
like  manner  we  see  a  mason  in  the  act  of  striking  a  stone  before  hearing  the 
sound. 

The  velocity  of  sound  in  air  has  often  been  the  subject  of  experimental 
determination.  The  most  accurate  of  the  direct  measurements  was  made 
by  Moll  and  Van  Beck  in  1823.  Two  hills,  near  Amsterdam,  Kooltjesberg 
and  Zevenboomen,  were  chosen  as  stations  :  their  distance  from  each  other 
as  determined  trigonometrically  was  57,971  feet,  or  nearly  eleven  miles. 
Cannons  were  fired  at  stated  intervals  simultaneously  at  each  station,  and  the 
time  which  elapsed  between  seeing  the  flash  and  hearing  the  sound  was 
noted  by  chronometers.  This  time  could  be  taken  as  that  which  the  sound 
required  to  travel  between  the  two  stations  ;  for  it  will  be  subsequently  seen 
that  light  takes  an  inappreciable  time  to  traverse  the  above  distance.  In- 
troducing corrections  for  the  barometric  pressure,  temperature,  and  hygro- 
metric  state,  and  eliminating  the  influence  of  the  wind,  Moll  and  Van  Beck's 
results  as  recalculated  by  Schroder  van  der  Kolk  give  109278  feet  as  the 
velocity  of  sound  in  one  second  in  dry  air  at  o°  C.  and  under  a  pressure  of 
760  mm.  Kendall,  in  a  North  Pole  expedition,  found  that  the  velocity  of 
sound  at  a  temperature  of  -40°  was  314  metres. 

The  velocity  of  sound  at  zero  may  be  taken  at  1,093  feet,  or  333  metres. 
This  velocity  increases  with  the  increase  of  temperature ;  it  may  be  calcu- 
lated for  a  temperature  t°  from  the  formula 

•v  =  1093  V  (i  +  0-003665^ 

where  1093  is  the  velocity  in  feet  at  o°  C.,  and  0-003665  the  coefficient  of  ex- 
pansion for  i°  C.  This  amounts  to  an  increase  of  nearly  two  feet  for  every 


-231]         Calculation  of  the  Velocity  of  Sound  in  Gases.  199 

degree  Centigrade.  For  the  same  temperature  it  is  independent  of  the  density 
of  the  air,  and  consequently  of  the  pressure.  It  is  the  same  for  the  same 
temperature  with  all  sounds,  whether  they  be  strong  or  weak,  deep  or  acute. 
Biot  found,  in  his  experiments  on  the  conductivity  of  sound  in  tubes,  that 
when  a  well-known  air  was  played  on  a  flute  at  one  end  of  a  tube  1,040  yards 
long,  it  was  heard  without  alteration  at  the  other  end,  from  which  he  con- 
cluded that  the  velocity  of  different  sounds  is  the  same.  For  the  same 
reason  the  tune  played  by  a  band  is  heard  at  a  great  distance  without  altera- 
tion, except  in  intensity,  which  could  not  be  the  case  if  some  sounds  travelled 
more  rapidly  than  others. 

This  cannot,  however,  be  admitted  as  universally  true.  Earnshaw,  by  a 
mathematical  investigation  of  the  laws  of  the  propagation  of  sound,  concludes 
that  the  velocity  of  a  sound  depends  on  its  strength  ;  and,  accordingly,  that 
.a  violent  sound  ought  to  be  propagated  with  greater  velocity  than  a  gentler 
one.  This  conclusion  is  confirmed  by  an  observation  made  by  Captain 
Parry  on  his  Arctic  expedition.  During  artillery  practice  it  was  found,  by 
persons  stationed  at  a  considerable  distance  from  the  guns,  that  the  report 
of  the  cannon  was  heard  before  the  command  to  fire  given  by  the  officer.  And 
more  recently,  Mallet  made  a  series  of  experiments  on  the  velocity  with  which 
sound  is  propagated  in  rocks,  by  observing  the  times  which  elapsed  before 
blastings,  made  at  Holyhead,  were  heard  at  a  distance.  He  found  that  the 
larger  the  charge  of  gunpowder,  and  therefore  the  louder  the  report,  the  more 
rapid  was  the  transmission.  With  a  charge  of  2,000  pounds  of  gunpowder 
the  velocity  was  967  feet  in  a  second,  while  with  a  charge  of  12,000  it  was 
1,210  feet  in  the  same  time. 

Jacques  made  a  series  of  experiments  by  firing  different  weights  of  pow- 
•der  from  a  cannon,  and  observing  the  velocity  of  the  report  at  different 
distances  from  the  gun  by  means  of  an  electrical  arrangement.  He  thus 
found  that,  nearest  the  gun,  the  velocity  is  least,  increasing  to  a  certain 
maximum  which  is  considerably  greater  than  the  average  velocity.  The 
velocity  is  also  greater  with  the  heavier  charge.  Thus  with  a  charge  of 
i£  pound  the  velocity  was  1187,  and  with  a  charge  of  \  pound  it  was 
1032  at  a  distance  of  from  30  to  50  feet  ;  while  at  a  distance  of  70  to  80 
it  was  1267  and  1 120  ;  and  at  90  to  loofeet  it  was  1262  and  1 1 14  respectively. 

Bravais  and  Martins  found,  in  1844,  that  sound  travelled  with  the  same 
velocity  from  the  base  to  the  summit  of  the  Faulhorn,  as  from  the  summit  to 
the  base. 

231.  Calculation  of  the  velocity  of  sound  in  gases. — From  theoretical 
considerations  Newton  gave  a  rule  for  calculating  the  velocity  of  sound  in 
gases,  which  may  be  represented  by  the  formula 


-V5 


in  which  v  represents  the  velocity  of  the  sound,  or  the  distance  it  travels  in 
a  second,  e  the  elasticity  of  the  gas,  and  d  its  density. 

This  formula  expresses  that  the  velocity  of  the  propagation  of  sound  in 
gases  is  directly  as  the  square  root  of  the  elasticity  of  the  gas,  and  inversely 
\as  the  square  root  of  its  density.  It  follows  that  the  velocity  of  sound  is  the 
same  under  any  pressure  ;  for  although  the  elasticity  increases  with  increased 


2OO  On  Sound.  [231— 

pressure,  according  to  Boyle's  law,  the  density  increases  in  the  same  ratio.. 
At  Quito,  where  the  mean  pressure  is  only  21*8  inches,  the  velocity  is  the 
same  as  at  the  sea-level,  provided  the  temperature  is  the  same. 

Now  the  measure  of  the  elasticity  of  a  gas  is  the  pressure  to  which  it  is 
subjected  ;  hence,  if  g  be  the  force  of  gravity,  h  the  barometric  height 
reduced  to  the  temperature  zero,  and  8  the  density  of  mercury,  also  at  zero, 
then  for  a  gas  under  the  ordinary  atmospheric  pressure  and  for  zero,  e  = ght :. 
Newton's  formula  accordingly  becomes 


Now,  if  we  suppose  the  temperature  of  a  gas  to  increase  from  o°  to  /°,  its 
volume  will  increase  from  unity,  at  zero,  to  I  +  at  at  /,  a  being  the  coefficient 
of  expansion  of  the  gas.  But  the  density  varies  inversely  as  the  volumey 
therefore  d  becomes  d ~-  (i  +  at}.  Hence 


Substituting  in  this  formula  the  values  in  centimetres  and  grammes,, 
£•  =  981,  h  =76,  ^  =  0-001293,  we  get  for  the  value  v  a  number  29,795  centi- 
metres =  297-95  metres,  which  is  considerably  less  than  the  experimental! 
result.  Laplace  assigned  as  a  reason  for  this  discrepancy  the  heat  produced 
by  pressure  in  the  condensed  waves  ;  and,  by  considerations  based  on  this 
idea,  Poisson  and  Biot  found  that  Newton's  formula  ought  to  be  written' 


—(i  +  at]  -r\  c  being  the  specific  heat  of  the  gas  for  a  constant 

pressure,  and  c'  its  specific  heat  for  a  constant  volume  (460).  The  average 
value  of  this  constant  is  1-4,  and  if  the  formula  be  modified  by  the  introduc- 
tion of  the  value  \/i*4  the  calculated  numbers  agree  with  the  experimental 
results. 

The  physical  reason  for  introducing  the  constant  A/-§  into  the  equation 

for  the  velocity  of  sound  may  be  understood  from  the  following  considera- 
tions :  —  We  have  already  seen  (225)  that  sound  is  propagated  in  air  by  a 
series  of  alternate  condensations  and  rarefactions  of  the  layers.  At  each 
condensation  heat  is  evolved,  and  this  heat  increases  the  elasticity,  and  thus 
the  rapidity  with  which  each  condensed  layer  acts  on  the  next  ;  but  in  the 
rarefaction  of  each  layer  the  same  amount  of  heat  disappears  as  was  deve- 
loped by  the  condensation,  and  its  elasticity  is  diminished  by  the  cooling. 
The  effect  of  this  diminished  elasticity  of  the  cooled  layer  is  the  same  as  if 
the  elasticity  of  an  adjacent  wave  had  been  increased,  and  the  rapidity  with 
which  this  latter  would  expand  upon  the  dilated  wave  would  be  greater. 
Thus,  while  the  average  temperature  of  the  air  is  unaltered,  both  the  heating 
which  increases  the  elasticity,  and  the  chilling  which  diminishes  it,  concur- 
in  increasing  the  velocity. 

Knowing  the  velocity  of  sound,  we  can  calculate  approximately  the  dis- 
tance at  which  it  is  produced.  Light  travels  with  such  velocity  that  the 
flash  or  the  smoke  accompanying  the  report  of  a  gun  may  be  considered  to^ 
be  seen  simultaneously  with  the  explosion.  Counting  then  the  number  of 


-233]  Doppler's  Principle.  201 

seconds  which  elapse  between  seeing  the  flash  and  hearing  the  sound, 
and  multiplying  this  number  by  1125,  we  get  the  distance  in  feet  at  which 
the  gun  is  discharged.  In  the  same  way  the  distance  of  thunder  may  be 
estimated. 

232.  Velocity  of  sound  in  various  gases.  —  Approximately  the  same 
results  haveVbeen  obtained  for  the  velocity  of  sound  in  air  by  another  method, 
by  which  the  velocity  in  other  gases  could  be  determined.  As  the  wave- 
length X  is  the  distance  which  sound  travels  during  the  time  of  one  oscillation> 

that   is,  —  of  a  second,  the  velocity  of  sound  or  the  distance  traversed  in  a 
n 

second  is  v  =  n\.  Now  the  length  of  an  open  pipe  is  half  the  -wave-length 
of  the  fundamental  note  of  that  pipe  ;  and  that  of  a  closed  pipe  is  a  quarter 
of  the  wave-length  (275).  Hence,  if  we  know  the  number  of  vibrations  of 
the  note  emitted  by  any  particular  pipe,  which  can  be  easily  ascertained  by 
means  of  a  syren,  and  we  know  the  length  of  this  pipe,  we  can  calculate  v. 
Taking  the  temperature  into  account,  Wertheim  found  in  this  way  1,086  feet 
for  the  velocity  of  sound  in  air  at  zero. 

Further,  since  in  different  gases  which  have  the  same  elasticity,  but  differ 
in  density,  the  velocity  of  sound  varies  inversely  as  the  square  root  of  the 
density,  knowing  the  velocity  of  sound  in  air,  we  may  calculate  it  for  other 
gases  ;  thus  in  hydrogen  it  will  be 


This  number  cannot  be  universally  accurate,  for  the  co-efficient  -,  differs 

somewhat  in  different  gases.  And  when  pipes  were  sounded  with  different 
gases,  and  the  number  of  vibrations  of  the  notes  multiplied  with  twice  the 
length  of  the  pipe,  numbers  were  obtained  which  differed  from  those  cal- 
culated by  the  above  formula.  When,  however,  the  calculation  was  made 
introducing  for  each  gas  its  special  value  of  ^  the  theoretical  results  agreed 

very  well  with  the  observed  ones. 

By  the  above  method  the  following  values  have  been  obtained  :- 
Chlorine         .      /.,  $    ,        ..  /    .       ^  ^        677  feet  in  a  second. 
Carbonic  acid        .         ...    .   ..      •      ;  .v  '  ,,  •         856          » 

Oxygen          .         .  /     .        /      ,..-      /'"    -       IO4° 
Air         .....       "V       ,   "   V      1093 

Carbonic  oxide       .       ;.        ,.      f^ia^\  jt;Trr   n°6  " 

Hydrogen      .     ;•.       .«;...••        •         •        •       4l63          » 

233.  i>oppler's  principle.—  When  a  sounding  body  approaches  the  ear, 
the  tone  perceived  is  somewhat  higher  than  the  true  one  ;  but  if  the  s 
of  sound  recedes  from  the  ear,  the  tone  perceived  is  lower 
this,  which  is  known  as  DoppleSs  principle,  will  be  apparent  from  tl 
ing  considerations  :—  When  the  source  of  sound  and  the  ear  are  at  i 
ear  perceives  n  waves  in  a  second  ;  but  if  the  ear  approaches  the  sound,  01 
the  sound  approaches  the  ear,  it  perceives  more  ;  just  as  a  ship  mee  ts  mor, 
when  it  ploughs  through  them  than  if  it  is  at  rest.  Conversely  the  ear 
smaller  number  when  it  recedes  from  the  source  of  sound. 


waves 
receives  a 


202  On  Sound.  [233- 

effect  in  the  first  case  is  as  if  the  sounding  body  emitted  more  vibrations  in 
a  second  than  it  really  does,  and  in  the  second  case  fewer.  Hence  in  the 
first  case  the  note  appears  higher  ;  in  the  second  case  lower. 

If  the  distance  which  the  ear  traverses  in  a  second  towards  the  source  of 
sound  (supposed  to  be  stationary)  is  s  feet,  and  the  wave-length  of  the  par- 

ticular tone  is  X  feet,  then  there  are^  waves   in  a  second  ;    or  also    ~,  for 

A  c 

X  =  £}  where  c  is  the  velocity  of  sound  (230).     Hence  the  ear  receives  not 
n 

only  the  n  original  waves,  but  also  .—  in  addition.  Therefore  the  number 
of  vibrations  which  the  ear  actually  perceives  is 


for  an  ear  which  approaches  a  tone  ;  and  by  similar  reasoning  it  is 
n'  =  n-^  =  n(i-  f) 

for  an  ear  receding  from  a  tone. 

To  test  Doppler's  theory  Buys  Ballot  stationed  trumpeters  on  the  Utrecht 
railways  and  also  upon  locomotives,  and  had  the  height  of  the  approaching 
or  receding  tones  compared  with  stationary  ones  by  musicians.  He  thus 
found  both  the  principle  and  the  formula  fully  confirmed.  Similar  conclu- 
sive experiments  were  made  by  Scott  Russell  on  English  railways.  The 
observation  may  often  be  made  as  a  fast  train  passes  a  station  in  which 
an  electrical  alarum  is  sounding.  Independently  of  the  difference  in  loud- 
ness,  an  attentive  ear  can  detect  a  difference  in  pitch  on  approaching  or  on 
leaving  the  station.  A  speed  of  about  40  miles  an  hour  sharpens  the  note 
of  the  whistle  of  an  approaching  train  by  a  semitone,  and  flattens  it  to  that 
extent  as  the  train  recedes. 

Doppler's  principle  may  also  be  established  by  direct  laboratory  ex- 
periments. Rollmann  fixed  a  long  rod  on  a  turning  machine,  at  the  end 
of  which  was  a  large  glass  bulb  with  a  slit  in  it,  which  sounded  like  a 
humming-top  when  a  tangential  current  of  air  was  blown  against  the  slit. 
The  uniform  and  sufficiently  rapid  rotation  of  the  sphere  developed  such 
a  current  and  produced  a  steady  note,  the  pitch  of  which  was  higher  or 
lower  in  each  rotation  according  as  the  bulb  came  nearer,  or  receded  from, 
the  observer. 

234.  Velocity  of  sound  in  liquids.  —  The  velocity  of  sound  in  water 
was  investigated  in  1827  by  Colladon  and  Sturm.  They  moored  two  boats 
at  a  known  distance  in  the  Lake  of  Geneva.  The  first  supported  a  bell 
immersed  in  water,  and  a  bent  lever  provided  at  one  end  with  a  hammer 
which  struck  the  bell,  and  at  the  other  with  a  lighted  wick,  so  arranged  that 
it  ignited  some  powder  the  moment  the  hammer  struck  the  bell.  To  the 
second  boat  was  affixed  an  ear-trumpet,  the  bell  of  which  was  in  water, 
while  the  mouth  was  applied  to  the  ear  of  the  observer,  so  that  he  could 
measure  the  time  between  the  flash  of  light  and  the  arrival  of  sound  by  the 
water.  By  this  method  the  velocity  was  found  to  be  4,708  feet  in  a  second 
at  the  temperature  8°'i,  or  four  times  as  great  as  in  air. 


-235]  Velocity  of  Sound  in  Solids.  203 

The  velocity  of  sound,  which  is  different  in  different  liquids,  can  be  cal- 
culated by  a  formula  analogous  to  that  given  above  (230)  as  applicable  to 


gases,  that  is  v  =  A/^  5  in  which  g,  h,  and  d  have  their  previous  signi- 
ficance ;  while  p,  is  the  coefficient  of  the  compressibility  for  the  liquid  in 
question — that  is,  its  diminution  in  volume  by  a  pressure  of  one  atmosphere 
— and  d  is  the  density.  In  this  way  were  obtained  the  numbers  given  in  the 
following  table.  As  in  the  case  of  gases,  the  velocity  varies  with  the  tem- 
perature, which  is  therefore  appended  in  each  case. 

River  water  (Seine)          .         .         .  I3°C.    =   4714  feet  in  a  second. 

»_  „  ...  30  =  5013 

Artificial  sea-water  ....  20  =  4761 

Solution  of  common  salt .  .  .  18  =5132 

„  chloride  of  calcium  .  23  -  6493 

Absolute  alcohol  .  .  .  .23  =  3854 

Turpentine 24  =  3976 

Ether  .  \  ' .  .  .  .  =  3801 

It  will  be  seen  how  close  is  the  agreement  between  the  two  values  for 
the  velocity  of  sound  in  water,  the  only  case  in  which  they  have  been 
•directly  compared.  There  is  considerable  uncertainty  about  the  values  for 
other  liquids,  owing  to  the  doubt  as  to  the  values  for  their  compressibility. 

235.  Velocity  of  sound  in  solids. — As  a  general  rule,  the  elasticity  of 
solids,  as  compared  with  the  density,  is  greater  than  that  of  liquids,  and 
•consequently  the  propagation  of  sound. is  more  rapid. 

The  difference  is  well  seen  in  an  experiment  by  Biot,  who  found  that  when 
a  bell  was  struck  by  a  hammer,  at  one  end  of  an  iron  tube  3,120  feet  long, 
two  sounds  were  distinctly  heard  at  the  other  end.  The  first  of  these  was 
transmitted  by  the  tube  itself  with  a  velocity  x  ;  and  the  second  by  the  en- 
closed air  with  a  known  velocity  a.  The  interval  between  the  sounds  was 
2-5  seconds.  The  value  of  x  obtained  from  the  equation 

3I20_3I20  = 

a          x 

shows  that  the  velocity  of  sound  in  the  tube  is  nearly  9  times  as  great  as 
that  in  air. 

That  the  report  of  the  firing  of  cannon  is  heard  at  far  greater  distances 
than  peals  of  thunder,  is  doubtless  owing  to  the  fact  that  the  sound  in  the 
former  case  is  mainly  transmitted  through  the  earth. 

To  this  class  of  phenomena  belongs  the  fact  that  if  the  ear  is  held  against 
a  rock  in  which  a  blasting  is  being  made  at  a  distance,  two  distinct  reports 
are  heard— one  transmitted  through  the  rock  to  the  ear,  and  the  other  trans- 
mitted through  the  air.  The  conductivity  of  sound  in  solids  is  also  wel 
illustrated  by  the  fact  that  in  manufacturing  telegraph  wires  the  filing  at  any 
particular  part  can  be  heard  at  distances  of  miles  by  placing  one  end  of  the 
wire  in  the  ear.  The  toy  telephone  also  is  based  on  this  fact. 

The  velocity  of  sound   in  wires  has  also  been  determined  theoretically 

by  Wertheim  and  others,  by  the  formula  v  -  A/^in  which  /* is  the  modulus 


204  On  Sound.  [235— 

of  elasticity  (89),  while  d  is  the  mass  in  unit  volume,  which   is  equal  to  the 
specific  gravity,  or  the  weight  of  unit  volume  divided  by  the  acceleration  of 

gravity,  or  -. 

This  may  be  illustrated  from  a  determination  by  Wertheim  of  the  velocity 
of  sound  in  a  specimen  of  annealed  steel  wire,  the  specific  gravity  s  of  which 
was  7-631  and  its  modulus  21,000  (88).  That  is,  a  weight  of  21,000  kilo- 
grammes would  double  the  unit  length  of  a  wire  i  sq.  mm.  in  cross  section,  if 
this  were  possible  without  exceeding  the  limit  of  elasticity.  This  is  equal  to 
2,100,000,000,  or  21  x  10*8,  grammes  on  a  wire  I  sq.  cm.  in  cross  section. 
Hence 

/2 100000000  X  98 1 


The  following  table  gives  the  velocity  in  various  bodies,  expressed  in  feet 
per  second  : — 

Caoutchouc     .  " :  l,         .  197  Oak     ....  12622 

Tallow    .         .    >;r':.    *    .  1170  Elm    .         .         .         .  13516 

Wax      _.,     ., ,,.     -   ,   -  ,.  2811  Walnut        .         .         .  15095 

Lead       .       ,.   ,    ,.    :     .  4030  Fir      .         .       ,..       .  15218 

Gold       .        ,.;;,   fjf        .  5717  Ash     ....  15314 

Silver     .         ...-'.        .  8553  Steel  wire  '.         »;.•       .  15470 

Pine       .        .                 .  10900  Cedar.         .         .         .  16503 

Copper.         *;,,»-       .  11666  Iron     .         .         .         .  16822 

In  the  case  of  wood  these  velocities  are  in  the  directions  of  the  fibres,. 
and  are  considerably  greater  than  across  the  rings  or  along  the  rings  ;  thus, 
with  fir  the  velocities  are  4382  and  2572  for  these  directions  respectively. 

Mallet  investigated  the  velocity  of  the  transmission  of  sound  in  various 
rocks,  and  found  that  it  is  as  follows  : — 

Wet  sand       . 825  feet  in  a  second. 

Contorted,  stratified  quartz  and  slate  rock     .       1088  „ 

Discontinuous  granite 1306  „ 

Solid  granite .         .  .         .         .         .       1664  „ 

A  direct  experimental  method  of  determining  the  velocity  of  sound  in 
solids,  gases,  and  vapours  will  be  described  subsequently  (277). 

If  a  medium  through  which  sound  passes  is  heterogeneous,  the  waves  of 
sound  are  reflected  on  the  different  surfaces,  and  the  sound  becomes  rapidly 
enfeebled.  Thus  a  soft  earth  conducts  sound  badly,  while  a  hard  ground 
which  forms  a  compact  mass  conducts  it  well.  So  also  we  hear  badly 
through  air  spaces  which  are  filled  with  porous  materials,  such  as  shavings,, 
sawdust,  cinders,  and  the  like. 

236.  Reflection  of  sound. — So  long  as  sound-waves  are  not  obstructed 
in  their  motion  they  are  propagated  in  the  form  of  concentric  spheres  ;  but 
when  they  meet  with  an  obstacle,  they  follow  the  general  law  of  elastic 
bodies  ;  that  is,  they  return  upon  themselves,  forming  new  concentric  waves, 
which  seem  to  emanate  from  a  second  centre  on  the  other  side  of  the  obstacle. 
This  phenomenon  constitutes  the  reflection  of  sound. 

Fig.  199  represents  a  series  of  incident  waves  reflected  from  an  obstacle 


-237] 


Echoes  and  Resonances. 


PQ.     Taking,  for  example,  the  incident  wave  MCDN,  emitted  from  the 
centre  A,  the  corresponding  reflected  wave  is  represented  by  the  arc  CKD 
of  a  circle  whose  centre  a  is  as  far  behind  the  obstacle  PQ  as  A  is  before 

If  any  point,  C,  of  the  reflecting  surface  be  joined  to  the  centre  of  sound' 
and  if  the  perpendicular  CH  be  let  fall  on  the  surface  of  this  body,  the  an-le 
ACH  is  called  the  angle  of  incidence,  and  the  angle  BCH,  formed  bv  th 
prolongation  of  «C,  is  the  angle  of  reflection. 


Fig. 


The  reflection  of  sound  is  subject  to  the  two  following  laws  : 

I.  The  angle  of  reflection  is  equal  to  the  angle  of  incidence. 

II.  The  incident  sonorous  ray  and  the  reflected  ray  are  in  the  same  plane 
perpendicular  to  the  reflecting  surface. 

From  these  laws  it  follows  that  the  wave  which  in  the  figure  is  propa- 
gated in  the  direction  AC,  takes  the  direction  CB  after  reflection,  so  that  an 
observer  placed  at  B  hears  a  second  sound,  which  appears  to  come  from  C, 
besides  the  sound  proceeding  from  the  point  A. 

The  laws  of  the  reflection  of  sound  are  the  same  as  those  for  light  and 
radiant  heat,  and  may  be  demonstrated  by  similar  experiments.  One  of  the 
simplest  of  these  is  made  with  conjugate  mirrors  (see  chapter  on  Radiant 
Heat)  ;  if  in  the  focus  of  one  of  these  mirrors  a  watch  is  placed,  the  ear 
placed  in  the  focus  of  the  second  mirror  hears  the  ticking  very  distinctly 
even  when  the  mirrors  are  at  a  distance  of  12  or  13  yards. 

237.  Echoes  and  resonances. — An  echo  is  the  repetition  of  a  sound  in 
the  air,  caused  by  its  reflection  from  some  obstacle. 

A  very  sharp  quick  sound  can  produce  an  echo  when  the  reflecting 
surface  is  55  feet  distant ;  but  for  articulate  sounds  at  least  double  that 
distance  is  necessary,  for  it  may  be  easily  shown  that  no  one  can  pronounce 
or  hear  distinctly  more  than  five  syllables  in  a  second.  Now,  as  the  velo- 
city of  sound  at  ordinary  temperatures  may  be  taken  at  1125  feet  in  a  second, 
in  a  fifth  of  that  time  sound  would  travel  225  feet.  If  the  reflecting  surface 
is  112-5  feet  distant,  in  going  and  returning  sound  would  travel  through  225 
feet.  The  time  which  elapses  between  the  articulated  and  the  reflected 
sound  would,  therefore,  be  a  fifth  of  a  second,  the  two  sounds  would  not 
interfere,  and  the  reflected  sound  would  be  distinctly  heard.  A  person 


206  On  Sound.  [237- 

speaking  with  a  loud  voice  in  front  of  a  reflector,  at  a  distance  of  112-5  fe^t,. 
can  only  distinguish  the  last  reflected  syllable  :  such  an  echo  is  said  to  be 
monosyllabic.  If  the  reflector  were  at  a  distance  of  two  or  three  times  112-5 
feet,  the  echo  would  be  dissyllabic,  trisyllabic,  and  so  on. 

When  the  distance  of  the  reflecting  surface  is  less  than  112-5  feet  the 
direct  and  the  reflected  sound  are  confounded.  They  cannot  be  heard 
separately,  but  the  sound  is  strengthened.  This  is  what  is  often  called 
resonance,  and  is  frequently  observed  in  large  rooms.  Bare  walls  are  very 
resonant ;  but  tapestry  and  hangings,  which  are  bad  reflectors,  deaden 
the  sound.  To  diminish  or  eliminate  the  effects  of  resonance  is  a  difficult 
problem  in  the  acoustics  of  the  building  art. 

Multiple  echoes  are  those  which  repeat  the  same  sound  several  times  ; 
this  is  the  case  when  two  opposite  surfaces  (for  example,  two  parallel  walls) 
successively  reflect  sound.  There  are  echoes  which  repeat  the  same  sound 
20  or  30  times.  An  echo  in  the  chateau  of  Simonetta,  in  Italy,  repeats  a 
sound  30  times.  At  Woodstock  there  is  one  which  repeats  from  17  to  20 
syllables. 

As  the  laws  of  reflection  of  sound  are  the  same  as  those  of  light  and 
heat,  curved  surfaces  produce  acoustic  foci  like  the  luminous  and  calorific 
foci  produced  by  concave  reflectors.  If  a  person  standing  under  the  arch  of 
a  bridge  speaks  with  his  face  turned  towards  one  of  the  piers,  the  sound  is 
reproduced  near  the  other  pier  with  such  distinctness  that  a  conversation 
can  be  kept  up  in  a  low  tone,  which  is  not  heard  by  anyone  standing  in  the 
intermediate  spaces. 

There  is  a  square  room  with  an  elliptical  ceiling,  on  the  ground  floor  of 
the  Conservatoire  des  Arts  et  Metiers,  in  Paris,  which  presents  this  pheno- 
menon in  a  remarkable  degree  when  persons  stand  in  the  two  foci  of  the 
ellipse. 

Whispering  galleries  are  formed  of  smooth  walls  having  a  continuous 
curved  form.  The  mouth  of  the  speaker  is  presented  at  one  point,  and 
the  ear  of  the  hearer  at  another  and  distant  point.  In  this  case,  the 
sound  is  successively  reflected  from  one  point  to  the  other  until  it  reaches 
the  ear. 

In  the  whispering  gallery  of  St.  Paul's,  the  faintest  sound  is  thus  conveyed 
from  one  side  to  the  other  of  the  dome,  but  it  is  not  heard  at  any  intermediate 
points.  Placing  himself  close  to  the  upper  wall  of  the  Colosseum,  a  circular 
building  1 30  feet  in  diameter,  Wheatstone  found  a  word  to  be  repeated,  a 
great  many  times.  A  single  exclamation  sounded  like  a  peal  of  laughter, 
while  the  tearing  of  a  piece  of  paper  resembled  the  patter  of  hail. 

It  is  not  merely  by  solid  surfaces,  such  as  walls,  rocks,  ships'  sails,  &c., 
that  sound  is  reflected.  It  is  also  reflected  by  clouds,  and  it  has  even  been 
shown  by  direct  experiment  that  a  sound  in  passing  from  a  gas  of  one  density 
into  another  is  reflected  at  the  surface  of  separation  as  it  would  be  against 
a  solid  surface.  Now  different  parts  of  the  earth's  surface  are  unequally 
heated  by  the  sun,  owing  to  the  shadows  of  trees,  evaporation  of  water,  and 
other  causes,  so  that  in  the  atmosphere  there  are  numerous  ascending  and 
descending  currents  of  air  of  different  density.  Whenever  a  sound-wave 
passes  from  a  medium  of  one  density  into  another  it  undergoes  partial  reflec- 
tion, which,  though  not  strong  enough  to  form  an  echo,  distinctly  weakens 


-238]  Refraction  of  Sound.  207 

the  direct  sound.  This  is  doubtless  the  reason,  as  Humboldt  remarked,  why 
sound  travels  further  at  night  than  at  daytime,  even  in  the  South  American 
forests,  where  the  animals,  which  are  silent  by  day,  fill  the  atmosphere  at 
night  with  thousands  of  confused  sounds.  To  this  may  be  added  that  at 
night  and  in  repose,  when  other  senses  are  at  rest,  that  of  hearing 
becomes  more  acute.  This  is  the  case  with  persons  who  have  become 
blind. 

It  has  generally  been  considered  that  fog  in  the  atmosphere  is  a  great 
deadener  of  sound  ;  it  being  a  mixture  of  air  and  globules  of  water,  at  each 
of  the  innumerable  surfaces  of  contact  a  portion  of  the  vibration  is  lost. 
The  evidence  as  to  the  influence  of  this  property  is  conflicting  ;  recent  re- 
searches of  Tyndall  show  that  a  white  fog,  or  snow,,  or  hail,  are  not  important 
obstacles  to  the  transmission  of  sound,  but  that  aqueous  vapour  is.  Expe- 
riments made  on  a  large  scale,  in  order  to  ascertain  the  best  form  of  fog 
signals,  gave  some  remarkable  results. 

On  some  days  which  optically  were  quite  clear,  certain  sounds  could  not 
be  heard  at  a  distance  far  inferior  to  that  at  which  they  could  be  heard  even 
during  a  thick  haze.  Tyndall  ascribes  this  result  to  the  presence  in  the 
atmosphere  of  aqueous  vapour,  which  forms  in  the  air  innumerable  striae 
that  do  not  interfere  with  its  optical  clearness,  but  render  it  acoustically 
turbid,  the  sound  being  reflected  by  this  invisible  vapour  just  as  light  is  by 
the  visible  cloud. 

These  conclusions  first  drawn  from  observations  have  been  verified  by 
laboratory  experiments.  Tyndall  has  shown  that  a  medium  consisting  of 
alternate  layers  of  light  and  heavy  gas,  such  as  coal  gas  and  carbon 
dioxide,  deadens  sound,  and  also  that  a  medium  consisting  of  alternate  strata 
of  heated  and  ordinary  air  exerts  a  similar  influence.  The  same  is  the  case 
with  an  atmosphere  containing  the  vapours  of  volatile  liquids.  So  long  as 
the  continuity  of  air  is  preserved,  sound  has  great  power  of  passing  through 
the  interstices  of  solids  ;  thus  it  will  pass  through  twelve  folds  of  a  dry  silk 
handkerchief,  but  is  stopped  by  a  single  layer  if  it  is  wetted. 

238.  Refraction  of  sound. — It  will  be  found  in  the  sequel  that  refraction 
is  the  change  of  direction  which  light  and  heat  experience  on  passing  from 
one  medium  to  another.  It  has  been  shown  by  Hajech  that  the  laws  of  the 
refraction  of  sound  are  the  same  as  those  for  light  and  heat :  he  used  tubes 
filled  with  various  gases  and  liquids,  and  closed  by  membranes  ;  the  mem- 
brane at  one  end  was  at  right  angles  to  the  axis  of  the  tube,  while  the^other 
made  an  angle  with  it.  When  these  tubes  were  placed  in  an  aperture  in  the 
wall  between  two  rooms,  a  sound  produced  in  front  of  the  tube  in  one  room,, 
that  of  a  tuning-fork  for  instance,  was  heard  in  directions  in  the  other  vary- 
ing with  the  nature  of  the  substance  with  which  the  tube  was  filled.  Accu- 
rate measurements  showed  that  the  law  held  that  the  sines  of  the  angle  of 
incidence  and  of  refraction  are  in  a  constant  ratio,  which  is  equal  to  the  ratio 
of  the  velocity  of  sound  in  the  two  media. 

Sondhauss  has  confirmed  the  analogy  of  the  refraction  of  sound-waves, 
to  those  of  light  and  heat.     He  constructed  lenses  of  gas  by  cutting  equ; 
segments  out  of  a  large  collodion  balloon,  and  fastening  them  on  the  two. 
sides  of  a  sheet  iron  ring  a  foot  in  diameter,  so  as  to  form  a  double  convex 
lens  about  4  inches  thick  in  the  centre.     This  was  filled  with  carbonic  acidv 


208  On  Sound,  [238- 

and  a  watch  was  placed  in  the  direction  of  the  axis  :  the  point  was  then 
sought  on  the  other  side  of  the  lens  at  which  the  sound  was  most  distinctly 
heard.  It  was  found  that  when  the  ear  was  removed  from  the  axis,  the 
sound  was  scarcely  perceptible  ;  but  that  at  a  certain  point  on  the  axial  line 
it  was  very  distinctly  heard.  Consequently,  the  sound-waves  in  passing 
from  the  lens  had  converged  towards  the  axis,  their  direction  had  been 
changed  ;  in  other  words,  they  had  been  refracted. 

The  refraction  of  sound  may  be  easily  demonstrated  by  means  of  one  of 
the  very  thin  india-rubber  balloons  used  as  children's  toys,  inflated  by 
carbonic  acid.  If  the  balloon  be  filled  with  hydrogen,  no  focus  is  detected  ; 
it  acts  like  a  concave  lens,  and  the  divergence  of  the  rays  is  increased, 
instead  of  their  being  converged  to  the  ear. 

It  has  long  been  known  that  sound  is  propagated  in  a  direction  against 
that  of  the  wind  with  less  velocity  than  with  the  wind.  This  is  probably 
due  to  a  refraction  of  sound  on  a  large  scale.  The  velocity  of  wind  along 
the  ground  is  always  considerably  less  than  at  a  greater  height ;  thus,  the 
velocity  at  a  height  of  8  feet  has  been  observed  to  be  double  what  it  is  at  a 
height  of  one  foot  above  the  ground.  Hence  the  front  of  a  condensed  wave 
{fig.  197),  which  was  originally  vertical,  becomes  tilted  upwards  and  with  the 
lower  part  forward  ;  and,  as  the  direction  of  the  wave-motion  is  at  right 
angles  to  the  front  of  the  wave,  the  effect  of  the  coalescence  of  a  number  of 
these  rays,  thus  directed  upwards,  is  to  produce  an  increase  of  the  sound  in 
the  higher  regions.  The  rays  which  travel  with  the  wind  will,  for  similar 
reasons,  be  refracted  downwards,  and  thus  the  sound  be  better  heard. 

239.  Speaking  trumpet.  Ear  trumpet.— These  instruments  depend 
both  on  the  reflection  of  sound  and  on  its  conductibility  in  tubes. 

The  speaking  trumpet,  as  its  name  implies,  is  used  to  render  the  voice 
audible  at  great  distances,  more  especially  on  board  ship.  It  consists  of  a 
slightly  conical  tin  or  brass  tube  (fig.  200),  very  much  wider  at  one  end  (which 


Fig.  200. 

is  called  the  bell],  and  provided  with  a  mouthpiece  at  the  other.     They  are 
as  much  as  7  feet  in  length,  the  bell  being  i  foot  in  diameter. 

The  larger  the  dimensions  of  this  instrument  the  greater  is  the  distance 
at  which  the  voice  is  heard.  Its  action  is  usually  ascribed  to  the  successive 
reflections  of  sound-waves  from  the  sides  of  the  tube,  by  which  the  waves 
tend  more  and  more  to  pass  in  a  direction  parallel  to  the  axis  of  the 
instrument.  It  has,  however,  been  objected  to  this  explanation,  that  the 
sounds  emitted  by  the  speaking  trumpet  are  not  stronger  solely  in  the 
direction  of  the  axis,  but  in  all  directions  \  that  the  bell  would  not  tend  to 
produce  parallelism  in  the  sound-wave,  whereas  it  certainly  exerts  consider- 
able influence  in  strengthening  the  sound.  According  to  Hassenfratz  the  bell 


-240] 


Stethoscope. 


209 


acts  by  allowing  a  large  mass  of  air  to  be  set  in  consonant  vibration  before 
it  begins  to  be  diffused. 

The  ear  trumpet  is  used  by  persons  who  are  hard  of  hearing.  It  is 
essentially  an  inverted  speaking  trumpet,  and  consists  of  a  conical  metallic 
tube,  one  of  whose  extremities,  terminating  in  a  bell,  receives  the  sound,  while 
the  other  end  is  introduced  into  the  ear.  This  instrument  is  the  reverse  of 
the  speaking  trumpet.  The  bell  serves  as  a  mouthpiece  ;  that  is,  it  receives 
the  sound  coming  from  the  mouth  of  the  person  who  speaks.  These  sounds 
are  transmitted  by  a  series  of  reflections  to  the  interior  of  the  trumpet,  so 
that  the  waves,  which  would  become  greatly  diffused,  are  concentrated  on 
the  ear,  and  produce  a  far  greater  effect  than  divergent  waves  would  have 
done. 

240.  stethoscope. — One  of  the  most  useful  applications  of  acoustical 
principles  is  the  stethoscope.  Figs.  201,  202,  represent  an  improved  form  of 
this  instrument  devised  by  Konig.  Two  sheets  of  caoutchouc,  c  and  #,  are 
fixed  to  the  circular  edge  of  a  hollow  metal  hemisphere  ;  the  edge  is  provided 
with  a  stopcock,  so  that  the  sheets  can  be  inflated,  and  then  present  the  ap- 
pearance of  a  double  convex  lens,  as  represented  in  section  in  fig.  201.  To 


Fig.  201. 


Fig.  202. 


a  tubulure  on  the  hemisphere  is  fixed  a  caoutchouc  tube  terminated  by  horn 
or  ivory,  £,  which  is  placed  in  the  ear  (fig.  202). 

When  the  membrane  c  of  the  stethoscope  is  applied  to  the  chest  of  a  sick 
person  the  beating  of  the  heart  and  the  sounds  of  respiration  are  transmitted 
to  the  air  in  the  chamber  <s,  and  from  thence  to  the  ear  by  means  of  the 
flexible  tube.  If  several  tubes  are  fixed  to  the  instrument,  as  many  observers 
may  simultaneously  auscultate  the  same  patient. 


210  On  Sound.  [241- 


CHAPTER   II. 

MEASUREMENT   OF  THE   NUMBER   OF  VIBRATIONS. 

241.  Savart's  apparatus. — Savart  s  toothed  wheel \  so  called  from  the 
name  of  its  inventor,  is  an  apparatus  by  which  the  absolute  number  of  vibra- 
tions corresponding  to  a  given  note  can  be  determined.  It  consists  of  a 
solid  oak  frame  in  which  there  are  two  wheels,  A  and  B  (fig.  203)  ;  the  larger 


Fig.  203. 

wheel,  A,  is  connected  with  the  toothed  wheel  by  means  of  a  strap  and  a 
multiplying  wheel,  thereby  causing  the  toothed  wheel  to  revolve  with  great 
velocity ;  a  card,  E,  is  fixed  on  the  frame,  and,  in  revolving,  the  toothed 
wheel  strikes  against  it,  and  causes  it  to  vibrate.  The  card  being  struck  by 
each  tooth,  makes  as  many  vibrations  as  there  are  teeth.  At  the  side  of  the 
apparatus  there  is  an  indicator,  H,  which  gives  the  number  of  revolutions  of 
the  wheel,  and  consequently  the  number  of  vibrations  in  a  given  time. 

When  the  wheel  is  moved  slowly,  the  separate  shocks  against  the  card 
are  distinctly  heard  ;  but  if  the  velocity  is  gradually  increased,  the  sound 
becomes  higher  and  higher.  Having  obtained  the  sound  whose  number  of 
vibrations  is  to  be  determined,  the  revolution  of  the  wheel  is  continued  with 
the  same  velocity  for  a  certain  number  of  seconds.  The  number  of  turns  of 
the  toothed  wheel  B  is  then  read  off  on  the  indicator,  and  this  multiplied 
by  the  number  of  teeth  in  the  wheel  gives  the  total  number  of  vibrations. 
Dividing  this  by  the  corresponding  number  of  seconds,  the  quotient  gives 
the  number  of  vibrations  per  second  for  the  given  sound. 

242.  Syren. — The  syren  is  an  apparatus  which,  like  Savart's  wheel,  is 
used  to  measure  the  number  of  vibrations  of  a  body  in  a  given  time.  The 


-242] 


Syren. 


211 

name  'syren'  was  given  to  it  by  its  inventor,  Cagniard  Latour,  because  it 
yields  sounds  under  water. 

It  is  made  entirely  of  brass.  Fig.  204  represents  it  fixed  on  the  table  of 
a  bellows,  by  which  a  continuous  current  of  air  can  be  sent  through  it  Fies 
205  and  206  show  the  internal  details.  The  lower  part  consists"  of  a  cylin- 
drical box,  O,  closed  by  a  fixed  plate,  B.  On  this  plate  a  vertical  rod  T  rests 
to  which  is  fixed  a  disc,  A,  moving  with  the  rod.  In  the  plate  B  there  are 
equidistant  circular  holes,  and  in  the  disc  A  are  an  equal  number  of  holes  of 
the  same  size,  and  the  same  distance  from  the  centre  as  those  of  the  plate 
These  holes  are  not  perpendicular  to  the  disc  :  they  are  all  inclined  to  the 
same  extent  in  the  same  direction  in  the  plate,'  and  are  inclined  to  the  same 
extent  in  the  opposite  direction  in  the  disc,  so  that  when  they  are  opposite 
each  other  they  have  the  appearance  represented  in  mn,  fig.  205.  Conse- 
quently, when  a  current  of  air  from  the  bellows  reaches  the  hole,  m,  it  strikes 


Fig.  204. 


Fig.  206. 


obliquely  against  the  sides  of  the  hole  #,  and  imparts  to  the  disc  A  a  rotatory 
motion  in  the  direction  ;zA. 

For  the  sake  of  simplicity,  let  us  first  suppose  that  in  the  movable  disc 
A  there  are  eighteen  holes,  and  in  the  fixed  plate  B  only  one,  which  faces 
one  of  the  upper  holes.  The  wind  from  the  bellows  striking  against  the 
sides  of  the  latter,  the  movable  disc  begins  to  rotate,  and  the  space  between 
two  of  its  consecutive  holes  closes  the  hole  in  the  lower  plate.  But  as  the 
disc  continues  to  turn  from  its  acquired  velocity,  two  holes  are  again  opposite 
each  other,  a  new  impulse  is  produced,  and  so  on.  During  a  complete 
revolution  of  the  disc  the  lower  hole  is  eighteen  times  open  and  eighteen 
times  closed.  A  series  of  effluxes  and  stoppages  is  thus  produced,  which 
makes  the  air  vibrate,  and  ultimately  produces  a  sound  when  the  successive 
impulses  are  sufficiently  rapid.  If  the  fixed  plate,  like  the  moving  disc,  had 
eighteen  holes,  each  hole  would  separately  produce  the  same  effect  as  a 
separate  one,  the  sound  would  be  eighteen  times  as  intense,  but  the  number 
of  vibrations  would  not  be  increased. 

p  2 


212  On  Sound.  [224- 

In  order  to  know  the  number  of  vibrations  corresponding  to  the  sound 
produced,  it  is  necessary  to  know  the  number  of  revolutions  of  the  disc  A  in 
a  second.  For  this  purpose  an  endless  screw  on  the  rod  T  transmits  the 
motion  to  a  wheel,  a,  with  100  teeth.  On  this  wheel,  which  moves  by  one 
tooth  for  every  turn  of  the  disc,  there  is  a  catch  P,  which  at  each  complete 
revolution  moves  one  tooth  of  a  second  wheel,  b  (fig.  206).  On  the  axis  of 
these  wheels  there  are  two  needles,  which  move  round  dials  represented  in 
fig.  204.  One  of  these  indices  gives  the  number  of  turns  of  the  disc  A,  the 
other  the  number  of  hundreds  of  turns.  By  means  of  two  screws,  D  and  C, 
the  wheel  a  can  be  uncoupled  from  the  endless  screw. 

Since  the  pitch  of  the  sound  rises  in  proportion  to  the  velocity  of  the  disc 
A,  the  wind  is  forced  until  the  desired  sound  is  produced.  The  same  current 
is  kept  up  for  a  certain  time — two  minutes,  for  example — and  the  number  of 
turns  read  off.  This  number  multiplied  by  18,  and  divided  by  120,  gives 
the  number  of  vibrations  in  a  second.  For  the  same  velocity  of  rotation  the 
syren  gives  the  same  sound  in  air  as  in  water  ;  the  same  is  the  case  with 
all  gases  ;  and  it  appears,  therefore,  that  any  given  sound  depends  on  the 
number  of  vibrations,  and  not  on  the  nature  of  the  sounding  body. 

The  buzzing  and  humming  noise  of  certain  insects  is  not  vocal,  but  is 
produced  by  very  rapid  flapping  of  the  wings  against  the  air  or  the  body. 
The  syren  has  been  ingeniously  applied  to  count  the  velocity  of  the  undula- 
tions thus  produced,  which  is  effected  by  bringing  it  into  unison  with  the 
sound.  It  has  thus  been  found  that  the  wings  of  a  gnat  flap  at  the  rate  of 
15,000  times  in  a  second.  If  a  report  is  produced  in  a  space  with  two 
parallel  walls  at  no  great  distance  apart,  the  sound  is  reflected  from  one  to 
the  other  and  reaches  the  ear  at  regular  and  frequent  intervals  ;  that  is,  the 
repetition  of  the  echo  acts  as  a  note. 

243.  Bellows. — In  acoustics   a  bellows  is  an  apparatus  by  which  wind 
instruments,  such  as  the  syren  and  organ-pipes,  are  worked.     Between  the 
four  legs  of  a  table  there  is  a  pair  of  bellows,  S  (fig.  207),  which  is  worked 
by  means  of  a  pedal,  P.    D  is  a  reservoir  of  flexible  leather,  in  which  is  stored 
the  air  forced  in  by  the  bellows.     If  this  reservoir  is  pressed  by  means  of 
weights  on  a  rod  T,  moved  by  the  hand,  the  air  is  driven  through  a  pipe,  E, 
into  a  chest,  C,  fixed  on  the  table.     In  this  chest  there  are  small  holes  closed 
by  leather  valves,  which  can  be  opened  by  pressing  on  keys  in  front  of  the 
box.     The  syren  or  sounding  pipe  is  placed  in  one  of  these  holes. 

244.  Limit  of  perceptible  sounds. — Previous  to  Savart's  researches, 
physicists  assumed  that  the  ear  could  not  perceive  a  sound  when  the  number 
of  vibrations  was  below  16  for  deep  sounds,  or  above  9,000  for  acute  sounds. 
But  he  showed  that  these  limits  were  too  close,  and  that  the  faculty  of  per- 
ceiving sounds  depends  rather  on  their  intensity  than  on  their  height ;  so 
that  when  extremely  acute  sounds  are  not  heard,  it  arises  from  the  fact  that 
they  have  not  been  produced  with  sufficient  intensity  to  affect  the  organ  of 
hearing. 

By  increasing  the  diameter  of  the  toothed  wheel,  and  consequently  the 
amplitude  and  intensity  of  the  vibrations,  Savart  pushed  the  limit  of  acute 
sounds  to  24,000  vibrations  in  a  second. 

For  deep  sounds  he  substituted  for  the  toothed  wheel  an  iron  bar  about 
two  feet  long,  which  revolved  on  a  horizontal  axis  between  two  thin  wooden 


-245] 


DuhameVs  Graphic  Method. 


213 


plates,  about  cro8  of  an  inch  from  the  bar.  As  often  as  the  bar  passed  -i 
grave  sound  was  produced,  due  to  the  displacement  of  the  air.  As  the 
motion  was  accelerated,  the  sound  became  continuous,  very  grave  and 
deafening.  By  this  means  Savart  found  that,  with  7  to  8  vibrations  in  a 
second,  the  ear  perceived  a 
distinct  but  very  deep  sound. 

Despretz,  however,  who 
investigated  the  same  sub- 
ject, disputed  Savart's  results 
as  to  the  limits  of  deep 
sounds,  and  considers  that 
no  sound  it  audible  that  is 
made  by  less  than  16  vibra- 
tions per  second.  Helm- 
holtz  holds  that  the  percep- 
tion of  a  sound  begins  at  30 
vibrations,  and  only  has  a 
definite  musical  value  when 
the  number  is  more  than  40. 
Below  30  the  impression  of 
a  number  of  separate  beats 
is  produced.  On  the  other 
hand  acute  sounds  are  audi- 
ble up  to  those  correspond- 
ing to  38,000  vibrations  in  a 
second. 

The  discordant  results 
obtained  by  these  and  other 
observers  for  the  limit  of 
audibility  of  higher  notes  are 
no  doubt  due  to  the  circumstance  that  different  observers  have  different 
capacities  for  the  perception  of  sounds.  Preyer  has  investigated  this  subject 
by  means  of  experimental  methods  of  greater  precision  than  any  that  have 
hitherto  been  applied  for  this  purpose.  The  minimum  limit  for  the  normal 
ear  he  found  to  lie  between  16  and  24  single  vibrations  in  a  second;  the 
maximum  limit  reached  41,000  ;  but  many  persons  with  average  powers  of 
hearing  were  found  to  be  absolutely  deaf  to  notes  of  16,000,  12,000,  or  even 
fewer  vibrations. 

245.  Duhamel's  graphic  method. — When  the  syren  or  Savart's  wheel 
is  used  to  determine  the  exact  number  of  vibrations  corresponding  to  a  given 
note,  it  is  necessary  to  bring  the  sounds  which  they  produce  into  unison 
with  the  given  note,  and  this  cannot  be  done  exactly  unless  the  experi- 
menter has  a  practised  ear.  DuhameFs  graphic  method  is  very  simple  and 
exact,  and  free  from  this  difficulty.  It  consists  in  fixing  a  fine  point  to  the 
body  emitting  the  note,  and  causing  it  to  trace  the  vibrations  on  a  properly 
prepared  surface. 

The  apparatus  consists  of  a  wood  or  metal  cylinder,  A  (fig.  208),  fixed  to 
a  vertical  axis,  O,  and  turned  by  a  handle.  The  lower  part  of  the  axis  is  a 
screw  working  in  a  fixed  nut,  so  that,  according  as  the  handle  is  turned  from 


Fig.  207. 


2I4 


On  Sound. 


[245- 


left  to  right,  or  from  right  to  left,  the  cylinder  is  raised  or  depressed.  Round 
the  cylinder  is  rolled  a  sheet  of  paper  covered  with  an  inadhesive  film  of 
lampblack.  On  this  film  the  vibrations  register  themselves  This  is  effected 
as  follows.  Suppose  the  body  emitting  the  note  to  be  a  steel  rod.  It  is  held 
firmly  at  one  end,  and  carries,  at  the  other,  a  fine  point  which  grazes  the  sur- 
faces of  the  cylinder.  If  the  rod  is  made  to  vibrate  and  the  cylinder  is  at  rest, 
the  point  would  describe  a  short  line  ;  but  if  the  cylinder  is  turned,  the  point 
produces  an  undulating  line,  containing  as  many  undulations  as  the  point 
has  made  vibrations.  Consequently  the  number  of  vibrations  can  be  counted. 
It  remains  only  to  determine  the  time  in  which  the  vibrations  were  made. 


There  are  several  ways  of  doing  this.  The  simplest  is  to  compare  the 
curve  traced  by  the  vibrating  rod  with  that  traced  by  a  tuning-fork  (251), 
which  gives  a  known  number  of  vibrations  per  second — for  example,  500. 
The  prong  of  the  fork  is  furnished  with  a, point,  which  is  placed  in  contact 
with  the  lampblack.  The  fork  and  the  rod  are  then  set  vibrating  together, 
and  each  produces  its  own  undulating  trace.  When  the  paper  is  unrolled, 
it  is  easy,  by  counting  the  number  of  vibrations  each  has  made  in  the  same 
distance,  to  determine  the  number  of  vibrations  made  per  second  by  the 
elastic  rod.  Suppose,  for  instance,  that  the  tuning-fork  made  150  vibrations 
while  the  rod  made  165  vibrations.  Now  we  already  know  that  the  tuning- 
fork  makes  one  vibration  in  the  ¥§5  part  of  a  second,  and  therefore  1 50 
vibrations  in  ||§  of  a  second.  But  in  the  same  time  the  rod  makes  165 

vibrations  ;  therefore  it  makes   one  vibration  in  the — ->-  of  a  second, 

500  x  165 

and  hence  it  makes  per  second  ^5      LJ  or  550  vibrations. 


-247]  Musical  Intervals.  215 


CHAPTER   III. 

THE  PHYSICAL  THEORY  OF  MUSIC. 

246.  Properties  of  musical  notes. — A  simple  musical  note  results  from 
continuous  rapid  isochronous  vibrations,  provided  the  number  of  the  vibra- 
tions falls  within  the  very  wide  limits  mentioned  in  the  last  chapter  (244). 
Musical  notes  are  in  most  cases   compound.     The   distinction  between  a 
simple  and  a  compound  musical  note  will  be  explained  later  in  the  chapter. 
The  tone  yielded  by  a  tuning-fork  furnished  with  a  proper  resonance-box  is 
simple  ',  that  yielded  by  a  wide-stopped  organ  pipe,  or  by  a  flute,  is  nearly 
simple ;  that  yielded  by  a  musical  string  is  compound. 

Musical  notes  have  three  leading  qualities,  namely,  pitch,  intensity,  and 
timbre  or  quality. 

i.  The  pitch  of  a  musical  note  is  determined  by  the  number  of  vibrations 
per  second  yielded  by  the  body  producing  the  note. 

ii.  The  intensity  of  the  note  depends  on  the  extent  of  the  vibrations.  It 
is  greater  when  the  extent  is  greater,  and  less  when  it  is  less.  It  is,  in  fact, 
proportional  to  the  square  of  the  extent  or  amplitude  of  the  vibrations  which 
produce  the  note. 

iii.  The  timbre  or  stamp  or  quality  is  that  peculiar  property  of  note  which 
distinguishes  a  note  when  sounded  on  one  instrument  from  the  same  note 
when  sounded  on  another.  Thus  when  the  C  of  the  treble  stave  is  sounded 
on  a  violin,  and  on  a  flute,  the  two  notes  will  have  the  same  pitch  ;  that  is 
are  produced  by  the  same  number  of  vibrations  per  second,  and  they  may 
have  the  same  intensity,  and  yet  the  two  notes  will  have  very  distinct  qualities  ; 
that  is,  their  timbre  is  different.  The  cause  of  the  peculiar  timbre  of  notes 
will  be  considered  later  in  the  chapter. 

247.  Musical  intervals.— Let  us  suppose  that  a  musical  note,  which  for 
the  sake  of  future  reference  we  will  denote  by  the  letter  C,  is  produced  by 
m  vibrations  per  second  ;  and  let  us  further  suppose  that  any  other  musical 
note,  X,  is  produced  by  n  vibrations  per  second,  n  being  greater   than  m  ; 
then  the  interval  from  the  note  C  to  the  note  X  is  the  ratio  n  ;  m,  the  interval 
between  two  notes,  being  obtained  by  division,  not  by  subtraction.     Although 
two  or  more  notes  may  be  separately  musical,  it  by  no  means  follows  that 
when  sounded  together  they  produce  a  pleasant   sensation.     On  the  con- 
trary, unless  they  are  concordant,  the  result  is  harsh,  and  usually  unpleasing. 
We  have,  therefore,  to  inquire  what  notes  are  fit  to  be  sounded  together. 
Now  when  musical  notes  are  compared  it  is  found  that  if  they  are  separated 
by  an  interval  of  2  :  i,  4  :  I,  &c.,  they  so  closely  resemble  one  another  the 
they  may  for  most  purposes  of  music  be  considered  as  the  same  note.     Thus, 
suppose  c  to  stand  for  a  musical  note  produced  by  2;*  vibrations  per  second, 
then  C  and  c  so  closely  resemble  one  another  as  to  be  called  in  music  by 
the  same  name.     The  interval  from  C  to  c  is  called  an  octave,  and  c  is 


216  On  Sound.  [247- 

said  to  be  an  octave  above  C,  and  conversely  C  an  octave  below  c.  If  we  now 
consider  musical  sounds  that  do  not  differ  by  an  octave,  it  is  found  that 
if  we  take  three  notes,  X,  Y,  and  Z,  resulting  respectively  from  p,  q,  and  r 
vibrations  per  second,  these  three  notes  when  sounded  together  will  be  con- 
cordant if  the  ratio  of/  :  q  :  r  equals  4:5:6.  Three  such  notes  form  a 
harmonic  triad,  and  if  sounded  with  a  fourth  note,  which  is  the  octave  of 
X,  constitute  what  is  called  in  music  a  major  chord.  Any  of  the  notes  of  a 
chord  may  be  altered  by  one  or  more  octaves  without  changing  its  distinc- 
tive character  ;  for  instance,  C,  E,  G,  and  c  are  a  chord,  and  C,  c,  e,  g  form 
the  same  chord. 

If,  however,  the  ratio  p  :  q  :  r  equals  10  :  12  :  15,  the  three  sounds  are 
slightly  dissonant,  but  not  so  much  so  as  to  disqualify  them  from  producing 
a  pleasing  sensation.  When  these  three  notes  and  the  octave  to  the  lower 
are  sounded  together  they  constitute  what  in  music  is  called  a  minor  chord. 

248.  Tlie  musical  scale. — The  series  of  sounds  which  connects  a  given 
note  C  with  its  octave  c  is  called  the  diatonic  scale  or  gamut.  The  notes 
composing  it  are  indicated  by  the  letters  C,  D,  E,  F,  G,  A,  B.  The  scale 
is  then  continued  by  taking  the  octaves  of  these  notes,  namely,  c,  d,  e,f,g,  a,  b 
and  again  the  octaves  of  these  last,  and  so  on. 

The  notes  are  also  known  by  names,  viz.,  do  or  ut,  re,  mi,  fa,  sol,  la,  si, 
do.  The  relations  existing  between  the  notes  are  these  : — C,  E,  G  form 
a  major  triad,  G,  B,  d  form  a  major  triad,  and  F,  A,  c  form  a  major  triad. 
C,  G,  and  F  have,  for  this  reason,  special  names,  being  called  respectively, 
the  tonic,  dominant,  and  sub-dominant,  and  the  three  triads  the  tonic, 
dominant,  and  sub-dominant  triads  or  chords  respectively.  Consequently, 
the  numerical  relations  between  the  notes  of  the  scale  will  be  given  by  the 
three  proportions — 


G 

2D 

2C 


Hence  if  m  denotes  the  number  of  double  vibrations  corresponding  to 
the  note  C,  the  number  of  vibrations  corresponding  to  the  remaining  notes 
will  be  given  by  the  following  table  — 

do         re         mi       fa         sol        la         si        do 
CDEFGAB^- 


m          m        m         m          m        m 


The  intervals  between  the  successive  notes  being  respectively  — 
C  to  D     D  to  E     E  to  F     F  to  G     G  to  A    A  to  B     B  to  c 

§10  IjS  9  10  9  1(3 

9  15  8  9  8  15 

It  will  be  observed  here  that  there  are  three  kinds  of  intervals,  f,  1I°,  and 
~  ;  of  these  the  two  former  are  called  a  tone,  the  last  a  semitone,  because  it 
is  about  half  as  great  as  the  interval  of  a  tone.  The  two  tones,  however,  are 
not  identical,  but  differ  by  an  interval  of  ~,  which  is  called  a  comma.  Two 
notes  which  differ  by  a  comma  can  be  readily  distinguished  by  an  educated 
ear.  The  interval  between  the  tonic  and  any  note  is  denominated  by  the 
position  of  the  latter  note  in  the  scale  ;  thus  the  interval  from  C  to  G  is  a 
fifth.  The  scale  we  have  now  considered  is  called  the  major  scale,  as  being 


-250]  On  Musical  Temperament.  217 

formed  of  major  triads.  If  the  minor  triad  were  substituted  for  the  major 
a  scale  would  be  formed  that  could  be  strictly  called  a  minor  scale.  As 
scales  are  usually  written,  however,  the  ascending  scale  is  so  formed  that 
the  tonic  bears  a  minor  triad,  the  dominant  and  sub-dominant  bear  major 
triads,  while  in  the  descending  scale  they  all  bear  minor  triads.  Practically 
in  musical  composition,  the  dominant  triad  is  always  major.  If  the  ratios 
given  above  are  examined,  it  will  be  found  that  in  the  major  scale  the 
interval  from  C  to  E  equals  f,  while  in  the  minor  scale  it  equals  f.  The 
former  interval  is  called  a  major  third,  the  latter  a  minor  third.  Hence  the 
major  third  exceeds  the  minor  third  by  an  interval  of  ff.  This  interval  is 
called  a  semitone,  though  very  different  from  the  interval  above  called  by 
that  name. 

249.  On  semitones  and  on  scales  with  different  key-notes.  —  It  will- 
be  seen  from  the  last  article  that  the  term  '  semitone  '  does  not  denote  a 
constant  interval,  being  in  one  case  equivalent  to  £f  and  in  another  to  ||. 
It  is  found  convenient  for  the  purposes  of  music  to  introduce  notes  inter- 
mediate to  the  seven  notes  of  the  gamut  ;  this  is  done  by  raising  or  lowering 
these  notes  by  an  interval  of  ff  .  When  a  note  (say  C)  is  increased  by  this 
interval,  it  is  said  to  be  sharpened,  and  is  denoted  by  the  symbol  Cfl  ,  called 
'  C  sharp  ;  '  that  is,  Cfl  -=-C  =  ff.  When  it  is  lowered  by  the  same  interval,  it 
is  said  to  be  flattened,  and  is  represented  thus—  Bb,  called  'B  flat  ;'  that  is, 
B-7-Bb=§|.  If  the  effect  of  this  be  examined,  it  will  be  found  that  the 
number  of  notes  in  the  scale  from  C  up  to  c  has  been  increased  from  seven 
to  twenty-one  notes,  all  of  which  can  be  easily  distinguished  by  the  ear. 
Thus  reckoning  C  to  equal  i,  we  have— 


C          C&  Db          D          D&  Eb          E        &c. 

i      ff      e      i     H      if    &c- 

Hitherto  we  have  made  the  note  C  the  tonic  or  key-note.  Any  other  of 
the  twenty-one  distinct  notes  above  mentioned,  e.g.  G,  or  F,  or  C*:,  £c., 
may  be  made  the  key-note,  and  a  scale  of  notes  constructed  with  reference 
to  it.  This  will  be  found  to  give  rise  in  each  case  to  a  series  of  notes,  some 
of  which  are  identical  with  those  contained  in  the  series  of  which  C  is  the 
key-note,  but  most  of  them  different.  And  of  course  the  same  would  be  true 
for  the  minor  scale  as  well  as  for  the  major  scale,  and  indeed  for  other  scales 
which  may  be  constructed  by  means  of  the  fundamental  triads. 

250.  On  musical  temperament.—  The  number  of  notes  that  arise  from 
the  construction  of  the  scales  described  in  the  last  article  is  so  great  as  to 
prove  quite  unmanageable  in  the  practice  of  music  ;  and  particularly  f 
music  designed  for  instruments  with  fixed  notes,  such  as  the  pianoforte  01 
harp.     Accordingly,  it  becomes  practically  important  to  reduce  the  numbei 
of  notes,  which  is  done  by  slightly  altering  their  just  proportions. 
process  is  called  temperament.     By  tempering  the  notes,  however,  more  or 
less  dissonance  is  introduced,  and  accordingly  several  different  systems  o 
temperament  have  been  devised  for  rendering  this  dissonance  as  slighi 
possible      The  system  usually  adopted  is  called  the  system  of  equal  tempei 
ment.     It  consists  in  the  substitution  between  C  and  c  of  eleven  note 
equal  intervals,  each  interval  being,  of  course,  the  twelfth  root  of  2,  or  i  -05946 
By  this  means  the  distinction  between  the  semitones  is  abolished,  sc 


218  On  Sound.  [250- 

for  example,  Cfl  and  Db  become  the  same  note.  The  scale  of  twelve  notes 
thus  formed  is  called  the  chromatic  scale.  It  of  course  follows  that  major 
triads  become  slightly  dissonant.  Thus,  in  the  diatonic  scale,  if  we  reckon  C 
to  be  i,  E  is  denoted  by  1-25000,  and  G  by  1-50000.  On  the  system  of  equal 
temperament,  if  C  is  denoted  by  i,  E  is  denoted  by  1-25992,  and  G  by  1*49831. 
If  individual  intervals  are  made  pure  while  the  errors  are  distributed  over 
the  others,  such  a  system  is  called  that  of  unequal  temperament.  Of  this 
class  is  Kirnberger^s,  in  which  nine  of  the  tones  are  pure. 

Although  the  system  of  equal  temperament  has  the  advantage  of  afford- 
ing the  greatest  variety  of  tones  with  as  small  a  number  of  notes  as 
possible,  yet  it  has  the  drawback  that  no  chord  of  an  equally  tempered 
instrument,  such  as  the  piano,  is  perfectly  pure.  And  as  musical  education 
mostly  has  its  basis  on  the  piano,  even  singers  and  instrumentalists  usually 
give  equally-tempered  intervals.  Only  in  the  case  of  string  quartet  players, 
who  have  freed  themselves  from  school  rules,  and  in  that  of  vocal  quartet 
singers,  who  sing  much  without  accompaniment,  does  the  natural  pure  tem- 
perament assert  itself,  and  thus  produce  the  highest  musical  effect. 

251.  The  number  of  vibrations  producing:  each  note.  The  tuning-- 
fork.— Hitherto  we  have  denoted  the  number  of  vibrations  corresponding  to 
the  note  C  by  ;;z,  and  have  not  assigned  any 
numerical  value  to  that  symbol.  In  the  theory 
of  music  it  is  frequently  assumed  that  the  middle 
C  corresponds  to  256  double  vibrations  in  a 
second.  This  is  the  note  which,  on  a  pianoforte 
of  seven  octaves,  is  produced  by  the  white  key 
on  the  left  of  the  two  black  keys  close  to  the 
centre  of  the  keyboard.  This  number  is  con- 
venient as  being  continually  divisible  by  two, 
and  is  therefore  frequently  used  in  numerical 
illustrations.  It  is,  however,  arbitrary.  An 
instrument  is  in  tune  provided  the  intervals 
between  the  notes  are  correct,  when  c  is  yielded 
by  any  number  of  vibrations  per  second  not 
differing  much  from  256.  Moreover,  two  instru- 
ments are  in  tune  with  one  another,  if,  being 
separately  in  tune,  they  have  any  one  note,  for 
instance  C,  yielded  by  the  same  number  of  vibra- 
tions. Consequently,  if  two  instruments  have 
one  note  in  common,  they  can  then  be  brought 
F-  into  tune  jointly  by  having  their  remaining  notes 

separately  adjusted  with  reference  to  the  funda- 
mental note.  A  timing-fork  or  diapason  is  an  instrument  yielding  a  con- 
stant sound,  and  is  used  as  a  standard  for  tuning  musical  instruments.  It 
consists  of  an  elastic  steel  rod,  bent  as  represented  in  fig.  209.  It  is  made 
to  vibrate  either  by  drawing  a  bow  across  the  ends,  or  by  striking  one  of 
the  legs  against  a  hard  body,  or  by  rapidly  separating  the  two  prongs  by 
means  of  a  steel  rod  as  shown  in  the  figure.  The  vibration  produces  a  note 
which  is  always  the  same  for  the  same  tuning-fork.  The  note  is  strengthened 
by  fixing  the  tuning-fork  on  a  box  open  at  one  end,  called  a  sounding  or 


-252]  Musical  Notation.     Musical  Range.  219 

resonance  box,  adjusted  so  as  to  strengthen  the  special  note  of  the  tuning-fork 
<255)« 

The  standard  tuning-fork  in  any  country  represents  its  accepted  concert 
pitch. 

It  has  been  remarked  for  some  years  that  not  only  has  the  pitch  of  the 
tuning-fork  been  getting  higher  in  the  large  theatres  of  Europe,  but  also 
that  it  is  not  the  same  in  London,  Paris,  Berlin,  Vienna,  Milan,  &c.  This  is 
a  source  of  great  inconvenience  both  to  composers  and  singers,  and  a  com- 
mission was  appointed  in  1859  to  establish  in  France  a  tuning-fork  of  uniform 
pitch,  and  to  prepare  a  standard  which  would  serve  as  an  invariable  type. 
In  accordance  with  the  recommendations  of  that  body,  a  normal  tuning-fork 
has  been  established,  which  is  compulsory  on  all  musical  establishments 
in  France,  and  a  standard  has  been  deposited  in  the  conservatory  of  music 
in  Paris.  It  performs  437-5  double  vibrations  per  second,  and  gives  the 
standard  note  a  or  /«,  or  the  a  in  the  treble  stave  (252).  Consequently,  with 
reference  to  this  standard,  the  middle  c  or  do  would  result  from  261  double 
vibrations  per  second. 

In  England  a  committee,  appointed  by  the  Society  of  Arts,  recommended 
that  a  standard  tuning-fork  should  be  one  constructed  to  yield  528  double 
vibrations  in  a  second,  and  that  this  should  represent  c'  in  the  treble  stave. 
This  number  has  the  advantage  of  being  divisible  by  2  down  to  33,  and  is  in 
fact  the  same  as  the  normal  tuning-fork  adopted  in  Stuttgardt  in  1834,  which 
makes  440  vibrations  in  the  second,  and,  like  the  French  one,  corresponds 
to  a  in  the  same  stave. 

In  exact  determinations  of  pitch  the  temperature  must  be  taken  into 
account.  Heat  acts  on  the  tuning-fork  by  expanding  it,  and  also  by 
diminishing  the  elasticity  of  the  metal.  Both  effects  concur  in  lowering 
the  pitch.  Thus  Konig  found  that  a  tuning-fork  which  made  512  vibrations 
at  20°  C.  varied  by  0-0572  for  each  degree  C.  Stone  and  McLeod  found  the 
number  0*055. 

252.  Musical  notation.  Musical  range. — It  is  convenient  to  have 
some  means  of  at  once  naming  any  particular  note  in  the  whole  range  of 
musical  sounds  other  than  by  stating  its  number  of  vibrations.  Perhaps  a 
convenient  practice  is  to  call  the  octave,  of  which  the  C  is  produced  by  an 
eight-foot  organ  pipe,  by  the  capital  letters  C,  D,  E,  F,  G,  A,  B  ;  the  next 
higher  octave  by  the  corresponding  small  letters,  c,  d,  e,f,g,a,b\  and  to 
designate  the  octaves  higher  than  this  by  the  index  placed  over  the  letter 
thus,  <:',  d',  *',/',  £-',  a',  £',  and  the  higher  series  in  a  similar  manner.  The 
same  principle  may  be  applied  to  the  notes  below  C  ;  thus  the  octave  below 
C  is  C,,  and  the  next  lower  one  C,,. 

Hence  we  have  the  series 

C,,   C,  C  *  *  c"  c'"  c*. 

In  musical  writing  the  notes  are  expressed  by  signs  which  indicate  the 
length  of  time  during  which  the  note  is  to  be  played  or  sung,  and  are  written 
on  a  series  of  lines  called  a  stave.  Thus 


220  On  Sound.  [252- 

stands  for  the  octave  in  the  treble  clef:  of  which  the  top  note  is  the  standard 
cf  and  the  bottom  is  the  middle  c.  When  the  five  lines  are  insufficient  they 
are  continued  above  and  below  the  stave  by  what  are  called  ledger  lines. 
In  order  to  avoid  confusion,  a  bass  clef  is  used  for  the  lower  notes  ;  and  it 


may  be  remarked  that  ffi?  •      j —    and  &   _— 1= — -  stand  for  the  same  note 

(251)  which  is  the  middle  c. 

The  deepest  note  of  orchestral  instruments  is  the  E  of  the  double  bassr 
which  makes  41^  vibrations,  taking  the  key-note  as  making  440  vibrations 
in  a  second.  Some  organs  and  pianofortes  go  as  low  as  C//x  with  32  vibra- 
tions in  a  second,  some  grand  pianos  even  as  low  as  Ax//  with  27^  vibrations. 
But  the  musical  character  of  all  these  notes  below  Ex  is  imperfect,  for  we 
are  near  the  limit  at  which  the  ear  can  combine  the  separate  vibrations  to  a 
musical  note  (244).  These  notes  can  only  be  used  musically  with  their  next 
higher  octave,  to  which  they  impart  a  certain  character  of  depth  and  richness. 

In  the  other  direction,  pianofortes  go  to  aiv  with  3520  or  even  c"  with  4224 
vibrations  in  a  second.  The  highest  note  of  the  orchestra  is  probably  the 
d*  of  the  piccolo  flute,  which  makes  4752  vibrations.  Although  the  ear  can 
distinguish  sounds  which  are  still  higher,  they  have  no  longer  a  pleasurable 
character.  And  while  the  notes  which  are  distinguishable  by  the  ear,  range 
between  16  and  38,000  vibrations,  or  n  octaves,  those  which  are  musically 
available,  range  from  about  40  to  4,000  vibrations,  or  within  7  octaves. 

253.  Wave-length   of   a    given   note.      Amplitude    of  oscillation. — 
Knowing  the   number  of  vibrations  which  a  sounding  body  makes  in  a 
second,  the  corresponding  wave-length  is  easily  calculated.    For  since  sound 
travels  at  about  1,120  feet  in  a  second,  if  a  body  only  made  one  vibration  in 
a  second  its  wave-length  would  be  1,120  feet;  if  it  made  two,  the  wave-length 
would  be  half  of  1,120  feet ;  if  it  made  three,  the  third,  and  so  on — that  is, 
that  the  wave-length  of  any  note  zs  the  quotient  obtained  by  dividing  the 
velocity  of  sound  by  the  number  of  vibrations  ;  and  this  whatever  the  height 
of  the  sound,  since  the  velocity  is  the  same  for  high  and  low  notes. 

Hence,  calling  v  the  velocity  of  sound,  /  the  wave-length,  n  the  number 

of  vibrations  in  a  second,  we  have  v  =  ln,  from  which  n  =  — ;  that  is,  that  the 

number  of  vibrations  is  inversely  as  the  wave-length. 

The  amplitude  of  oscillation  which  is  required  for  the  production  of 
audible  sounds  is  very  small.  Lord  Rayleigh  determined  it  in  the  case  of 
the  waves  due  to  a  pipe  which  sounded  the  note  _/iv,  and  which  could  be 
heard  at  a  distance  of  820  metres.  He  found  that  the  amplitude  of  the  oscil- 
lation of  these  waves  could  not  be  greater  than  0*0000001  of  a  millimetre. 

254.  On  compound  musical  tones  and  harmonics. — When  any  given 
note  (say  C)  is  sounded  on  most  musical  instruments,  not  that  tone  alone  is 
produced,  but  a  series  of  tones,  each  being  of  less  intensity  than  the  one 
preceding  it.     If  C,  which  may  be  called  the  primary  tone,  is  denoted  by 
unity,  the  whole  series  is  given  by  the  numbers  i,  2,  3,  4,  5,  6,  7,  &c.  ;  in 
other  words,  first  the  primary  C  is  sounded,  then  its  octave  becomes  audible, 
then  the  fifth  to  that  octave,  then  the  second  octave,  then  the  third,  fifth, 
and  a  note  between  the  sixth  and  seventh  to  the  second  octave,  and  so  on. 
These  secondary  notes  are  called  the  harmonics  of  the  primary  note.   Though 


-256]  Helmho It s* s  Analysis  of  Sound.  221 

feeble  in  comparison  with  the  primary  note,  they  may,  with  a  little  practice 
be  heard,  when  the  primary  note  is  produced  on  most  musical  instruments  • 
when,  for  instance,  one  of  the  lower  notes  is  sounded  on  the  pianoforte. 

255.  Helmholtz's  analysis  of  sound.— For  the  purpose  of  experimentally 
proving  the  presence  of  the  harmonics  as  distinct  tones,  Professor  Helmholtz 
devised  an  instrument  which  he  called  a  resonance  globe.  This  may  be  illus- 
trated by  the  following  experiment,  which  indeed  is  identical  in  principle 
with  that  described  in  article  229  :— If  an  empty  glass  cylinder  be  taken 
and  a  vibrating  tuning-fork  be  held  over  the  mouth  of  the  vessel,  the  column 
of  air  will  not  be  set  in  vibration  unless  the  column  of  air  be  of  a  certain 
definite  length  ;  such,  indeed,  that  the  wave-length  of  the  fundamental  note 
corresponds  to  the  wave-length  of  the  note  produced  by  the  tuning-fork. 
Now  by  pouring  in  water  we  can  regulate  the  length  of  the  column  of  air, 
and  by  trial  can  hit  off  the  exact  length  ;  when  this  is  attained  the  note  of 
the  tuning-fork  will  be  heard  to  be  powerfully  reinforced  (227).  A  resonance- 
globe  (fig.  210)  is  a  glass  globe  tuned  to  a  particular  note,  furnished  with 
two  openings,  one  of  which,  #,  is  turned  towards  the  origin  of  the  sound,  and 
the  other,  b,  by  means  of  an  india-rubber  tube,  is  applied  to  the  ear.  If  the 
tone  proper  to  the  resonance-globe  exists  among  the  harmonics  of  the  coin- 


Fig.  210.  Fig.  211. 

pound  tone  that  is  sounded  it  is  strengthened  by  the  globe,  and  thereby 
rendered  distinctly  audible.  Further,  other  things  being  the  same,  the 
note  proper  to  a  given  globe  depends  on  the  diameter  of  the  globe  and  that 
of  the  uncovered  opening.  Consequently,  by  means  of  a  series  of  such 
globes,  the  whole  series  of  harmonics  in  a  given  compound  tone  can  be  ren- 
dered distinctly  audible,  and  their  existence  put  beyond  a  doubt. 

Konig,  the  eminent  acoustical  instrument  maker,  has  made  an  important 
modification  in  the  resonance-globe,  to  which  he  has  given  the  form  repre- 
sented in  fig.  211.  The  resonator  is  cylindrical,  and  the  end  which  receives 
the  sound  can  be  drawn  out,  so  that  the  volume  may  be  increased  at  pleasure. 
As  the  sound  thereby  becomes  deeper,  the  same  resonator  may  be  tuned  to  a 
variety  of  notes.  On  the  tubulure  fits  a  caoutchouc  tube  by  which  the  vibra- 
tions may  be  transmitted  in  any  direction. 

It  may  here  be  mentioned  that  a  distinction  is  made  between  consonance 
and  resonance.  Consonance  is  the  excitation  of  a  body  to  independent 
vibrations  by  a  note,  while  resonance  is  the  strengthening  of  feeble  notes,  by 
the  consonant  vibrations  of  adjacent  bodies. 

256.  Xbnig's  apparatus  for  the  analysis  of  sound. — As  the  successive 
application  to  the  ear  of  various  resonators  is  both  slow  and  tedious,  Konig 


222 


On  Sound. 


[256- 


devised  a  remarkable  apparatus  in  which  a  series  of  resonators  act  on  mano- 
metric  flames  (288)  ;  the  sounds  thus,  as  it  were,  become  visible,  and  may 
be  shown  to  a  large  auditory. 

It  consists  of  an  iron  frame  (fig.  212)  on  which  are  fixed  in  two  parallel 
lines  fourteen  resonators  tuned  so  as  to  give  the  notes  from  F/  to  c" — that  is 
to  say,  four  octaves  and  a  half ;  or  notes  of  which  the  highest  give  the  lower 
harmonics  of  the  primary.  On  the  right  is  a  chamber  C,  which  is  supplied 
with  C9al  gas  by  the  caoutchouc  tube,  D,  and  on  which  are  placed  eight 


Fig.  212. 

gas  jets,  each  provided  with  a  manometric  capsule  (288).  Each  jet  is  con- 
nected with  the  chamber  C  by  a  special  caoutchouc  tube,  while  behind  the 
apparatus  a  second  tube  connects  the  same  jet  to  one  of  the  resonators. 
On  the  right  of  the  jets  is  a  system  of  rotating  mirrors  identical  with  that 
described  in  article  288. 

These  details  being  understood,  suppose  the  largest  resonator  on  the  right 
tuned  to  resound  with  the  note  I,  and  seven  others  with  the  harmonics  of 
this  note.  Let  the  sound  i  be  produced  in  part  of  this  apparatus  ;  if  it  is 
simple,  the  lower  resonator  alone  answers,  and  the  corresponding  flame  is 


-257] 


Helmholtz's  Synthesis  of  Sounds. 


223 


alone  dentated  ;  but  if  the  fundamental  note  is  accompanied  by  one  or  more 
of  its  harmonics,  the  corresponding  resonators  speak  at  the  same  time,  which 
is  recognised  by  the  dentation  of  their  flames  ;  and  thus  the  constituents  of 
each  sound  may  be  detected. 

257.  Synthesis  of  sounds. — Not  only  has  Helmholtz  succeeded  in  de- 
composing sounds  into  their  constituents  ;  he  has  verified  the  result  of  his 
analysis  by  performing  the  reverse  operation,  the  synthesis  ;  that  is,  he  has 
reproduced  a  given  sound  by  combining  the  individual  sounds  of  which  his 
resonators  had  shown  that  it  was  composed.  The  apparatus  which  he  used 
for  this  purpose  consists  of  eleven  tuning-forks,  the  first  of  which  yields  the 
fundamental  note  of  256  vibrations,  or  C,  nine  others  its  harmonics,  while  the 
eleventh  serves  as  make  and  break  to  cause  the  diapasons  to  vibrate  by  means 
of  electro-magnets.  Each  diapason  has  a  special  electro-magnet,  and  more- 
over a  resonator,  which  strengthens  it. 


Fig.  213- 

All  these  diapasons  and  their  accessories  are  arranged  in  parallel  lines  of 
five  (fig  213),  the  first  comprising  the  fundamental  note  and  its  uneven  har- 
monics, 3,  5,  7,  and  9  ;  the  second  the  even  harmonics,  24,  6,  8,  and  ic ; 
beyond,  there  is  the  diapason  break  K  arranged  horizontally.  One  of  i 
prono-s  is  provided  with  a  platinum  point  which  grazes  the  surface  of  mercury 
contained  in  a  small  cup,  the  bottom  of  which  is  connected,  by  a  copper 
wire,  with  an  electro-magnet  placed  in  front  of  the  diapason. 

The  apparatus  being  thus  arranged,  a  wire  from  a  voltaic  battery  is  con- 
nected with  the  binding  screw,  c,  and  this  with  the  electro-magnet  E  ;  which 
in  turn  is  connected  with  those  of  the  nine  following  diapasons    and  the 
with  the  diapason  K  itself.     So  long  as  the  diapason  does  not  vibrate,  tl 
current  does  not  pass,  for  the  platinum  point  does  not  dip  m  the  me 
cup  which  is  connected  with  the  other  pole  of  the  battery.     But  when  the 


224 


On  Sound. 


[257- 


diapason  is  made  to  vibrate  by  means  of  a  bow,  the  current  passes.  Owing 
to  their  elasticity,  the  limbs  of  the  tuning-fork  soon  revert  to  their  original 
position,  the  point  is  no  longer  in  the  mercury,  the  current  is  broken,  and  so 
on  at  each  double  vibration  of  the  diapason.  This  intermittence  of  the 
current  being  transmitted  to  all  the  other  electro-magnets,  they  are  alternately 
active  and  inactive.  Hence  they  communicate  to  all  the  diapasons  by  their 
attraction  the  same  number  of  vibrations.  This  is  the  case  with  the  diapason 
i,  which  is  tuned  in  unison  with  the  diapason  break  ;  but  the  diapason  3, 
being  tuned  to  make  three  times  as  many  vibrations,  makes  three  vibrations 
at  each  break  of  the  current ;  that  is  to  say,  the  electro-magnet  only  attracts 
it  at  every  third  vibration  ;  in  like  manner,  diapason  b  only  receives  a  fresh 
impulse  every  five  vibrations,  and  so  on. 

The  following  is  the  working  of  the  apparatus  : — The  resonator  of  each 
diapason  is  closed  by  a  clapper  O  (fig.  214),  so  that  the  sounds  made  by  the 

diapasons  are  scarcely 
perceptible  when  the  clap- 
pers are  lowered.  Each  of 
these  is  fixed  to  the  end  of 
a  bent  lever,  the  shorter 
arm  of  which  is  worked 
by  a  cord  «,  which  is  con- 
nected with  one  of  the 
keys  of  a  keyboard  placed 
in  front  of  the  apparatus 
(fig.  213).  When  a  key  is 
depressed,  the  cord  moves 
the  lever,  which  raises  the 
clapper,  and  the  resonator 
then  acts  by  strengthening 
its  diapason.  Hence  by 
depressing  any  key  we 
may  add  to  the  funda- 


Fig.  214. 


mental  sounds  any  of  the  nine  primary  harmonics,  and  thus  reproduce  the 
sounds  the  composition  of  which  has  been  determined  by  analysis.  Thus  by 
depressing  all  the  keys  at  once  we  obtain  the  sound  of  an  open  pipe  in  unison 
with  the  deepest  diapason.  By  depressing  the  key  of  the  fundamental  note 
and  those  of  its  uneven  harmonics,  we  obtain  the  sound  of  a  closed  pipe. 

258.  Results  of  HelmHoltz's  researches. — By  both  his  analytical  and 
synthetical  investigations  into  sounds  of  the  most  varied  kinds — those  from 
various  musical  instruments,  the  human  voice,  and  even  noises — Helmholtz 
has  fully  succeeded  in  explaining  the  different  timbre  or  quality  of  sounds.  It 
is  due  to  the  different  intensities  of  the  harmonics  which  accompany  the 
primary  tones  of  these  sounds.  The  leading  results  of  these  researches  into 
the  colour  of  sounds  may  be  thus  stated  :  — 

i.  Simple  notes,  as  those  produced  by  a  tuning-fork  with  a  resonance-box, 
and  by  wide  covered  pipes,  are  soft  and  agreeable  without  any  roughness, 
but  weak,  and  in  the  deeper  notes  dull. 

ii.  Musical  sounds  accompanied  by  a  series  of  harmonics,  say  up  to  the 
sixth,  in  moderate  strength,  are  full  and  musical.  In  comparison  with  simple 


-259]  Production  of  Vocal  Sounds.  225 

tones  they  are  grander,  richer,  and  more  sonorous.     Such  are  the  sounds  of 
open  organ-pipes,  of  the  pianoforte,  &c. 

iii.  If  only  the  uneven  harmonics  are  present,  as  in  the  case  of  narrow 
stopped  pipes,  of  pianoforte  strings  struck  in  the  middle,  clarionets,  &c.,  the 
sound  becomes  indistinct ;  and  when  a  greater  number  of  hanr^nics  are 
audible,  the  sound  acquires  a  nasal  character. 

iv.  If  the  harmonics  beyond  the  sixth  and  seventh  are  very  distinct, 
the  sound  becomes  sharp  and  rough.  If  less  strong,  the  harmonics  are  not 
prejudicial  to  the  musical  usefulness  of  the  notes.  On  the  contrary,  they 
are  useful,  as  imparting  character  and  expression  to  the  music.  Of  this  kind 
are  most  stringed  instruments,  and  most  pipes  furnished  with  tongues,  &c. 
Sounds  in  which  harmonics  are  particularly  strong  acquire  thereby  a  pecu- 
liarly penetrating  character  ;  such  are  those  yielded  by  brass  instruments. 

259.  Production  of  vocal  sounds. — The  trachea  or  windpipe  is  a  tube 
which  terminates  at  one  end  in  the  lungs,  and  at  the  other  in  the  laryn.r, 
which  is  the  true  organ  of  vocal  sound. 
Fig.  215  represents  a  horizontal  section  of 
this  organ.  It  consists  of  a  number  of  car- 
tilaginous structures,  bb,  which  are  connected 
by  various  muscles,  by  which  great  variety  and 
control  in  the  motions  are  attainable.  These 
muscles  are  connected  with,  and  move,  two 
elastic  membranes  or  bands  with  broad  bases 
fixed  to  the  larynx,  and  with  sharp  edges  cc  ; 
these  are  called  the  vocal  chords.  Accord- 
ing to  the  pressure  of  the  muscles  these 
chords  are  more  or  less  tightly  stretched, 
and  the  space  between  them,  the  vocal  slit,  Fig  2i. 

is  narrower  or  wider  accordingly.  In  ordi- 
nary breathing,  air  passes  through  the  triangular  aperture  o  ;  but  when  in 
singing  this  is  closed,  the  vocal  chords  are  stretched  and  are  put  in  vibration 
by  the  current  of  air,  and  produce  tones  which  are  higher  the  more  tightly 
the  chords  are  stretched,  and  the  narrower  is  the  vocal  slit.  These  changes 
can  be  effected  with  surprising  rapidity,  so  that  in  this  respect  the  human 
voice  far  exceeds  anything  that  can  be  made  artificially. 

The  notes  produced  by  men  are  deeper  than  those  of  women  or  boys, 
because  in  them  the  larynx  is  longer  and  the  vocal  chords  larger  and  thicker ; 
hence,  though  equally  elastic,  they  vibrate  less  swiftly.  The  vocal  chords 
are  18  millimetres  long  in  men,  and  12  millimetres  long  in  women.  Chest 
notes  are  due  to  the  fact  that  the  whole  membrane  vibrates,  while  the  fal- 
setto is  produced  by  a  vibration  of  the  extreme  edges  only.  The  ordinary 
compass  of  the  individual  voice  is  within  two  octaves,  though  this  is  exceeded 
by  some  celebrated  singers.  Catalini,  for  instance,  is  said  to  have  had  a 
range  of  3|  octaves. 

The  wave-length  of  the  sounds  emitted  by  a  man's  voice  in  ordinary  con- 
versation is  from  8  feet  to  12  feet,  and  that  of  women's  voice  is  from  2  feet  to 
4  feet,  in  a  second. 

The  vowel  sounds  can  be  produced  in  any  pitch,  and  the  difference  in 
them  arises  from  the  fact  that  to  form  a  given  vowel  sound  one  or  more 

Q 


226 


On  Sound. 


[259- 


characteristic  notes  which  are  always  the  same  must  be  added.  These 
change  with  the  syllable  pronounced,  but  depend  neither  on  the  height  of 
the  note,  nor  on  the  person  who  emits  them. 

The  form  and  cavity  of  the  mouth  can  be  greatly  modified  by  the  extent 
to  which  it  is  opened,  by  the  altered  position  of  the  tongue,  and  so  forth.  It 
thus  forms  a  resonator  which  can  be  quickly  and  completely  controlled. 
When  the  mouth  is  adjusted  so  as  to  produce  the  broad  A,  as  in  father,  it 
has  then  a  sort  of  funnel  shape,  with  the  wide  part  outward  ;  for  O,  as  in 
more,  the  effect  is  like  that  of  a  bottle  with  a  wide  neck ;  and  for  U,  as  in 
poor,  it  is  that  of  a  similar  bottle  with  a  narrow  neck.  For  the  other  vowels, 
such  as  A,  E,  and  I,  the  effect  is  as  if  the  bottle  were  prolonged  by  a  tube, 
formed  by  contracting  the  tongue  against  the  palate. 

If  now,  while  the  mouth  is  adjusted  for  the  position  in  which  it  could 
utter  the  vowel  U,  on  successively  holding  different  vibrating  tuning-forks  in 
front  of  it,  only  that  emitting  the  note  /  will  be  found  to  be  reinforced  by 
the  enclosed  column  of  air  vibrating  in  unison  with  it.  This  is  accordingly 
the  characteristic  note  of  that  vowel ;  in  like  manner  b'  is  the  note  for  O, 
and  b"  for  that  of  A.  The  other  vowel  sounds,  such  as  I,  have  a  higher  and 
lower  characteristic  note  ;  thus  those  of  A  as  in  day  are  d  and  a'",  of  \,f 
and  d>".  In  most  cases,  however,  the  deeper  notes  have  but  little  influence. 
260.  Perception  of  sounds.  The  ear. — The  organ  of  hearing  in  man 

consists  of  several  struc- 
tures ;  the  external  ear 
(fig.  216)  by  which  the 
sound  is  collected  and 
transmitted  through  the 
auditory  passage,  a,  to 
the  drum  or  tympanum,  t. 
This  is  a  delicate  tightly 
stretched  membrane  or 
skin  which  separates  the 
outer  ear  from  the  middle 
ear  or  tympanic  cavity. 
This  is  a  cavity  in  the 
temporal  bone  in  which 
are  several  small  bones 
whose  dimensions  are 
Flg>  2l6>  considerably  exaggerated 

in  the  figure.  One  of  these,  the  hammer,  d,  is  attached  at  one  end  to  the 
drum,  and  at  the  other  is  jointed  to  the  anvil,  e  :  the  latter  is  connected  by 
means  of  the  stirrup  bone,f,  to  the  oval  window,  an  aperture  closed  by  a 
fine  membrane  and  which  separates  the  tympanic  cavity  from  the  labyrinth. 
The  tympanic  cavity  is  also  connected  by  the  Eustachian  tube,  b,  with  the 
cavity  of  the  mouth,  so  that  the  air  in  it  is  always  under  the  same  pressure. 

The  labyrinth  is  a  complicated  structure  filled  with  fluid  ;  it  is  entirely  of 
bone,  with  the  exception  of  the  oval  window  already  mentioned  and  the 
round  window,  o.  The  labyrinth  consists  of  three  parts  :  the  vestibule, 
which  is  closed  by  the  oval  window  ;  the  three  semicircular  canals,  k  ;  and 
the  spiral-shaped  cochlea  or  snail-shell,  s.  This  is  separated  throughout  its 


-262]  Beats.  227 

entire  length  by  a  division  partly  of  bony  projection  and  partly  of  membrane  ; 
the  upper  part  of  this  division  is  connected  with  the  vestibule,  and  therefore 
with  the  oval  window,  while  the  lower  part  is  connected  with  the  round 
window.  In  the  labyrinthine  fluid  of  this  part  the  termination  of  the  auditory 
nerve  is  spread,  the  other  end  leading  to  the  brain. 

The  membranous  part  of  this  diaphragm  is  lined  with  about  3,000 
extremely  minute  fibres,  which  are  the  terminations  of  the  acoustic  nerve  n. 
Each  of  these,  which  are  called  Corti's  fibres,  seems  to  be  tuned  for  a 
particular  note  as  if  it  were  a  small  resonator.  Thus  when  the  vibrations  of 
any  particular  note  reach  these  fibres,  through  the  intervention  of  the  stirrup 
bone  and  the  fluid  of  the  labyrinth,  one  fibre  or  set  of  fibres  only  vibrates  in 
unison  with  this  note,  and  is  deaf  for  all  others.  Hence  each  simple  note 
only  causes  one  fibre  to  vibrate,  while  compound  notes  cause  several ;  just 
as  when  we  sing  with  a  piano,  only  the  fundamental  note  and  its  harmonics 
vibrate.  Thus,  however  complex  external  sounds  may  be,  these  microscopic 
fibres  can  analyse  it  and  reveal  the  constituents  of  which  it  is  formed. 

261.  Interference  of  sound. — If  two  waves  of  sound  of  the  same  length 
proceed  in  the  same   direction,  and  if  they  coincide  in  their  phases,  they 
strengthen  one  another  ;  if,  however,  their  phases  differ  by  half  a  wave-length 
they  neutralise  each  other,  and  silence  is  the  result.  This  is  called  the  inter- 
ference of  sound. 

It  may  be  illustrated  by  a  number  of  experiments,  of  which  that  repre- 
sented in  fig.  217  is  one  of  the  simplest  and  most  convenient.  Two  T-shaped 
glass  tubes,  obac  and  nedf,  are 
connected  at  one  end  by  a 
short  india-rubber  tube  ad, 
while  at  the  other  ends  they 
.are  connected  by  a  long 
india-rubber  tube,  cqf.  The 
end  o  provided  with  a  caout- 
chouc tube  is  held  in  one 

ear,    the    other     ear    being  Fig.  217. 

closed,  and  a  timing-fork  is 

sounded  in  front  of  the  long  free  tube,  nrs.  If  the  length  of  the  india-rubber 
tube  eg/be  half  the  wave-length  of  the  note  produced  by  the  fork,  the  sounds 
will  reach  the  ear  in  completely  opposite  phases  ;  they  will  accordingly 
neutralise  each  other  and  no  sound  will  be  heard.  But  if  this  india-rubber  tube 
is  closed  by  pinching  it,  the  note  is  at  once  heard.  If  the  tuning-fork  gives 
the  note  clt  the  note  it  produces  makes  528  vibrations  in  a  second,  and  the 
length  of  the  tube  should  be  34  centimetres. 

262.  Beats. — If  the  notes  are  different  and  are  not  quite  in  the  same 
phase,  they  alternately  weaken  and  strengthen  each  other  ;  they  are  said  to 
beat  with  one  another.    This  may  be  explained  as  follows  :— Suppose  AB,  in 
fig.  218,  to  be  a  row  of  particles  transmitting  the  sound  :  suppose  the  vibra- 
tions producing  the  one  note  to  be  indicated  by  the  continuous  curved  line; 
then,  on  the  one  hand,  the  ordinates  of  the  different  points  of  AB  give  the 
velocities  with  which  those  points  are  simultaneously  moving,  and,  on  the 
other  hand,  each  point  will  have  successively  the  different  velocities  repre- 
sented by  the  successive  ordinates.     In  like  manner  let  the  dotted  line  show 

Q2 


228  On  Sound.  [262- 

the  vibrations  which  produce  the  second  note.  And,  for  the  sake  of  distinct- 
ness, suppose  the  number  of  vibrations  in  a  second  producing  the  former 
note  to  be  to  that  producing  the  latter  in  the  ratio  of  3  :  2.  Now  let  us  con- 
sider any  point  which 
when  at  rest  occupies 
the  position  N  ;  draw 
the  ordinate,  cutting 
the  former  curve  in  P 
and  the  latter  in  O. 
If  the  notes  were 
sounded  separately, 
the  velocity  of  N  at  a 

7ig.  219.  given  distance    pro- 

duced by  the  former 

note  would  be  PN,  and  that  of  N  at  the  same  instant  produced  by  the  latter 
note  would  be  QN.  Consequently,  as  they  are  sounded  together,  the  actual 
velocity  of  N  at  the  given  instant  is  the  sum  of  these,  or  PN  +  ON.  If  at 
the  same  instant  we  consider  the  point  «,  its  velocity  will  consist  of  pn  and 
ng  jointly,  but,  as  these  are  in  opposite  directions,  its  actual  amount  will  be 
pn—7iq.  Hence  the  actual  velocity  resulting  from  the  co-existence  of  the  two 
notes  will  be  indicated  by  the  curve  in  fig.  219,  whose  ordinates  equal  the 
(algebraical)  sum  of  the  corresponding  ordinates  of  the  two  curves  in  fig. 
218  ;  that  is,  if  AN,  An,  .  .  .  represent  equal  distances  in  both  figures,  the 
curve  is  described  by  taking  RN  equal  to  PN  +  ON,  rn  equal  \<Q  pn  —  qn, 
and  so  on.  This  curve  shows  by  its  successive  ordinates  the  simultaneous 
velocities  of  the  different  particles  of  AB,  and  the  successive  velocities  com- 
municated to  the  drum  of  the  ear.  An  inspection  of  the  figure  will  show 
that  the  velocities  are  first  great,  then  small,  then  great,  and  so  on,  the  drum 
being  first  moved  rapidly  for  a  short  time,  then  for  a  short  time  nearly  brought 
to  rest,  and  so  on.  In  short,  the  effect  of  the  beating  of  notes  on  the  ear, 
as  compared  with  that  of  a  continuous  note,  is  strictly  analogous  o  the  effect 
produced  on  the  eye  by  a  flickering,  as  compared  with  a  steady,  light. 

It  may  be  proved  that  when  two  simple  notes  are  produced  by  m  and  n 
double  vibrations  per  second,  they  produce  m  —  n  beats  per  second  ;  thus,  if 
C  is  produced  by  128,  and  D  by  144,  double  vibrations  per  second,  on  being 
sounded  together  they  will  produce  1 6. beats  per  second.  It  has  been  ascer- 
tained that  the  beats  produced  by  two  notes  are  not  audible  unless  the  ratio 
m  :  n  is  less  than  the  ratio  6  :  5.  Hence,  in  the  case  represented  by  fig.  218, 
though  the  alternations  of  intensity  exist,  they  would  not  be  audible.  Also, 
if  the  notes  have  very  different  intensities,  the  intensity  of  the  beat  is  very 
much  disguised. 

It  is  found  that  when  beats  are  fewer  than  10  per  second  or  more  than  70 
per  second  they  are  disagreeable,  but  not  to  the  extent  of  producing  discord. 
Beats  from  10  to  70  per  second  may  be  regarded  as  the  source  of  all  discord 
in  music,  the  maximum  of  dissonance  being  attained  when  about  30  beats 
are  produced  in  a  second.  For  example,  if  c  and  B  are  sounded  together 
the  effect  is  very  discordant,  the  interval  between  those  notes  being  16  :  15, 
so  that  the  beats  are  audible,  and  the  number  of  beats  per  second  being  16. 
On  the  other  hand,  if  C,  E,  and  G  are  sounded  together  there  is  no  disso- 


-264]          The  Physical  Constitution  of  Musical  Chords.  229 

nance  ;  but  if  C,  E,  G,  B  are  sounded  together  the  discord  is  very  marked, 
since  C  produces  c,  which  is  discordant  with  B.  It  will  be  remarked  that 
C,  E,  G  is  a  major  triad,  while  E,  G,  B  is  a  minor  triad. 

A  compound  musical  note,  being  composed  of  simple  notes  represented 
by  i,  2,  3,  4,  5,  6,  7,  &c.,  does  not  give  rise  to  any  simple  notes  capable  of 
producing  an  audible  beat  up  to  the  seventh— the  sixth  and  seventh  are  the 
first  that  produce  an  audible  beat.  It  is  for  this  reason  that  there  is  no 
trace  of  roughness  in  a  compound  note,  unless  the  seventh  harmonic  be 
audible. 

If  we  were  to  represent  graphically  a  compound  note,  we  should  proceed 
to  construct  a  curve  out  of  simple  notes  of  different  intensities  in  the  same 
manner  as  fig.  219  is  constructed  from  two  simple  notes  of  equal  intensity 
represented  by  fig.  218.  It  is  evident  that  the  resulting  curve  will  take 
different  forms  according  to  the  presence  or  absence  of  different  harmonics 
and  their  different  intensities  ;  in  other  words,  the  quality  or  timbre  of  the 
notes  produced  by  different  instruments  will  depend  upon  \hzform  of  the 
vibrations  producing  the  sound. 

Beats  not  too  fast  to  be  readily  counted  arise  between  adjacent  notes  in 
the  lower  octaves  of  large  organs.  They  are  also  met  with  in  the  sounds 
of  church  bells,  and  in  those  emitted  by  telegraph  wires  when  vibrating 
powerfully  in  a  strong  wind.  They  are  heard  very  distinctly  in  the  latter 
case  by  pressing  one  ear  against  a  telegraph-post  and  closing  the  other. 

By  means  of  beats,  the  notes  emitted  by  two  musical  instruments  may  be 
brought  into  very  accurate  unison,  by  continuing  the  tuning  until  the  beats 
disappear.  In  order  to  make  tuning-forks  produce  the  normal  number  of 
440  vibrations,  an  auxiliary  tuning-fork  is  used  which  makes  436  vibrations  ; 
each  of  the  forks  under  experiment  must  then  make  with  this  4  beats  in  a 
second,  which  can  be  controlled  with  very  great  accuracy. 

263.  Combinational   notes.— Besides   the    beats  produced   when    two 
musical  notes  are  sounded  together,  there  is  another  and  distinct  pheno- 
menon, which  maybe   thus  described  :— Suppose  two  simple  notes  to  be 
simultaneously   produced   by   n   and    m   vibrations    per   second.      It   has 
been  shown  by  Helmholtz  that  they  generate  a  series  of  other  notes.     The 
principal  one  of  these,  which  may  be  called  the  differential  note,  is  produced 
by  n-m  vibrations  per  second.     Its  intensity  is  usually  very  small,  but  it  is 
distinctly  audible  in  beats.     It  has  been  called  the  grave  harmonic,  as  its 
pitch  is  generally  much  lower  than  that  of  the  notes  by  which  it  is  generated. 
It  has  been  supposed  to  be  caused  by  the  beats  becoming  too  numerous  to 
be  distinguished,  and  coalescing  into  a  continuous  sound,  and  this  supposition 
was  countenanced  by  the  fact  that  its  pitch  is  the  same  as  the  beat  number. 
The  supposition  is  shown   to  be  erroneous,  first,  by  the  existence  of  the 
differential  tones  for  intervals  that  do  not  beat ;  and,  secondly,  by  the  fact 
that,  under  certain  circumstances,  both  the  beats  and  the  differential  tones 
may  be  heard  together. 

264.  The  physical  constitution  of  musical  chords.— Let  us  suppose 
two  compound  notes  to  be  sounded  together,  say  C  and  G,  then  we  obtain 
two  series  of  notes  each  consisting  of  a  primary  and  its  harmonics,  namely, 

denoting  C  by  4,  the  two  series,  4,  8,  12,  1 6 and  6,  12,  1 8,  24,  &C.    Now, 

If  instead  of  producing  the  two  notes  C  and  G,  we  had  sounded  the  < 


230  On  Sound.  [264- 

below  C,  we  should  have  produced  the  series,  2,  4,  6,  8,  10,  12,  14,  16,  18 
&c.  It  is  plain  that  the  two  former  series  when  joined  differ  from  the  last  in 
the  following  respects : — (a)  The  primary  note  2  is  omitted.  (£)  In  the  case 
of  the  last  series,  the  consecutive  notes  continually  decrease  in  intensity  ; 
whereas  in  the  two  former  series,  4  and  6  are  of  the  same  intensity,  8  is  of 
lower  intensity,  but  the  two  I2's  will  strengthen  each  other,  and  so  on.  (c) 
Certain  of  the  harmonics  of  the  primary  2  are  omitted  ;  for  example,  10,  14, 
&c.,  do  not  occur  in  either  of  the  two  former  series.  In  spite  of  these  dif- 
ferences, however,  the  two  compound  notes  affect  the  ear  in  a  manner  very 
closely  resembling  a  single  compound  note  ;  in  short,  they  coalesce  into  a 
single  note  with  an  artificial  colour.  It  may  be  added  that  in  the  case  above 
taken  C  and  G  produce  as  a  combination  note  2  (that  is  6  -  4),  so  that, 
strictly  speaking,  the  2  is  not  wanted  in  the  series  produced  by  C  and  G, 
only  it  exists  in  very  diminished  intensity.  The  same  explanation  will 
apply  to  all  possible  chords  ;  for  example,  in  the  case  of  the  major  chord, 
C,  E,  G,  we  have  a  note  of  artificial  colour  expressed  by  the  series  of  simple 
tones,  4,  5,  6,  8,  10,  12,  15,  16,  18,  &c.,  together  with  the  combination  notes, 
i,  i,  2.  It  will  be  remarked  that  in  the  whole  of  this  series  there  are  no  dis- 
sonant notes  introduced,  except  15,  16,  and  16,  18,  and  this  dissonance  will 
be  inappreciably  slight,  since  15  is  the  third  harmonic  of  5,  and  16  the 
fourth  harmonic  of  4,  so  that  their  intensities  will  be  different,  as  also  will  be 
the  intensities  of  16  and  18.  On  the  other  hand,  nearly  all  the  notes  which 
form  a  natural  compound  note  are  present,  namely,  there  are  i,  2,  4,  5,  6,  8 

10,  12,  &c.,  in  place  of  i,  2,  3,  4,  5,  6,  7,  8,  9,  10,  11,  12,   &c.     In  short,  the 
major  triad  differs  only  from  a  natural  compound  note. in  that  it  consists  of 
a  series  of  simple  notes  of  different  intensities,  and  omits  those  which,  by 
beating  with  the  neighbouring  note,  would  produce  dissonance  ;  for  example 
7,  which  would  beat  with  6  and  8  ;  9,  which  would  beat  with  8  and  10  ;  and 

11,  which  would  beat  with  10  and  12.     It  is  this  circumstance  which  renders 
the  major  chord  of  such  great  importance  in  harmony.     If  the  constituents 
of  the  minor  chord  are  similarly  discussed,  namely,   three  compound  tones 
whose  primaries  are  proportional  to  10,  12,  15,  it  will  be  found  to  differ  from 
the  major  chord  in  the  following  principal  respects  :  (a)  The  primary  of  the 
natural  tone  to  which  it  approximates  is  very  much  deeper  than  that  of  the 
corresponding  major  chord,     (b)  It  introduces  the  differential  notes,  2,  3,  5, 
which  form  a  major  chord.     Now  it  has  already  been  remarked  that  when  a 
major  and  minor  chord  are  sounded  together,  they  are  distinctly  dissonant  ; 
for  example,  when  C,  E,  G,  A  are  sounded  together.     Accordingly,  the  fact 
of  the  differential  notes  forming  a  major  chord  shows  that  an   elementary 
dissonance  exists  in  every  minor  chord. 


-267]       Lazvs  of 'the  Transverse  Vibrations  of  Strings.  231 


CHAPTER   IV. 

VIBRATIONS   OF   STRETCHED   STRINGS   AND   OF  COLUMNS   OF  AIR. 

265.  Vibrations   of  strings. — By  a   string  is   meant   the   string    of  a 
musical  instrument,  such  as  a  violin,  which  is  stretched  by  a  certain  force, 
and  is   commonly  of  catgut,   or   is   a  metal   wire.     The  vibrations  which 
strings  experience  may  be  either  transverse  or  longitudinal,  but  practically 
the  former  are  alone  important.     Transverse  vibrations  may  be  produced 
by  drawing  a  bow  across  the  string,  as  in  the  case  of  the  violin  :  or  by 
striking  the  string,  as  in  the  case  of  the  pianoforte ;  or  by  pulling  it  trans- 
versely, and  then  letting  it  go  suddenly,  as  in  the  case  of  the  guitar  and  harp. 

266.  Sonometer. — The  sonometer  is  an  apparatus  by  which  the  trans- 
verse vibrations  of  strings  may  be  studied.     It  is  also  called  the  monochord^ 


Fig.  220. 

because  it  has  often  only  one  string.  In  addition  to  the  string,  it  consists 
of  a  thin  wooden  box  which  has  the  effect  of  strengthening  the  sound  ;  this 
it  does  by  presenting  a  far  larger  area  to  the  air  than  the  string  itself. 
On  this  there  are  two  fixed  bridges,  A  and  D  (fig.  220),  over  which  and 
over  the  pulley  «,  passes  the  string,  which  is  usually  a  metal  wire.  This 
is  fastened  at  one  end,  and  stretched  at  the  other  by  weights,  P,  which  can 
be  increased  at  will.  By  means  of  a  third  movable  bridge,  B,  the  length  c 
that  portion  of  the  wire  which  is  to  be  put  in  vibration  can  be  altered  at 
pleasure. 

267.  laws    of  the    transverse    vibrations  of  strings.— 
length  of  a  string— that  is,  the  vibrating  part  between  two  bridges,  A  and  B 
(fig.  220)— r  the  radius  of  the  string,  d  its  density,  P  the  stretching  weight, 
and  n  the  number  of  vibrations  per  second,  it  is  found  by  calculation  that 

^_1A/P£  •  TT  being  the  ratio  of  the  circumference  to  the  diameter,  g 

2>-/  v    ird" 
the  acceleration  of  gravity. 


232  On  Sound.  [267- 

The  above  formula  expresses  the  following  laws  : — 

I.  The  stretching  weight  or  tension  being  constant,  the  mnnber  of  vibra- 
tions in  a  second  is  inversely  as  the  length. 

II.  The  number  of  vibrations  in  a  second  is  inversely  as  the  diameter  of 
the  string. 

III.  The  number  of  vibrations  in  a  second  is  directly  as  the  square  root  of 
the  stretching  weight  or  tension. 

IV.  The  number  of  vibrations  in  a  second  of  a  string  is  inversely  as  the 
square  root  of  its  density. 

These  laws  are  applied  in  the  construction  of  stringed  instruments,  in 
which  the  length,  diameter,  tension,  and  material  of  the  strings  are  so 
chosen  that  given  notes  may  be  produced  from  them. 

268.  Experimental  verification  of  the  laws  of  the  transverse  vibra- 
tion of  strings. — Law  of  the  lengths.     In  order  to  prove  this   law,  we  may 
call  to  mind  that  the  relative  numbers  of  vibrations  of  the  notes  of  the  gamut 
are 

CDEFGABc 

T  9  J5  4  3  5  15,. 

8  4323  8  Z 

If  now  the  entire  length  of  the  sonometer  be  made  to  vibrate,  and  then,  by 
means  of  the  bridge  B,  the  lengths  f ,  f ,  f,  f ,  f ,  ^  |,  which  are  the  inverse  of 
the  above  numbers,  be  successively  made  to  vibrate,  all  the  notes  of  the 
gamut  are  successively  obtained,  which  proves  the  first  law. 

Law  of  the  diameters.  This  law  is  verified  by  stretching  upon  the  sono- 
meter two  cords  of  the  same  material,  the  diameters  of  which  are  as  3  to  2, 
for  instance.  When  these  are  made  to  vibrate,  the  second  cord  gives  the 
fifth  above  the  other  ;  which  shows  that  it  makes  three  vibrations  while  the 
first  makes  two. 

Law  of  the  tensions.  Having  placed  on  the  sonometer  two  identical 
strings,  they  are  stretched  by  weights  which  are  as  4  :  9.  The  second  now 
gives  the  fifth  of  the  first,  from  which  it  is  concluded  that  the  numbers  of 
their  vibrations  are  as  2  13;  that  is,  as  the  square  roots  of  the  tensions.  If 
the  two  weights  are  as  16  to  25,  the  major  third  or  f  would  be  obtained. 

Law  of  the  densities.  Two  strings  of  the  same  radius,  but  different 
densities,  are  fixed  on  the  sonometer.  Having  been  subjected  to  the  same 
stretching  weight,  the  position  of  the  movable  bridge  on  the  denser  one  is 
altered  until  it  is  in  unison  with  the  other  string.  If  then  d  and  d'  are  the 
densities  of  the  two  strings,  and  /  and  /'  the  lengths  which  vibrate  in  unison, 

we  find  -  =^__:     But  as  we  know  from  the  first  law  that  ^,  =  — ,  we  have 
/      *jd'  I     n 

,=  -r-^,  which  verifies  this  law.     Thus  if  a  copper  wire,  whose  density  is  9, 
n      inj d 

and  a  catgut  string  of  the  density  i,  are  of  equal  length  and  diameter,  and 
are  stretched  by  the  same  weight,  the  vibrations  of  the  copper  wire  will  be 
one-third  as  rapid  as  those  of  the  string. 

269.  Nodes  and  loops.— Let  us  suppose  the  string  AD  (fig.  220)  to  begin 
vibrating,  the  ends  A  and  D  being  fixed,  and  while  it  is  doing  so,  let  a  point 
B  be  brought  to  rest  by  a  stop,  and  let  us  suppose  DB  to  be  one-third  part 
of  AD.    The  part  DB  must  now  vibrate  about  B  and  D  as  fixed  points  in  the 


-270] 


Wind  Instruments. 


233 


manner  indicated  by  the  continuous  and  dotted  lines  (fig.  221)  ;  now  all  parts 
of  the  same  string  tend  to  make  a  vibration  in  the  same  time  ;  accordingly  the 
part  between  A  and  B  will  not  perform  a  single  vibration,  but  will  divide  into 
two  at  the  point  C,  and  vibrate  in  the  manner  shown  in  the  figure.  If  BD 
were  one-fourth  part  of  AD  (fig.  222),  the  part  AD  would  be  subdivided  at 
C  and  C'  into  three  vibrating  portions  each  equal  to  BD.  The  points  B,  C,  C' 
are  called  nodes  or  nodal  points  ;  the  middle  point  of  the  part  of  the  string 
between  any  two  consecutive  nodes  is  called  a  loop  or  ventral  segment.  It 
will  be  remarked  that  the  ratio  of  BD  :  BA  must  be  that  of  some  two  whole 
numbers,  for  example,  i  :  2,  i  :  3,  2  :  3,  &c.,  otherwise  the  nodes  cannot  be 
formed,  since  the  two  portions  of  the  string  cannot  then  be  made  to  vibrate 
.at  the  same  time,  and  the  vibrations  will  interfere  with  and  soon  destroy  one 
another. 

If  now  we  refer  to  fig.  221,  the  existence  of  the  node  at  C  can  be  easily 
proved  by  bending  some  light  pieces  of  paper,  and  placing  them  on  the  string, 
say  three  pieces,  one 

Fig.  221. 

D -  B 

fe 


at  C  and  the  others 
respectively  mid- 
way between  B  and 
C,  and  between  C 
and  A.  The  one  at 
C  experiences  only 
a  very  slight  motion, 
and  remains  in  its 
place,  thereby  prov- 
ing the  existence  of 
a  node  at  C  ;  the 
other  two  are  vio- 
lently shaken,  and 


'      -i 

Fig.   222. 

in  most  cases  thrown  off  the  string. 

When  a  musical  string  vibrates  between  fixed  points  A  and  B,  its  motion 
is  not  quite  so  simple  as  might  be  inferred  from  the  above  description.  In 
point  of  fact,  partial  vibrations  are  soon  produced,  and  superimposed  upon 
the  primary  vibrations.  The  partial  vibrations  correspond  to  the  half,  third, 
fourth,  &c.,  parts  of  the  string.  It  is  by  these  partial  vibrations  that  the 
harmonics  are  produced  which  accompany  the  fundamental  note  due  to  the 
primary  vibrations  ;  they  are  usually,  however,  so  feeble  as  to  be  impercep- 
tible to  ordinary  ears. 

270.  Wind  instruments.— In  the  cases  hitherto  considered,  the  sound 
results 'from  the  vibrations  of  solid  bodies,  and  the  air  only  serves  as  a  vehicle 
for  transmitting  them.     In  wind  instruments,  on  the  contrary,  when  the  s; 
of  the  tube  are  of  adequate  thickness,  the  enclosed  column  of  air  is  the  sound- 
ing body.     In  fact,  the  substance  of  the  tubes  is  without  influence  on  tl 
fundamental  note  ;  with  equal  dimensions,  it  is  the  same  whether  the  tube 
are  of  glass,  of  wood,  or  of  metal.     These  different  materials  simply  do 
more  than  give  rise  to  different  harmonics,  and  thereby  impart  a  d 
-quality  to  the  compound  tone  produced. 

In  reference  to  the  manner  in  which  the  air  in  tubes  is  made  ite, 

wind  instruments  are  divided  into  mouth  instruments  and  reed  instruments. 


234 


On  Sound. 


[271- 


Fig.  223. 


271.  Mouth  instruments. — In  mouth  instruments  all  parts  of  the  mouth- 
piece are  fixed.     Fig.  224  represents  the  mouthpiece  of  an  organ  pipe,  and 

fig.  223  that  of  a  whistle,  or  of  a  flageolet.  In  both 
figures,  the  aperture  ib  is  called  the  mouth ;  it  is 
here  that  air  enters  the  pipe  ;  b  and  o  are  the  lips^ 
the  upper  one  of  which  is  bevelled.  The  mouth- 
piece is  fixed  at  one  end  of  a  tube,  the  other  end  of 
which  may  be  either  opened  or  closed.  In  fig.  224 
the  tube  can  be  fitted  on  a  wind-chest  by  means  oi 
the  foot  P. 

When  a  rapid  current  of  air  enters  by  the  mouth, 
it  strikes  against  the  upper  lip,  and  a  shock  is  pro- 
duced which  causes  the  air  to  issue  from  bo  in  an 
intermittent  manner.  In  this  way,  pulsations  are 
produced  which,  transmitted  to  the  air  in  the  pipe, 
make  it  vibrate,  and  a  sound  is  the  result.  In 
order  that  a  pure  note  may  be  produced,  there  must 
be  a  certain  relation  between  the  form  of  the  lips 
and  the  magnitude  of  the  mouth  ;  the  tube  also 
ought  to  have  a  great  length  in  comparison  with  its  diameter.  The  number 
of  vibrations  depends  in  general  on  the  dimensions  of  the  pipe,  and  the 
velocity  of  the  current  of  air. 

272.  Reed  instruments. — In  reed  instruments  a  simple  elastic  tongue 
sets  the  air  in  vibration.     The  tongue,  which  is  either  of  metal  or  of  wood,  is 
moved  by  a  current  of  air.     The  mouthpieces  of  the  oboe,  the  bassoon,  the 
clarionet,  the  child's  trumpet,  are  different  applications  of  the  reed,  which, 
it  may  be  remarked,  is  seen  in  its  simplest  form  in  the  Jew's  harp.     Some 
organ  pipes  are  reed  pipes,  others  are  mouth  pipes. 

Fig.  225  represents  a  model  of  a  reed  pipe  as  commonly  shown  in 
lectures.  It  is  fixed  on  the  wind-chest  Q  of  a  bellows,  and  the  vibrations  of 
the  reed  can  be  seen  through  a  piece  of  glass,  E,  fitting  into  the  sides.  A 
wooden  horn,  H,  strengthens  the  sound. 

Fig.  226  shows  the  reed,  out  of  the  pipe.  It  consists  of  four  pieces  :  1st, 
a  rectangular  wooden  tube  closed  below  and  open  above  at  o ;  2nd,  a  copper 
plate  cc  forming  one  side  of  the  tube,  and  in  which  there  is  a  longitudinal 
aperture,  through  which  air  passes  from  the  tube  MN  to  the  orifice  o ;  3rd> 
a  thin  elastic  plate,  /',  called  the  tongue,  which  is  fixed  at  its  upper  end,  and 
which  grazes  the  edge  of  the  longitudinal  aperture,  nearly  closing  it ;  4th,  a 
curved  wire,  r,  which  presses  against  the  tongue,  and  can  be  moved  up  and 
down.  It  thus  regulates  the  length  of  the  tongue,  and  determines  the  pitch 
of  the  note.  It  is  by  this  wire  that  reed  pipes  are  tuned.  The  reed  being 
replaced  in  the  pipe  MN,  when  a  current  of  air  enters  by  the  foot  P,  the 
tongue  is  compressed,  it  bends  inwards,  and  affords  a  passage  to  air,  which 
escapes  by  the  orifice  o.  But,  being  elastic,  the  tongue  regains  its  original 
position,  and  performing  a  series  of  oscillations  successively  opens  and  closes 
the  orifice.  In  this  way  sonorous  waves  result  and  produce  a  note,  whose 
pitch  increases  with  the  velocity  of  the  current. 

In  this  reed  the  tongue  vibrates  alternately  before  and  behind  the  aper- 
ture, and  just  escapes  grazing  the  edges,  as  is  seen  in  the  harmonium,  con- 


-274] 


Nodes  and  Loops  of  an  Organ  Pipe. 


235 


certina,  £c.  ;  such  a  reed  is  called  a  free  reed.     But  there  are  other  reeds 
called  beating  or  striking  reeds,  in  which  the  tongue,  which  is  larger  than 
the  orifice,  strikes  against  the  edges  at  each  oscillation.     The  reed  of  the 
clarionet,  represented  in  fig.  227, 
is  an  example  of  this  ;  it  is  kept 
in  its  place  by  the  pressure  of  the 
lips.     The  reeds  of  the  hautboy 
and  bassoon  are  also  of  this  kind. 

273.  Of  the  notes  produced 
by    the     same    pipe. — Daniel 
Bernouilli    discovered   that   the 
same  organ  pipe  can  be  made 
to  yield  a  succession  of  notes  by 
properly  varying  the  force  of  the 
current  of  air.     The  results  he 
arrived  at  may  be  thus  stated  :— 

i.  If  the  pipe  is  open  at  the 
end  opposite  to  the  mouthpiece, 
then,  denoting  the  fundamental 
note  by  i,  we  can,  by  gradually 
increasing  the  force  of  the  cur- 
rent of  air,  obtain  successively 
the  notes  2,  3,  4,  5,  &c.  ;  that  is 
to  say,  the  harmonics  of  the 
primary  note. 

ii.  If  the  pipe  is  closed  at  the 
end  opposite  to  the  mouthpiece, 
then,  denoting  the  fundamental 
note  by  i,  we  can,  by  gradually  increasing  the  force  of  the  current  of  air, 
obtain  successively  the  notes  3,  5,  7,  &c. ;  that  is  to  say,  the  uneven  harmonics 
of  the  primary  note. 

A  closed  and  an  open  pipe  yield  the  same  fundamental  note,  if  the  closed 
pipe  is  half  the  length  of  the  open  pipe,  and  in  other  respects  they  are  the  same. 

In  any  case  it  is  impossible  to  produce  from  the  given  pipe  a  note  not 
included  in  the  above  series  respectively. 

Although  the  above  laws  are  enunciated  with  reference  to  an  organ  pipe, 
they  are  of  course  true  of  any  other  pipe  of  uniform  section. 

274.  On  the  nodes  and  loops  of  an  organ  pipe. — The  vibrations  of 
the  air  producing  a  musical  note  take  place  in  a  direction  parallel  to  the  axis 
of  the  pipe — not  transversely,  as  in  the  case  of  the  portions  of  a  vibrating 
string.     In  the  former  case,  however,  as  well  as  in  the  latter,  the  phenomena 
of  nodes  and  loops  may  be  produced.     But  now  by  a  node  must  be  under- 
stood a  section  of  the  column  of  air  contained  in  the  pipe,  where  the  particles 
remain  at  rest,  but  where  there  are  rapid  alternations  of  condensation  and 
rarefaction.     By  a  loop  or  ventral  segment  must  be  understood  a  section  of 
the  column  of  air  contained  in  the  pipe  where  the  vibrations  of  the  particles 
of  air  have  the  greatest  amplitudes,  and  where  there  is  no  change  of  density. 
The  sections  of  the  column  of  air  are,  of  course,  made  at  right  angles  to  its 
axis.     When  the  column  of  air  is  divided  into  several  vibrating  portions,  it 


Fig.  225. 


Fig.  226. 


Fig.  227. 


236 


On  Sound. 


[274 


is  found  that  the  distance  between  any  two  consecutive  loops  is  constant, 
and  that  it  is  bisected  by  a  node.  We  can  now  consider  separately  the  cases 
of  the  open  and  closed  pipes. 

i.  In  the  case  of  a  stopped  pipe,  the  bottom  is  always  a  node,  for  the 
layer  of  air  in  contact  with  it  is  necessarily  at  rest,  and  only  undergoes 
variations  in  density.  At  the  mouthpiece,  on  the  contrary,  where  the  air  has 
a  constant  density,  that  of  the  atmosphere,  and  the  vibration  is  at  its  maxi- 
mum, there  is  always  a  loop.  In  any  stopped  pipe  there  is  at  least  one  node 
and  one  loop  (fig.  228)  ;  the  pipe  then  yields  its  fundamental  note,  and  the 


f 

Fig.   22 


N 

\ 

\ 

v' 

GT' 

N 

v' 

-- 

N 

T 

y 

T 

V 

g.  229.         Fig.  230. 

f1 


V 


Fig.  231.        Fig.  232.        Fig.  233. 


•distance  VN  from  the  loop  to  the  node  is  equal  to  half  a  condensed  or 
rarefied  wave-length. 

If  the  current  of  air  be  forced,  the  mouthpiece  always  remains  a  loop, 
and  the  bottom  a  node,  the  column  divides  into  three  equal  parts  (fig.  229), 
and  an  intermediate  node  and  loop  are  formed.  The  sound  produced  is  the 
first  harmonic.  When  the  second  harmonic  (5)  is  produced,  there  are  two 
intermediate  nodes  and  two  loops,  and  the  tube  is  then  subdivided  into  five 
•equal  parts  (fig.  230),  and  so  on. 

ii.  In  the  case  of  the  open  pipe,  whatever  note  it  produces,  there  must  be 
a  loop  at  each  end,  since  the  enclosed  column  of  air  is  in  contact  with  the 
external  air  at  those  points.  When  the  primary  note  is  produced,  there  will 
be  a  loop  at  each  end,  and  a  node  at  the  middle  section  of  the  pipe,  the  nodes 
and  loops  dividing  the  column  into  two  equal  parts  (fig.  231).  When  the 
first  harmonic  (2)  is  produced,  there  will  be  a  loop  at  each  end,  and  a  loop 
in  the  middle,  the  column  being  divided  into/0z/r  equal  parts  by  the  alternate 
loops  and  nodes  (fig.  232).  When  the  second  harmonic  (3)  is  produced,  the 
column  of  air  will  be  divided  into  six  equal  parts  by  the  alternate  nodes  and 
loops,  and  so  on  (fig.  233).  It  will  be  remarked  that  the  successive  modes 
of  division  of  the  vibrating  column  are  the  only  ones  compatible  with  the 


274] 


Nodes  and  Loops  of  an  Organ  Pipe. 


237 


alternate  recurrence  at  equal  intervals  of  nodes  and  loops,  and  with  the 
occurrence  of  a  loop  at  each  end  of  the  pipe. 

There  are  several  experiments  by  which  the  existence  of  nodes  and  loops 
can  be  shown. 

(a)  If  a  fine  membrane  is  stretched  over  a  pasteboard  ring,  and  has 
sprinkled  on  it  some  fine  sand,  it  can  be  gradually  let  down  a  tube,  as  shown 
in  fig.  236.  Now  suppose  the  tube  to  be  producing  a  musical  note.  As  the 
membrane  descends,  it  will  be  set  in  vibration  by  the  vibrating  air.  But 
when  it  reaches  a  node  it  will  cease  to  vibrate,  for  there  the  air  is  at  rest 


Fig.  235. 


Fig.  237. 


Consequently  the  grains  of  sand,  too,  will  be  at  rest,  and  their  quiescence 
will  indicate  the  position  of  the  node.  On  the  other  hand,  when  the  mem- 
brane reaches  a  loop— that  is,  a  point  where  the  amplitude  of  the  vibrations 
of  the  air  attains  a  maximum — it  will  be  violently  agitated,  as  will  be  shown 
by  the  agitation  of  the  grains  of  sand.  And  thus  the  positions  of  the  loops 
can  be  rendered  manifest. 

(&}  Again,  suppose  a  pipe  to  be  constructed  with  holes  bored  in  one  of 
its  sides,  and  these  covered  by  little  doors  which  can  be  opened  and  shut,  as 
shown  in  fig.  234.  Let  us  suppose  the  little  doors  to  be  shut  and  the  pipe  to 


238  On  Sound.  [274- 

be  caused  to  produce  such  a  note  that  the  nodes  are  at  N  and  N'  and  the 
loops  at  V,  V,  V".  At  the  latter  points  the  density  is  that  of  the  external 
air,  and  consequently  if  the  door  at  V'  is  opened  no  change  is  produced  in 
the  note.  At  the  former  points,  N  and  N',  condensation  and  rarefaction  are 
alternately  taking  place.  If  now  the  door  at  N'  is  opened,  this  alternation 
of  density  is  no  longer  possible,  for  the  density  at  this  open  point  must  be 
the  same  as  that  of  the  external  air,  and  consequently  N'  becomes  a  loop, 
and  a  note  yielded  by  the  tube  is  changed.  The  change  of  notes,  produced 
by  changing  the  fingering  of  the  flute,  is  one  form  of  this  experiment. 

(c)  Suppose  A,  in  fig.  235,  to  be  a  pipe  emitting  a  certain  note,  and  sup- 
pose P  to  be  a  plug,  fitting  the  tube,  fastened  to  the  end  of  a  long  rod  by 
which  it  can  be  forced  down  the  tube.     Now  when  the  plug  is  inserted, 
whatever  be  its  position,  there  will  be  a  node  in  contact  with  it.     Conse- 
quently, as  it  is  gradually  forced  down,  the  note  yielded  by  the  pipe  will 
keep  on  changing.     But  every  time  it  reaches  a  position  which  was  occupied 
by  a  node  before  its  insertion,   the  note  becomes  the  same  as  the  note 
originally  yielded.     For  now  the  column  of  air  vibrates  in  exactly  the  same 
manner  as  it  did  before  the  plug  was  put  in. 

(d)  Fig.  237  shows  another  mode  of  illustrating  the  same  point,  which  is 
identical  in  principle  with  Konig's  manometric  flames.     The  figure  repre- 
sents an  organ  pipe,  on  one  side  of  which  is  a  chest,  P,  filled  with  coal  gas, 
by  means  of  the  tube  S.     The  gas  from  the  chest  comes  out  in  three  jets,  A, 
B,  C,  and  is  then  ignited.     The  manner  in  which  the  gas  passes  from  the 
chest  to  the  point  of  ignition  is  shown  in  the  smaller  figure,  which  is  an 
enlarged  section  of  A.     A  circular  hole  is  bored  in  the  side  of  the  pipe  and 
covered  with  a  membrane  r.     A  piece  of  wood  is  fitted  into  the  hole  so  as 
to  leave  a  small  space  between  it  and  the  membrane.     The  gas  passes  from 
the  chest,  in  the  direction  indicated  by  the  arrow,  into  the  space  between 
the  membrane  and  the  piece  of  wood,  and  so  out  of  the  tube,  ;;z,  at  the  mouth 
of  which   it  is  ignited.     Now  suppose  the  pipe  to  be  caused  to  yield  its 
primary  note,  then  as  it  is  an  open  pipe  there  ought  to  be  a  node  at  B, 
its  middle  point.     Consequently  there  ought  to  be  rapid  changes  of  density 
at  B  ;  these  would  cause  the  membrane,  r,  to  vibrate,  and  thereby  blow  out 
the  flame,  ?;z,  and  this  is  what  actually  happens.     If  by  increasing  the  forpe 
of  the  wind  the  octave  to  the  primary  note  is  produced,  B  will  be  a  loop, 
and  A  and  C  nodes.     Consequently  the  flames  at  A  and  C  will  now  be  ex- 
tinguished, as  is,  in  point  of  fact,  the  case.     But  at  B,  there  being  no  change 
of  density,  the  membrane  is  unmoved,  and  the  flame  continues  to  burn 
steadily. 

By  each  and  all  of  these  experiments  it  is  shown  that  in  a  given  pipe, 
whether  open  or  closed,  there  are  always  a  certain  number  of  nodes,  and 
midway  between  any  two  consecutive  nodes  there  is  always  a  loop  or  ventral 
segment. 

275.  Formulae  relative  to  the  number  of  vibrations  produced  by  a 
musical  pipe. —  It  follows  from  what  has  been  said  that  the  column  of  air 
<\  in  stopped  pipes  is  always  divided  by  the  nodes  and  loops  into  an  uneven 
number  of  parts  which  are  equal  to  each  other,  and  each  of  which  is  a  quarter 
of  a  complete  vibration  (figs.  228,  229,  and  230),  while  in  an  open  pipe  it  is 
divided  into  an  even  number  of  such  parts  (figs,  231,  232,  233).  If  L  be  the 


-276]  Nodes  and  Loops  in  a  Musical  Pipe.  239 

length  of  the  pipe,  /  the  wave-length  of  the  sound  which  it  emits,  and  p  any 
whole   number,    then   for  stopped   pipes   we   have  L  =  (2/+i)^;    and  for 

/     4)1  ^' 

open  pipes  L  =  2/-  *4±     Replacing  in  each  of  these  formula  /  by  its  value 

I  (253)  we  have  L  .  (2/  +  0J£  and  L-|£  ;  from  which  for  stopped  pipes 

we  have  n  =  £^±112,  and  for  open  ones  «  =  & 
4L  2L* 

If,  in  the  first  formula,  we  give  to/  the  successive  values  o,  i,  2,  3,  4,  &c., 
we  have  »  =  ^  J^,  |^,  that  is,  the  fundamental  sound  and  all  its  uneven 

harmonics  ;  and  in  the  formula  for  the  open  pipe  we  get  similarly^-,  — ,  3^» 

&c.,  that  is,  the  fundamental  note  and  all  its  harmonics  even  and  uneven. 

276.  Explanation  of  the  existence  of  nodes  and  loops  in  a  musical 
pipe — The  existence  of  nodes  and  loops  is  to  be  explained  by  the  co- 
existence in  the  same  pipe  of  two  equal  waves  travelling  in  contrary 
directions. 

Let  A  (fig.  238)  be  a  point  from  which  a  series  of  waves  sets  out  towards 
B,  and  let  the  length  of  these  waves,  whether  of  condensation  or  rarefaction, 


A, 


be  AC,  CD,  DB.  And  let  B  be  the  point  from  which  the  series  of  exactly 
equal  waves  sets  out  towards  A.  It  must  be  borne  in  mind  that  in  the  case 
of  a  wave  of  condensation  originating  at  A  the  particles  move  in  the  direc- 
tion A  to  B,  but  in  a  wave  of  condensation  originating  at  B  they  move  in  the 
direction  B  to  A.  Now  let  us  suppose  that  condensation  at  C,  caused  by  the 
wave  from  A,  begins  at  the  same  instant  that  condensation  caused  by  the 
wave  from  B  begins  at  D.  Consequently,  restricting  our  attention  to  the 
particles  in  the  line  CD,  at  any  instant  the  velocities  of  the  particles  in  CD 
due  to  the  former  wave  will  be  represented  by  the  ordinates  of  the  curve 
SPRT,  while  those  due  to  the  wave  from  B  will  be  represented  by  the  co- 
ordinates of  the  curve  TQrS.  Then,  since  the  waves  travel  with  the  same 
velocity,  and  are  at  C  and  D  respectively  at  the  same  instant,  we  must  have 
for  any  subsequent  instant,  CR  equal  to  Dr.  If,  therefore,  N  is  the  middle 
point  between  C  and  D,  we  must  have  rN  equal  to  RN,  and  consequently 
PN  equal  to  QN  ;  that  is  to  say,  if  the  particle  at  N  transmitted  only  one 
vibration,  its  motion  at  each  instant  would  be  in  the  opposite  phase  to  that 
of  its  motion  if  it  transmitted  only  the  other  vibration.  In  other  words,  the 
particle  N  will  at  every  instant  tend  to  be  moved  with  equal  velocity  in 
opposite  directions  by  the  two  waves,  and  therefore  will  be  permanently  at 
rest.  That  point  is  therefore  a  node.  In  like  manner  there  is  a  node  at  N' 


240  On  Sound.  [276- 

midway  between  A  and  C,  and  also  at  N"  midway  between  B  and  D.  In 
regard  to  the  motion  of  the  remaining  particles,  it  is  plain  that  their  respec- 
tive velocities  will  be  the  (algebraical)  sum  of  the  velocities  they  would  at 
each  instant  receive  from  the  waves  separately.  Hence,  at  the  instant  indi- 
cated by  the  diagram,  they  are  given  by  the  ordinates  of  the  curve  HNK. 
This  curve  will  change  from  instant  to  instant,  and  at  the  end  of  the  time 
occupied  by  the  passage  of  a  wave  of  condensation  (or  of  rarefaction)  from 
C  to  D  will  occupy  the  position  shown  by  the  dotted  line  hNk.  It  is  evident 
therefore  that  particles  near  N  have  but  small  changes  of  velocity,  whilst  those 
near  C  and  D  experience  large  changes  of  velocity. 

If  the  curve  H  K  were  produced  both  ways,  it  would  always  pass  through 
N'  and  N";  the  part,  however,  between  N  and  N'  would  sometimes  be  on 
one  side,  and  sometimes  on  the  other  side  of  AB.  Hence  all  the  particles 
between  N'  and  N  have  simultaneously,  first  a  motion  in  the  direction  A  to 
B,  and  then  a  motion  in  the  direction  B  to  A,  those  particles  near  C  having 
the  greatest  amplitude  of  vibrations.  Accordingly  near  N  and  N'  there  will 
be  alternately  the  greatest  condensation  and  rarefaction. 

This  explanation  applies  to  the  case  in  which  AB  is  the  axis  of  an  open 
organ-pipe,  A  being  the  end  where  the  mouthpiece  is  situated.  The  waves 
from  B  have  their  origin  in  the  reflections  of  the  series  of  waves  from  A.  In 
the  particular  case  considered,  the  note  yielded  by  the  pipe  is  that  indicated 
by  3  ;  that  is,  the  fifth  above  the  octave  to  the  primary  note.  A  similar  ex- 
planation can  obviously  be  applied  to  all  other  cases,  and  whether  the  end 
be  opened  or  closed.  But  in  the  latter  case  the  series  of  waves  from  the 
closed  end  must  commence  at  a  point  distant  from  the  mouthpiece  by  a 
space  equal  to  one  half,  or  three  halves,  or  five  halves,  &c.,  of  the  length  of 
a  wave  of  condensation  or  expansion. 

y  277.  Xundt's  determination  of  the  velocity  of  sound. — Kundt  has 
devised  a  method  of  determining  the  velocity  of  sound  in  solids  and  in 
gases  which  can  be  easily  performed  by  means  of  simple  apparatus,  and  is 
capable  of  great  accuracy.  A  glass  tube,  BB',  about  two  yards  long  (fig.  239) 
and  two  inches  in  internal  diameter,  is  closed  at  one  end  by  a  movable 
stopper,  b  ;  the  other  end  is  fitted  with  a  cork,  KK,  which  tightly  grasps  a 
glass  tube,  AA',  of  smaller  dimensions.  This  is  closed  at  one  end  by  a 
piston,  a,  which  moves  with  gen'le  friction  in  the  outer  tube,  BB'.  Then  by 
rubbing  the  free  end  of  the  tube,  AA',  with  a  wet  cloth,  it  produces  longi- 
tudinal vibrations,  and  these  transmit  their  motion  to  the  air  in  the  tube  ab, 
If  the  tube  ab  contain  some  lycor  odium  powder,  this  is  set  in  active  vibra- 
tion and  then  arranges  itself  in  small  patches  in  a  certain  definite  order  as 
represented  in  the  figure,  the  nature  and  arrangement  of  which  depend  on 
the  vibrating  part  of  the  rod  and  Lhe  tube. 

These  heaps  represent  the  nodes,  and  the  mean  distance  d  between  them 
can  be  measured  with  great  accuracy  ;  it  represents  the  distance  between 
two  nodes,  or,  half  a  wave-length  ;  that  is,  the  wave-length  of  the  sound  in 
air  is  id.  If  the  rod  has  the  length  s  and  Is  grasped  in  the  middle  by  the 
cork  KK,  from  the  law  of  the  longitudinal  vibrations  of  rods  (281),  the  wave- 
length of  the  sound  it  then  emits  is  twice  its  length,  or  2s.  That  is,  the 
wave-length  of  the  vibrating  column  of  air  is  to  that  in  the  rod  as  id :  is. 
As  the  velocity  of  sound  in  any  body  is  equal  to  the  wave-length  in  that 


-278] 


C/iemical  Harmonicon. 


241 


body  multiplied  by  the  number  of  vibrations  in  a  second  ;  and  since  the 
number  of  vibrations  is  here  the  same  in  both  cases,  for  the  note  is  the 
same,  the  velocity  of  sound  in  the  glass  is  to  the  velocity  of 
sound  in  air  as  2sn  :  2dn,  that  is,  as  s  :  d.  Thus  when  the  glass 
tube  was  clamped  in  the  middle  by  KK,  so  that  the  length  ab 
was  equal  to  half  the  length  of  the  tube  AA',  the  number  of  the 
ventral  segments  was  eight.  This  corresponds  to  a  ratio  of 
wave-length  of  i  to  16  ;  in  other  words,  the  velocity  of  sound  in 
glass  is  1  6  times  that  in  air. 

The  method  is  capable  of  great  extension.  By  means  of 
the  stopcock  ;;/,  different  gases  could  be  introduced  instead  of 
air,  and  corresponding  differences  found  for  the  length  of  the 
ventral  segments  ;  from  which,  by  a  simple  calculation,  the  cor- 
responding velocities  were  found.  Thus  the  velocities  of  sound 
in  carbonic  acid,  coal  gas,  and  hydrogen,  were  found  to  be 
respectively  0-8,  r6,  and  3-56  that  of  air,  or  nearly  as  the  inverse 
squares  of  the  densities. 

So  also  by  varying  the  material  of  the  rod  AA',  different 
velocities  are  obtained.  Tfyus  the  velocity  in  steel  was  found  to 
be  15*24,  and  that  in  brass  10-87  that  of  air. 

Kundf's  figures  may  also  be  obtained  by  providing  glass 
tubes  a  yard  or  two  in  length  with  lycopodium  powder,  as  in 
the  above  experiment,  and  hermetically  sealing  them  at  both 
ends.  The  tubes  are  then  put  into  longitudinal  vibrations  ;  in- 
stead of  air  they  may  be  filled  with  hydrogen  or  any  other 


278.  Chemical  harmonicon.  —  The  air  in  an  open  tube 
may  be  made  to  give  a  sound  by  means  of  a  luminous  jet  of 
hydrogen,  coal  gas,  &c.  When  a  glass  tube  about  12  inches 
long  is  held  over  a  lighted  jet  of  hydrogen  (fig.  240),  a  note  is 
produced,  which,  if  the  tube  is  in  a  certain  position,  is  the  funda- 
mental note  of  the  tube.  The  sounds,  doubtless,  arise  from 
the  successive  explosions  produced  by  the  periodic  combina- 
tions of  the  atmospheric  oxygen  with  the  issuing  jet  of  hydrogen. 
The  apparatus  is  called  the  chemical  harmonicon. 

The  note  depends  on  the  size  of  the  flame  and  the  length 
of  the  tube  :  with  a  long  tubez  by  varying  the  position  of  the  jet 
in  the  tube,  the  series  of  notes,  in  the  ratio  I  :  2  ;  3  :  4  :  5  is 
obtained. 

If,  while  the  tube  emits(  a  certain  sound,  the  voice  or  the  syren  (242) 
be  gradually  raised  to  the  .same  height,  as  soon  as  the  note  is  nearly  in 
unison  with  the  harmonicon,  the  flame  becomes  agitated,  jumps  up  and 
down,  and  is  finally  steady  ^when  the  two  sounds  are  in  unison.  If  the 
note  of  the  syren  is  gradually  heightened  the  pulsations  again  commence  ; 
?they  are  the  optical  expressions  of  the  beats  (262)  which  occur  near  perfect 
unison. 

If,  while  the  jet  burns  in  the  tube  and  produces  a  note,  the  position  of 
the  tube  is  slightly  altered,  a  .point  is  reached  at  which  no  sound  is  heard. 
If  now  the  voice,  or  the  syren,  or  the  tuning-fork,  be  pitched  at  the  note 
produced  by  the  jet,  it  begins  to  sing,  and  continues  to  sing  even  after  the 

R 


242 


On  Sound. 


[278- 


syren  is  silent.     A  mere  noise,  or  shouting  at  an  incorrect  pitch,  affects  the 
flame,  but  does  not  cause  it  to  sing. 

These  effects  may  be  conveniently  studied  by  means  of  a  gas-burner., 
over  which,  at  a  distance  of  four  inches,  a  ring  covered  with  fine  wire  gauze 
is  fixed.  The  gas  is  lighted  above  the  gauze,  and  forms  a  very  sensitive 
flame,  especially  when  a  moderately  wide  tube  is  held  over  the  gauze.  If 
the  gauze  is  raised  with  the  tube,  the  flame  becomes  duller  and  smaller,  but 
begins  to  sound  with  a  uniform  loud  tone.  If  now  the  gauze  is  lowered  so- 
that  the  flame  is  just  silent,  it  begins  at  once  when  any  noise  is  made,  but 
ceases  with  the  noise. 

279.  Stringed  instruments. — Stringed  musical  instruments  depend  on. 
the  production  of  transverse  vibrations.  In  some,  such  as  the  piano,  the 
sounds  are  constant,  and  each  note  requires  a  sepa- 
rate string ;  in  others,  such  as  the  violin  and  guitar, 
the  sounds  are  varied  by  the  fingering,  and  can  be 
produced  by  fewer  strings. 

In  the  piano  the  vibrations  of  the  strings  are  pro- 
duced by  the  stroke  of  the  hammer^  which  is  moved 
by  a  series  of  bent  levers  communicating  with  the 
keys.  The  sound  is  strengthened  by  the  vibrations 
of  the  air  in  the  sounding  board  on  which  the  strings 
are  stretched.  Whenever  a  key  is  struck,  a  damper 
is  raised  which  falls  when  the  finger  is  removed  from 
the  key,  and  stops  the  vibrations  of  the  correspond- 
ing string.  By  means  of  a  pedal  all  the  dampers  can 
be  simultaneously  raised,  and  the  vibrations  then 
last  for  some  time. 

The  harp  is  a  sort  of  transition  from  the  instru- 
ments with  constant  to  those  with  variable  sounds. 
Its  strings  correspond  to  the  natural  notes  of  the 
scale  ;  by  means  of  the  pedals  the  lengths  of  the 
vibrating  parts  can  be  changed,  so  as  to  produce 
sharps  and  flats.  The  sound  is  strengthened  by 
the  sounding-box,  and  by  the  vibrations  of  all  the 
strings  harmonic  with  those  played. 

In  the  violin  and  guitar  each  string  can  give  a 
great  number  of  sounds  according  to  the  length  of  the  vibrating  part,  which 
is  determined  by  the  pressure  of  the  fingers  of  the  left  hand  while  the  right 
hand  plays  the  bow,  or  the  strings  themselves.  In  both  these  instruments 
the  vibrations  are  communicated  to  the  upper  face  of  the  sounding  box,  by 
means  of  the  bridge  over  which  the  strings  pass.  These  vibrations  are  com- 
municated from  the  upper  to  the  lower  face  of  the  box,  either  by  the  sides  or 
by  an  intermediate  piece  called  the  sound-post.  The  air  in  the  interior  is 
set  in  vibration  by  both  faces,  and  the  strengthening  of  the  sound  is  produced 
by  all  these  simultaneous  vibrations.  The  value  of  the  instrument  consists 
in  the  perfection  with  which  all  possible  sounds  are  intensified,  which  depends 
essentially  on  the  quality  of  the  wood,  and  the  relative  arrangement  of  the 
parts. 

The  number  and  strength  of  the  harmonics  produced  in  a  twitched  or 


Fig.  240. 


-280]  Wind  Instruments.  243 

stroked  string  varies  with  the  manner  in  which  it  is  sounded  and  with  the 
nature  of  the  string.  The  sharper  the  edge  of  the  exciting  body  the  shorter 
and  broader  are  the  waves,  and  therefore  the  higher  and  stronger  are  the 
harmonics  and  the  shriller  the  clang  ;  if  the  strings  are  struck  with  a  metal 
rod  the  harmonics  are  so  predominant  that  the  fundamental  note  is  scarcely 
heard,  and  thus  what  is  called  an  empty  sound  is  produced.  The  tone  is 
fullest  when  struck  with  the  ringer,  and  somewhat  less  so  with  a  soft  hammer, 
as  in  the  piano.  The  deeper  harmonics  are  often  stronger  than  the  funda- 
mental note,  so  that  the  note  is  not  so  strong  but  is  richer ;  all  the  har- 
monics, whose  nodes  are  in  the  place  struck,  are  wanting.  If  a  string  is  struck 
in  the  middle,  none  of  the  even  harmonics  are  produced,  and  therefore  all  the 
octaves  of  the  fundamental  note  are  wanting ;  the  tone  is  nasal  and  hollow. 
This  is  the  characteristic  of  a  note  which  is  wanting  in  the  harmonics  nearer 
and  most  allied  to  the  fundamental  note.  If  the  string  is  struck  near  one  end, 
the  clang  has  a  jingling  character.  The  piano  is  struck  at  about  one-seventh 
of  the  length  of  the  string  ;  in  this  way  the  seventh  and  ninth  harmonics,  which 
are  unharmonic  with  each  other,  are  deadened,  while  the  deeper  harmonics — 
octaves,  fifths,  thirds — preponderate,  and  the  clang  is  rich  and  harmonious. 
The  higher  harmonics  fade  away  in  gut-strings  more  rapidly  than  with 
metal ;  hence  the  guitar  and  the  harp  are  not  so  jingling  as  the  zither. 

280.  Wind  instruments. — All  wind  instruments  may  be  referred  to  the 
different  types  of  sounding  tubes  which  have  been  described.  In  some,  such 
as  the  organ,  the  notes  are  fixed,  and  require  a  separate  pipe  for  each  note, 
in  others  the  notes  are  variable,  and  are  produced  by  only  one  tube  :  the 
flute,  horn,  &c.,  are  of  this  class. 

In  the  organ  the  pipes  are  of  various  kinds  ;  namely,  mouth  pipes,  open 
and  stopped,  and  reed  pipes  with  apertures  of  various  shapes.  By  means  of 
stops  the  organist  can  produce  any  note  by  both  kinds  of  pipe. 

In  they^te,  the  mouthpiece  consists  of  a  simple  lateral  circular  aperture  ; 
the  current  of  air  is  directed  by  means  of  the  lips,  so  that  it  grazes  the  edge 
of  the  aperture.  The  holes  at  different  distances  are  closed  either  by  the 
fingers  or  by  keys  ;  when  one  of  the  holes  is  opened,  a  loop  is  produced  in 
the  corresponding  layer  of  air,  which  modifies  the  distribution  of  nodes  and 
loops  in  the  interior,  and  thus  alters  the  note.  The  whistling  of  a  key  is 
similarly  produced. 

The  pandcean  pipe  consists  of  tubes  of  different  sizes  corresponding  to  the 
different  notes  of  the  gamut. 

In  the  trumpet,  the  horn,  the  trombone,  cornet-a-piston,  and  ophicleide, 
the  lips  form  the  reed,  and  vibrate  in  the  mouthpiece.  In  the  horn,  different 
notes  are  produced  by  altering  the  distance  of  the  lips.  In  the  trombone, 
one  part  of  the  tube  slides  within  the  other,  and  the  performer  can  alter 
at  will  the  length  of  the  tube,  and  thus  produce  higher  or  lower  notes.  In 
the  cornet-a-piston  the  tube  forms  several  convolutions  ;  pistons  placed  at 
different  distances  can,  when  played,  cut  off  communication  with  other  parts 
of  the  tube,  and  thus  alter  the  length  of  the  vibrating  column  of  air. 


R  2 


244 


On  Sound. 


[281- 


CHAPTER   V. 

VIBRATION   OF   RODS,    PLATES,   AND   MEMBRANES. 

281.  Vibration  of  rods. — Rods  and  narrow  plates  of  wood,  of  glass, 
and  especially  of  tempered  steel,  vibrate  in  virtue  of  their  elasticity  ;  like 
strings  they  have  two  kinds  of  vibrations,  longitudinal  and  transverse.  The 
latter  are  produced  by  fixing  the  rods  at  one  end,  and  passing  a  bow 
over  the  free  part.  Longitudinal  vibrations  are  produced  by  fixing  the 
rod  at  any  part,  and  rubbing  it  lengthwise  with  a  piece  of  cloth  sprinkled 

with  resin.  But  in  the  latter  case 
the  sound  is  only  produced  when 
the  point  of  the  rod  at  which  it 
has  been  fixed  is  some  aliquot  part 
of  its  length,  as  a  half,  a  third,  or  a 
quarter. 

It  is  shown  by  calculation  that 
the  number  of  transverse  vibratio?is 
made  in  a  given  time  by  rods  and 
thin  plates  of  the  same  kind  is 
directly  as  their  thickness  and  in- 
versely as  the  square  of  their  length. 
The  width  of  the  plate  does  not 
affect  the  number  of  vibrations.  A 
wide  plate,  however,  requires  a 
greater  force  to  set  it  in  motion  than 
a  narrow  one.  It  is,  of  course,  under- 
stood that  one  end  of  the  vibrating 
plate  is  held  firmly. 

The  laws  of  the  longitudinal  vi- 
brations of  strings  are  expressed  in 


the  formula  n  = 


in  which 


»,  r,  /,  d,  and  g  have  all  the  same 
meaning  as  in  the  formula  for  the 
transverse  vibrations,  while  p.  is  the 
Fis-  24i.  modulus  of  elasticity  of  the  string, 

the  number  which   expresses   the 

weight   by  which   it   must  be   stretched   in  order  to  elongate  by  its  own 

length  (88). 

Fig.  241  represents  an  instrument  invented  by  Marloye,  and  known  as 

MarloyJs  harp^  based  on  the  longitudinal  vibration  of  rods.     It  consists  of 

a  solid  wooden  pedestal,  in  which  are  fixed  twenty  thin   deal  rods,  some 


-282]  Vibration  of  Plates.  24$ 

coloured  and  others  white.  They  are  of  such  a  length  that  the  white  rods 
give  the  diatonic  scale,  while  the  coloured  ones  give  the  semitones  and 
complete  the  chromatic  scale.  The  instrument  is  played  by  rubbing  the 
rods  in  the  direction  of  their  length  between  the  ringer  and  thumb,  which 
have  been  previously  covered  with  powdered  resin.  The  notes  produced 
resemble  those  of  a  pandaean  pipe. 

The  tuning-fork,  the  triangle,  and  musical  boxes,  are  examples  of  the 
transverse  vibrations  of  rods.  In  musical  boxes  small  plates  of  steel  of 
different  dimensions  are  fixed  on  a  rod,  like  the  teeth  of  a  comb.  A  cylinder 
whose  axis  is  parallel  to  this  rod,  and  whose  surface  is  studded  with  steel 
teeth,  arranged  in  a  certain  order,  is  placed  near  the  plates.  By  means  of 
a  clockwork  motion,  the  cylinder  rotates,  and  the  teeth  striking  the  steel 
plate  set  them  in  vibration,  producing  a  tune,  which  depends  on  the  arrange- 
ment of  the  teeth  on  the  cylinder. 

If  a  given  rod  be  clamped  either  in  the  middle,  or  at  both  ends,  the 
wave-length  of  the  note  produced  by  making  it  vibrate  longitudinally  is 
double  its  own  length  ;  and  if  it  be  clamped  at  one  end  only,  and  made  to 
vibrate  longitudinally,  the  wave-length  of  the  sound  is  four  times  its  own 
length.  Thus  the  former  case  is  analogous  to  an  open  pipe,  and  the  latter  to 
a  stopped  pipe,  in  respect  of  the  sounds  produced. 

Chladni  determined  the  velocity  of  sound  in  solids  by  making  a  rod 
clamped  at  one  end  vibrate  longitudinally,  and  producing  the  same  note 
by  sounding  a  stopped  pipe.  The  lengths  of  the  rod  and  the  pipe  are  thus 
in  the  same  ratio  as  the  velocities  in  sound  and  in  air. 

Stefan  has  determined  the  velocity  of  sound  in  soft  bodies  by  attaching 
them,  in  the  form  of  rods,  to  long  glass  or  wooden  rods.  The  compound 
rod  was  made  to  vibrate  and  the  number  of  vibrations  of  the  note  was  de- 
termined. Knowing  this  and  also  the  velocity  of  sound  in  the  longer  rod, 
the  velocity  in  the  shorter  rod  was  at  once  obtained.  By  this  method  some 
of  the  numbers  in  the  table  in  article  235  were  obtained. 

Scratching  and  scraping  sounds  are  produced  by  moving  a  rod  over  a 
smooth  surface ;  the  rod  is  thereby  put  in  vibration,  which  vibrations  for 
a  short  interval  are  regular,  but  frequently  change  their  period  during  the 
motion. 

282.  Vibration  of  plates. — In  order  to  make  a  plate  vibrate,  it  is  fixed 
in  the  centre  (fig.  242),  and  a  bow  rapidly  drawn  across  one  of  the  edges  ; 
or  else  it  is  fixed  at  any  point  of  its  surface,  and  caused  to  vibrate  by 
rapidly  drawing  a  string  covered  with  resin  against  the  edges  of  a  central 
hole  (fig.  243). 

Vibrating  plates  contain  nodal  lines  (269),  which  vary  in  number  and 
position  according  to  the  form  of  the  plates,  their  elasticity,  the  mode  of 
excitation,  and  the  number  of  vibrations.  These  nodal  lines  may  be  made 
visible  by  covering  the  plate  with  fine  sand,  before  it  is  made  to  vibrate. 
As  soon  as  the  vibrations  commence,  the  sand  leaves  the  vibrating  parts, 
and  accumulates  on  the  nodal  lines,  as  seen  in  figs.  242  and  243. 

The  position  of  the  nodal  lines  may  be  determined  by  touching  the 
points  at  which  it  is  desired  to  produce  them.  Their  number  increases  with 
the  number  of  vibrations  ;  that  is,  as  the  note  given  by  the  plates  is  higher. 
The  nodal  lines  always  possess  great  symmetry  of  form  and  the  same  form 


246 


On  Sound.  [282- 

under  the  same  conditions.     They 


is  always  produced  on  the  same  plate 
were  discovered  by  Chladni. 

The  vibrations  of  plates  are  governed  by  the  following  law  : — In  plates 
of  the  same  kind  and  shape,  and  giving  the  same  system  of  nodal  lines,  the 
number  of  vibrations  z;z  a  second  is  directly  as  the  thickness  of  the  plates,  and 
inversely  as  their  area. 


Fig.  242. 


Fig.  243. 


Gongs  and  cymbals  are  examples  of  instruments  in  which  sounds  are 
produced  by  the  vibration  of  metal  plates.  The  glass  and  the  steel  harmo- 
nicon  depend  on  the  vibrations  of  glass  and  of  steel  plates  respectively. 

283.*  Vibration  of  membranes. — In  consequence  of  their  flexibility, 
membranes  cannot  vibrate  unless  they  are  stretched,  like  the  skin  of  a  drum. 
The  sound  they  give  is  more  acute  in  proportion  as  they  are  smaller  and 


Fig.  244. 

more  tightly  stretched.     To  obtain  vibrating  membranes,  Savart  fastened 
gold-beater's  skin  on  wooden  frames. 

In  the  drum,  the  skins  are  stretched  on  the  ends  of  a  cylindrical  box. 
When  one  end  is  struck,  it  communicates  its  vibrations  to  the  internal 
column  of  air,  and  the  sound  is  thus  considerably  strengthened.  The  cords 
stretched  against  the  lower  skin  strike  against  it  when  it  vibrates,  and  pro- 
duce the  sound  characteristic  of  the  drum. 


-283]  Vibration  of  Membranes.  247 

Membranes  either  vibrate  by  direct  percussion,  as  in  the  drum,  or  they 
may  be  set  in  vibration  by  the  vibrations  of  the  air,  as  Savart  has  observed, 
provided  these  vibrations  are  sufficiently  intense.  Fig.  244  shows  a  mem- 
brane vibrating  under  the  influence  of  the  vibrations  in  the  air  caused  by 
a  sounding  bell.  Fine  sand  strewn  on  the  membrane  shows  the  formation 
of  nodal  lines  just  .as  upon  plates. 

There  are  numerous  instances  in  which  solid  bodies  are  set  in  vibration 
by  the  vibrations  of  the  air.  The  condition  most  favourable  for  the  produc- 
tion of  this  phenomenon  is,  that  the  body  to  be  set  in  vibration  is  under 
such  conditions  that  it  can  readily  produce  vibrations  of  the  same  duration 
as  those  transmitted  to  it  by  the  air.  The  following  are  some  of  these 
phenomena  : 

If  two  violoncello  strings  tuned  in  unison  are  stretched  on  the  same 
sound-box,  as  soon  as  one  of  them  is  sounded,  the  other  is  set  in  vibration. 
This  is  also  the  case  if  the  interval  of  the  strings  is  an  octave,  or  a  perfect 
fifth.  A  violin  string  may  also  be  made  to  vibrate  by  sounding  a  tuning- 
fork. 

Two  large  glasses  are  taken  of  the  same  shape,  and  as  nearly  as  possible 
of  the  same  dimensions  and  weight,  and  are  brought  in  unison  by  pouring 
into  them  proper  quantities  of  water.  If  now  one  of  them  is  sounded,  the 
other  begins  to  vibrate,  even  if  it  is  at  some  distance  ;  but  if  water  be  added 
to  the  latter,  it  ceases  to  vibrate. 

Breguet  found  that  if  two  clocks,  whose  time  was  not  very  different, 
were  fixed  on  the  same  metallic  support,  they  soon  attained  exactly  the  same 
time. 

Membranes  are  eminently  fitted  for  taking  up  the  vibrations  of  the  air, 
on  account  of  their  small  mass,  their  large  surface,  and  the  readiness  with 
which  they  subdivide.  With  a  pretty  strong  whistle,  nodal  lines  may  be 
produced  in  a  membrane  stretched  on  a  frame,  even  at  the  distant  end  of  a 
large  room. 

The  phenomenon  so  easily  produced  in  easily-moved  bodies  is  also  found 
in  larger  and  less  elastic  masses  ;  all  the  pillars  and  walls  of  a  church  vibrate 
anore  or  less  while  the  bells  are  being  rung. 


248 


On  Sound. 


[284- 


CHAPTER  VI. 

GRAPHICAL   METHOD   OF  STUDYING  VIBRATORY  MOTIONS. 

284.  Xiissajous'  method  of  making  vibrations  apparent. — The  method 
of  Lissajous  exhibits  the  vibratory  motion  of  bodies  either  directly  or  by 
projection  on  a  screen.  It  has  also  the  great  advantage  that  the  vibratory 
motions  of  two  sounding  bodies  may  be  compared  without  the  aid  of  the  ear, 
so  as  to  obtain  the  exact  relation  between  them. 

This  method,  which  depends  on  the  persistence  of  visual  sensations  on 
the  retina,  consists  in  fixing  a  small  mirror  on  the  vibrating  body,  so  as  to 
vibrate  with  it,  and  impart  to  a  luminous  ray  a  vibratory  motion  similar  to 
its  own. 

Lissajous  uses  tuning-forks,  and  fixes  to  one  of  the  prongs  a  small 
metallic  mirror,  m  (fig.  245),  and  to  the  other  a  counterpoise,  ;/,  which  is 


•/\AMt 


i 


Fig.  245. 

necessary  to  make  the  tuning-fork  vibrate  regularly  for  a  long  time.  At  a 
few  yards'  distance  from  the  mirror  there  is  a  lamp  surrounded  by  a  dark 
chimney,  in  which  is  a  small  hole  giving  a  single  luminous  point.  The 
tuning-fork  being  at  rest,  the  eye  is  placed  so  that  the  luminous  point  is  seen 
at  o.  The  tuning-fork  is  then  made  to  vibrate,  and  the  image  elongates  so 
as  to  form  a  persistent  image,  <#,  which  diminishes  in  proportion  as  the 


loDJ 


Combination  of  two  Vibratory  Motions. 


amplitude  of  the  oscillation  decreases.  If,  during  the  oscillation  of  the 
mirror,  it  is  made  to  rotate  by  rotating  the  tuning-fork  on  its  axis,  a  sinuous 
line,  otx,  is  produced  instead  of  the  straight  line  oi.  These  different  effects 
are  explained  by  the  successive  displacements  of  the  luminous  pencil  and 
by  the  duration  of  these  luminous  impressions  on  the  eye  after  the  cause 
has  ceased—  a  phenomenon  to  which  we  shall  revert  in  treating  ot 
vision. 

If  instead  of  viewing   these  effects  directly,  they  are  projected  on  a 
screen,  the  experiment  is  arranged  as  shown  in  fig.  246,  the  pencil  reflected 


Fig.  246. 


from  the  vibrating  mirror  is  reflected  a  second  time  from  the  fixed  mirror, ;;/, 
which  sends  it  towards  an  achromatic  lens,  /,  placed  so  as  to  project  the 
images  on  the  screen. 

285.   Combination  of  two  vibratory  motions  in  the  same  direction. — 

Lissajous  resolved  the  problem  of  the  optical  combination  of  two  vibratory 
motions — vibrating  at  first  in  the  same  direction,  and  then  at  right  angles  to 
each  other. 

Fig.  247  represents  the  experiment  as  arranged  for  combining  two 
parallel  motions.  Two  tuning-forks  provided  with  mirrors  are  so  arranged 
that  the  light  reflected  from  one  of  them  reaches  the  other,  which  is  almost 
parallel  to  it,  and  is  then  sent  towards  a  screen  after  having  passed  through 
a  lens. 

If  now  the  first  tuning-fork  alone  vibrates,  the  image  on  the  screen  is 
the  same  as  in  figure  247  ;  but  if  they  both  vibrate,  supposing  they  are  in 
unison,  the  elongation  increases  or  diminishes  according  as  the  simultaneous 
motions  imparted  to  the  image  by  the  vibrations  of  the  mirrors  do  or  do  not 
coincide. 


250 


On  Sound. 


[285- 


If  the  tuning-forks  pass  their  position  of  equilibrium  in  the  same  time 
and  in  the  same  direction,  the  image  attains  its  maximum  ;  and  the  image 
is  at  its  minimum  when  they  pass  at  the  same  time  but  in  opposite  direc- 
tions. Between  these  two  extreme  cases,  the  amplitude  of  the  image  varies 
according  to  the  time  which  elapses  between  the  exact  instant  at  which  the 
tuning-forks  pass  through  their  position  of  rest  respectively.  The  ratio  of 


Fig.  247. 

this  time  to  the  time  of  a  double  vibration  is  called  a  difference  of  phase  of 
the  vibration. 

If  the  tuning-forks  are  exactly  in  unison,  the  luminous  appearance  on  the 
screen  experiences  a  gradual  diminution  of  length  in  proportion  as  the  ampli- 
tude of  the  vibration  diminishes  ;  but  if  the  pitch  of  one  is  very  little  altered, 
the  magnitude  of  the  image  varies  periodically,  and,  while  the  beats  resulting 


Fig.  248. 

from  the  imperfect  harmony  are  distinctly  heard,  the  eye  sees  the  concomi- 
tant pulsations  of  the  image. 

286.  Optical  combination  of  two  vibratory  motions  at  right  angles 
to  each  other. — The  optical  combination  of  two  rectangular  vibratory 
motions  is  effected  as  shown  in  figure  248  ;  that  is,  by  means  of  two  tuning- 
forks,  one- of  which  is  horizontal  and  the  other  vertical,  and  both  provided 


-286]  Optical  Combination  of  Vibratory  Motions.  251 

with  mirrors.  If  the  horizontal  fork  first  vibrates  alone,  a  horizontal  luminous 
outline  is  seen  on  the  screen,  while  the  vibration  of  the  other  produces 
a  vertical  image.  If  both  tuning-forks  vibrate  simultaneously,  the  two  mo- 
tions combine,  and  the  reflected  pencil  describes  a  more  or  less  complex 
curve,  the  form  of  which  depends  on  the  number  of  vibrations  of  the  two 
tuning-forks  in  a  given  time.  This  curve  gives  a  valuable  means  of  com- 
paring the  number  of  vibrations  of  two  sounding  bodies. 


Fig.  249. 

Fig.  249  shows  the  luminous  image  on  the  screen  when  the  tuning-forks 
are  in  unison  ;  that  is,  when  the  number  of  vibrations  is  equal. 

The  fractions  below  each  curve  indicate  the  differences  of  phase  between 
them.  The  initial  form  of  the  curve  is  determined  by  the  difference  of  phase. 
The  curve  retains  exactly  the  .same  form  when  the  tuning  forks  are  in  unison, 
provided  that  the  amplitudes  of  the  two  rectangular  vibrations  decrease  in 
the  same  ratio. 


Fig.  250. 


If  the  tuning-forks  are  not  quite  in  unison,  the  initial  difference  of  phase 
is  not  preserved,  and  the  curve  passes  through  all  its  variations. 

Fig.  250  represents  the  different  appearances  of  the  luminous  image 
when  the  difference  between  the  tuning-forks  is  an  octave  ;  that  is,  when  the 


252 


On  Sound. 


[286- 


numbers'of  their  vibrations  are  as  i  :  2  ;  and  fig.  251  gives  the  series  of  curves 
when  the  numbers  of  the  vibrations  are  as  3  :  4. 

It  will  be  seen  that  the  curves  are  more  complex  when  the  ratios  of  the 


numbers  of  vibrations  are  less  simple.     Lissajous  examined  these  curves 
theoretically,  and  has  calculated  their  general  equations. 

When   these   experiments  are  made  with  the  electric  light  instead  of 
an  ordinary  lamp,  the  phenomena  are  remarkably  brilliant. 


Fig.  252. 

287.  3Leon  Scott's  P  fa  on  auto  graph. — This  apparatus  registers  not  only 
the  vibrations  produced  by  solid  bodies  but  also  those  produced  by  wind 
instruments,  by  the  voice  in  singing,  and  even  by  any  noise  whatsoever ;  for 


-287] 


The  Phonautograph. 


253 


instance,  that  of  thunder,  or  the  report  of  a  cannon.  It  consists  of  an  ellip- 
soidal barrel,  AB,  about  a  foot  and  a  half  long  and  a  foot  in  its  greatest 
diameter,  made  of  plaster  of  Paris.  The  end  A  is  open,  but  the  end  B  is 
closed  by  a  solid  bottom,  to  the  middle  of  which  is  fixed  a  brass  tube  #,  bent 
at  an  elbow  and  terminated  by  a  ring  on  which  is  fixed  a  flexible  membrane 
which  by  means  of  a  second  ring  can  be  stretched  to  the  required  amount. 
Near  the  centre  of  the  membrane,  fixed  by  sealing-wax,  is  a  hog's  bristle, 
which  acts  as  a  style,  and,  of  course,  shares  the  movements  of  the  membrane. 
In  order  that  the  style  shall  not  be  at  a  node,  the  stretching  ring  is  fitted 
with  a  movable  piece,  /,  or  subdivider,  which,  being  made  to  touch  the 
membrane  first  at  one  point  and  then  at  another,  enables  the  experimenter 
to  alter  the  arrangements  of  the  nodal  lines  at  will.  By  means  of  the  sub- 
divider  the  point  is  made  to  coincide  with  a  loop ;  that  is,  a  point  where  the 
vibrations  of  the  membrane  are  at  a  maximum. 

When  a  sound  is  produced  near  the  apparatus,  the  air  in  the  ellipsoid, 
the  membrane,  and  the  style  will  vibrate  in  unison  with  it,  and  it  only 
remains  to  trace  on  a  sensitive  surface  the  vibrations  of  the  style,  and  to 
fix  them.  For  this  purpose  there  is  placed  in  front  of  the  membrane  a  brass 
cylinder,  C,  turning  round  a  horizontal  axis  by  means  of  a  handle,  m.  On 


Fig.  253. 


Fig-  254- 


Fig.  255. 

the  prolonged  axis  of  the  cylinder  a  screw  is  cut  which  works  in  a  nut ; 
consequently,  when  the  handle  is  turned,  the  cylinder  gradually  advances 
in  the  direction  of  its  axis.  Round  the  cylinder  is  wrapped  a  sheet  of  paper 
covered  with  a  thin  layer  of  lampblack. 

The  apparatus  is  used  by  bringing  the  prepared  paper  into  contact  with  the 
point  of  the  style,  and  then  setting  the  cylinder  in  motion  round  its  axis.  So 
long  as  no  sound  is  heard  the  style  remains  at  rest,  and  merely  removes  the 
lampblack  along  a  line  which  is  a  helix  on  the  cylinder,  but  which  becomes 
straight  when  the  paper  is  unwrapped.  But  when  a  sound  is  heard,  the 
membrane  and  the  style  vibrate  in  unison,  and  the  line  traced  out  is  no 
longer  straight,  but  undulates ;  each  undulation  corresponding  to  a  double 


254  On  Sound.  [287- 

vibration  of  the  style.     Consequently  the  figures  thus  obtained  faithfully 
denote  the  number,  amplitude,  and  isochronism  of  the  vibrations. 

Fig.  253  shows  the  trace  produced  when  a  simple  note  is  sung,  and 
strengthened  by  means  of  an  upper  octave.  The  latter  note  is  represented 
by  the  curve  of  lesser  amplitude.  Fig.  254  represents  the  sound  produced 
jointly  by  two  pipes  whose  notes  differ  by  an  octave.  The  lower  line  of  fig. 

2 55  represents  the  rolling  sound  of  the  letter  R  when  pronounced  with  a 
ring. 

The  upper  line  of  fig.  255  represents  the  perfectly  isochronous  vibrations 
of  a  tuning-fork  placed  near  the  ellipsoid.  This  line  was  traced  by  a  fine 
point  on  one  branch  of  the  fork,  which  was  thus  found  to  make  exactly  500 
vibrations  per  second.  Hence,  each  undulation  of  the  upper  line  corresponds 
to  the  ~  part  of  a  second  ;  and  thus  these  lines  become  very  exact  means 
of  measuring  short  intervals  of  time.  For  example,  in  fig.  255  each  of  the 
separate  shocks  producing  the  rolling  sound  of  the  letter  R  corresponds  to 
about  1 8  double  vibrations  of  the  tuning-fork,  and  consequently  lasts  about 
_i_8_  or  about  ^  of  a  second. 

288.  Xonigs  manometric  flames. — Konig's  method  consists  in  trans- 
mitting the  motion  of  the  waves  which  form  a  sound  to  gas  flames,  which, 
by  their  pulsations,  indicate  the  nature  of  the  sounds.  For  this  purpose  a 


Fig.  256. 


metal  capsule,  represented  in  section  at  A,  fig.  256,  is  divided  into  two  com- 
partments by  a  thin  membrane  of  caoutchouc  ;  on  the  right  of  the  figure 
is  a  gas  jet,  and  below  it  a  tube  conveying  coal  gas  ;  on  the  left  is  a  tubu- 
lure,  to  which  may  be  attached  a  caoutchouc  tube.  The  other  end  of  this 


-288] 


Konigs  Manometric  Flames. 


may  be  placed  at  the  node  of  an  organ-pipe  (274),  or  it  terminates  in  a 
mouthpiece,  in  front  of  which  a  given  note  may  be  sung  ;  this  is  the  arrange- 
ment represented  in  fig.  256. 

Fig.  257. 


Fig.  258. 

When  the  sound-waves  enter  the  capsule  by  the  mouthpiece  and  the 
tube,  the  membrane  yielding  to  the  condensation  and  rarefaction  of  the 
waves,  the  coal  gas  in  the  compartment  on  the  right  is  alternately  contracted 
and  expanded,  and  hence  are  produced  alternations  in  the  length  of  the 

Fig.  259. 


Fig.  260. 


flame,  which  are,  however,  scarcely  perceptible  when  the  flame  is  observed 
directly.  But  to  render  them  distinct  they  are  received  on  a  mirror  with 
four  faces,  M,  which  may  be  turned  by  two  cog-wheels  and  a  handle.  As 


On  Sound.  [288- 

long  as  the  flame  burns  steadily  there  appears  in  the  mirror,  when  turned,  a 
continuous  band  of  light.  But  if  the  capsule  is  connected  with  a  sounding 
tube  yielding  the  fundamental  note,  the  image  of  the  flame  takes  the  form 
represented  in  fig.  257,  and  that  of  the  figure  258  if  the  sound  yields  the 
octave.  If  the  two  sounds  reach  the  capsule  simultaneously,  the  flame  has 
the  appearance  of  fig.  259  ;  in  that  case,  however,  the  tube  leading  to  the 
capsule  must  be  connected  by  a  T-pipe  with  two  sounding-tubes,  one  giving 
the  fundamental  note,  and  the  other  the  octave.  If  one  gives  the  funda- 
mental note  and  the  other  the  third,  the  flame  has  the  appearance  of  figure 
260. 

If  the  vowel  E  be  sung  in  front  of  the  mouthpiece  first  upon  <r,  and  then 

Fig.  261. 


Fig.  262. 

upon  c\  the  rotating  mirror  gives  the  flames  represented  in  figs.  261  and 
262. 

289.  Determination  of  the  intensity  of  sounds. — Meyer  has  devised 
a  plan  by  which  the  intensities  of  two  sounds  of  the  same  pitch  may  be 
directly  compared.  The  two  sounds  are  separated  from  each  other  by  a 
medium  impervious  to  sound,  and  in  front  of  each  of  them  is  a  resonance 
globe  (255)  accurately  tuned  to  the  sound.  Each  of  these  resonance  globes 
is  attached  by  means  of  caoutchouc  tubes  of  equal  length  to  the  two  ends  of 
a  U  tube,  in  the  middle  of  the  bend  of  which  is  a  third  tube  provided  with  a 
inanometric  capsule. 

If  the  resonance  globes  are  each  at  the  same  distance  from  the  sounding 
bodies,  and  if  the  note  of  only  one  of  them  is  produced,  the  flame  vibrates. 
If  both  sounds  are  produced,  and  they  are  of  the  same  intensity,  and  in  the 
same  phase,  they  interfere  completely  in  the  tube,  so  that  the  flame  of  the 
inanometric  capsule  is  quite  stationary,  and  appears  in  the  turning  mirror  as 
a  straight  luminous  band. 

If,  however,  the  sounds  are  not  of  the  same  intensity,  the  interference 
will  be  incomplete,  and  the  luminous  band  will  be  jagged  at  the  edge.  The 


-291]  Edison's  Phonograph.  2 $7 

distance  of  one  of  the  sounds  from  the  resonance  globes  is  altered  until  the 
flame  is  stationary.  The  intensities  of  the  two  sounds  are  thus  directly  as 
the  squares  of  their  distances  from  the  resonators. 

290.  Acoustic  attraction  and  repulsion. — It  was  observed  by  Guyot, 
and  afterwards  independently  by  Guthrie  and  by  Schellbach,  that  a  sound- 
ing body,  one  in  a  state  of  vibration   therefore,  exercises  an  action  on  a 
body  in  its  neighbourhood  which  is  sometimes  one  of  attraction  and  some- 
times of  repulsion.     The  vibrations  of  an  elastic  medium  attract  bodies 
which  are  specifically  heavier  than  itself,  and  repel  those  which  are  specific- 
ally lighter.     Thus  a  balloon  of  goldbeater's  skin  filled  with  carbonic  acid 
is  attracted  towards  the  opening  of  a  resonance-box  on  which  is  a  vibrating 
tuning-fork  ;  while  a  similar  balloon  filled  with  hydrogen  and  tied  down  by 
a  thread  is  repelled.     This  result  always  follows,  even  when  the  hydrogen 
balloon  is  made  heavier  than  air  by  loading  it  with  wax. 

A  light  piece  of  cardboard  suspended  and  held  near  a  tuning-fork  moves 
towards  it  when  the  fork  is  made  to  vibrate.  If  the  tuning-fork  is  suspended 
and  is  then  made  to  vibrate,  it  moves  towards  the  card  if  the  latter  is  fixed. 
Two  suspended  tuning-forks  in  a  state  of  vibration  move  towards  each 
other.  The  flame  of  a  candle  placed  near  the  end  of  a  sounding  tuning- 
fork  was  repelled  if  held  near  it ;  if  held  underneath  it  was  flattened  out 
to  a  disc.  A  gas  flame  near  the  end  of  the  tuning-fork  was  divided  into  two 
arms. 

Guthrie  finds  that  when  one  prong  of  a  tuning-fork  is  inclosed  in  a  tube 
provided  with  a  capillary  tube  dipping  into  a  liquid  and  is  set  in  vibration 
by  bowing  the  free  prong,  the  air  around  the  enclosed  prong  is  expanded, 
and  he  thence  concludes  that  the  approach,  above  described,  of  a  suspended 
body  to  the  sounding-fork,  is  due  to  the  diminution  of  the  pressure  of  the 
air  between  the  fork  and  the  body  below  that  on  the  other  side  of  the 
body. 

Light  resonators  of  glass  or  metal  are  repelled  when  brought  near  the 
sounding-box  of  a  tuning-fork,  vibrating  in  unison  with  the  resonators. 
When  a  small  mill  with  four  arms,  each  provided  with  a  small  resonator,  is 
placed  near  the  open  end  of  the  sounding-box,  the  repulsion  is  so  strong  as 
to  produce  a  uniform  rotation. 

These  phenomena  do  not  seem  to  be  due  to  the  aspirating  action  of  cur- 
rents of  air,  nor  are  they  caused  by  any  heating  effect ;  and  it  must  be  con- 
fessed that  the  phenomena  require  further  elucidation  ;  they  are  of  special 
interest  as  furnishing  a  possible  clue  to  the  solution  of  the  problem  of  attrac- 
tion in  general. 

291.  Edison's  Phonograph. — Edison  has  devised  an  apparatus  for  repro- 
ducing sound,  which  is  equally  remarkable  for  the  simplicity  of  its  construc- 
tion and  for  the  striking  character  of  the  results  which  it  produces. 

Fig.  263  represents  a  mouthpiece  E,  which  is  closed  by  a  thin  elastic 
metallise.  By  means  of  a  spring  a  small  steel  point,  rounded  at  the  end,  is 
fixed,  at  the  back  of  the  disc  ;  this  point  gently  presses  against  the  surface 
of  tinfoil,  to  which  it  transfers  the  vibrations  of  the  disc  by  the  intervention 
of  small  pieces  of  india-rubber  tubing.  Another  small  piece  of  tubing  helps 
to  deaden  the  vibrations  of  the  spring  itself.  This  arrangement  is  repre- 
sented on  a  larger  scale  in  fig.  264. 

S 


258 


On  Sound. 


[291 


The  tinfoil  is  placed  on  the  circumference  of  a  long  cylinder  C,  on  the 
surface  of  which  is  a  very  accurately  constructed  spiral  groove,  the  threads 


Fig.  263. 


Fig.  264. 


being  about  ~  of  an  inch  apart.  The  cylinder  works  on  a  screw  AA',  the 
thread  of  which  is  the  same  as  that  on  the  cylinder  ;  it  is  turned  by  a 
handle  M,  the  motion  being  regulated  by  a  large  fly- 
wheel. There  is  also  an  arrangement  \surn  by  which 
the  position  of  the  mouthpiece,  and  its  pressure  against 
the  tinfoil,  may  be  adjusted. 

When  the  disc  is  made  to  vibrate,  by  speaking  or 
singing  into  the  mouthpiece,  while,  at  the  same  time,  the 
cylinder  is  turned  with  a  uniform  motion,  a  series  of 
dots  or  indentations  are  produced  upon  the  tinfoil, 
which,  being  a  non-elastic  substance,  retains  them. 

If  now  the  part  which  the  mouthpiece  plays  be  re- 
versed, the  indented  tinfoil  can  be  used  to  reproduce 
the  sound.  This  is  best  effected  by  having  a  special 
mouthpiece  of  larger  size,  with  a  diaphragm  of  similar  construction.  This 
is  so  adjusted  that  the  point  is  made  to  work  along  the  indentations  in 
the  groove,  this  sets  the  diaphragm  in  vibrations,  and  these  being  communi- 
cated to  the  air  by  the  mouthpiece  reproduce  the  sound.  For  loudness,  a 
thin  elastic  membrane  is  best,  while  for  distinctness  a  stouter  rigid  plate  is 
preferable. 

In  this  way  sound  has  been  reproduced  so  as  to  be  audible  to  a  large 
audience  ;  the  articulation  is  distinct  though  feeble  :  it  reproduces  the 
quality  of  the  person's  voice  who  speaks  into  it,  but  with  a  nasal  intonation. 
Speech  may  thus  be  treasured  up  on  a  sheet  of  tinfoil  and  kept  for  an  inde- 
finite period  }  the  sound  may  be  reproduced  more  than  once  by  means  of 
its  tinfoil  register,  but  after  the  second  reproduction  the  strength  is  greatly 
diminished. 

If  the  velocity  of  rotation  is  greater  than  before,  the  pitch  of  the  speech 
is  altered  ;  and  if  it  is  not  uniform,  then,  in  the  case  of  a  song,  the  reproduc- 
tion is  incorrect.  In  order  to  produce  a  uniform  velocity,  clockwork  may  be 
used. 

There  is  great  difference  in  the  distinctness  with  which  the  various  con- 
sonants and  vowels  are  reproduced ;  the  s,  for  instance,  is  very  difficult. 
If  the  phonograph  be  rotated  in  the  reverse  direction,  the  individual  letters 
retain  their  character,  but  the  words  as  well  as  the  letters  are  reproduced  in 
the  reverse  order. 


291]  Edison's  Phonograph.  259 

If  the  instrument  be  reset  to  the  starting-point  of  the  phonographic 
record  of  a  song,  and  be  again  sung  into,  it  will  reproduce  both  series  of 
sounds,  as  if  two  persons  were  singing  at  the  same  time  ;  and  by  repeating 
the  same  process,  a  third  or  fourth  part  may  be  added,  or  one  or  more 
instrumental  parts. 

The  impressions  on  the  tinfoil  appear  at  first  sight  as  a  series  of  successive 
points  or  dots,  but  when  examined  under  a  microscope  they  are  seen  to  have 
a  distinct  form  of  their  own.  When  a  cast  is  taken  by  means  of  fusible 
metal,  and  a  longitudinal  section  made,  the  outline  closely  resembles  the 
lagged  edge  of  a  Konig's  flame.  According  to  Edison's  statement,  as 
many  as  40,000  words  can  be  registered  on  a  space  not  exceeding  10  square 
inches. 

The  phonograph  has  been  used  by  Jenkins  and  King  for  the  analysis  of 
vocal  sounds,  for  which  purpose  it  is  better  suited  than  Konig's  flames. 


s  2 


260  On  Heat.  [292 


BOOK   VI. 

ON  HEAT. 


CHAPTER    I. 

PRELIMINARY   IDEAS.      THERMOMETERS. 

292.  Beat.  Hypothesis  as  to  its  nature. — In  ordinary  language  the 
term  heat  is  used  not  only  to  express  a  particular  sensation,  but  also  to  de- 
scribe that  particular  state  or  condition  of  matter  which  produces  this  sensa- 
tion. Besides  producing  this  sensation,  heat  acts  variously  upon  bodies  ;  it 
melts  ice,  boils  water,  makes  metals  red-hot,  produces  electrical  currents, 
decomposes  compound  bodies,  and  so  forth. 

Two  theories  as  to  the  cause  of  heat  have  been  propounded  :  these  are, 
the  theory  oj  emission,  and  the  theory  of  undulation. 

On  the  first  theory,  heat  is  caused  by  a  subtle  imponderable  fluid,  which 
surrounds  the  molecules  of  bodies,  and  which  can  pass  from  one  body  to 
another.  These  heat  atmospheres,  which  thus  surround  the  molecules,  exert 
a  repelling  influence  on  each  other,  in  consequence  of  which  heat  acts  in 
opposition  to  the  force  of  cohesion.  The  entrance  of  this  substance  into  our 
bodies  produces  the  sensation  of  warmth,  its  egress  the  sensation  of  cold. 

On  the  second  hypothesis  the  heat  of  a  body  is  caused  by  an  extremely 
rapid  oscillating  or  vibratory  motion  of  its  molecules  ;  and  the  hottest  bodies 
are  those  in  which  the  vibrations  have  the  greatest  velocity  and  the  greatest 
amplitude.  At  any  given  time  the  whole  of  the  molecules  of  a  body  possess 
a  sum  of  "vis  viva,  which  is  the  heat  they  contain.  To  increase  their  tempera- 
ture is  to  increase  their  vis  viva  ;  to  lower  their  temperature  is  to  decrease 
their  vis  viva.  Hence,  on  this  view,  heat  is  not  a  substance  but  a  condition 
of  matter,  and  a  condition  which  can  be  transferred  from  one  body  to  another. 
When  a  heated  body  is  placed  in  contact  with  a  cooler  one  the  former  cedes 
more  molecular  motion  than  it  receives ;  but  the  loss  of  the  former  is  the 
equivalent  of  the  gain  of  the  latter. 

It  is  also  assumed  that  there  is  an  imponderable  elastic  ether,  which  per- 
vades all  matter  and  infinite  space.  A  hot  body  sets  this  in  rapid  vibration, 
and  the  vibrations  of  this  ether  being  communicated  to  material  objects  set 
them  in  more  rapid  vibration  ;  that  is,  increase  their  temperature.  Here  we 
have  an  analogy  with  sound  ;  a  sounding  body  is  in  a  state  of  vibration,  and 


292]  Heat.     Hypothesis  as  to  its  Nature.  261 

its  vibrations  are  transmitted  by  atmospheric  air  to  the  auditory  apparatus 
in  which  is  produced  the  sensation  of  sound. 

This  hypothesis  as  to  the  nature  of  heat  is  now  admitted  by  the  most 
distinguished  physicists.  It  affords  a  better  explanation  of  all  the  phenomena 
of  heat  than  any  other  theory,  and  it  reveals  an  intimate  connection  between 
heat  and  light.  It  will  be  subsequently  seen  that  by  the  friction  of  bodies 
against  each  other  an  indefinite  quantity  of  heat  is  produced.  Experiment 
has  shown  that  there  is  an  exact  equivalence  between  the  motion  thus  de- 
stroyed and  the  heat  produced.  These  and  many  other  facts  are  utterly 
inexplicable  on  the  assumption  that  heat  is  a  substance,  and  not  a  form  of 
motion. 

In  what  follows,  however,  the  phenomena  of  heat  will  be  considered,  as 
far  as  possible,  independently  of  either  hypothesis  ;  but  we  shall  subsequently 
return  to  the  reason  for  the  adoption  of  the  latter  hypothesis. 

Assuming  that  the  heat  of  bodies  is  due  to  the  motion  of  their  particles, 
we  may  admit  the  following  explanation  as  to  the  nature  of  this  motion  in 
the  various  forms  of  matter  : — 

In  solids  the  molecules  have  a  kind  of  vibratory  motion  about  certain 
fixed  positions.  This  motion  is  probably  very  complex  ;  the  constituents  of 
the  molecule  may  oscillate  about  each  other,  besides  the  oscillation  of  the 
molecule  as  a  whole  ;  and  this  latter  again  may  be  a  to-and-fro  motion,  or  it 
may  be  a  rotatory  motion  about  the  centre.  In  cases  in  which  external 
forces,  such  as  violent  shocks,  act  upon  the  body,  the  molecules  may  per- 
manently acquire  fresh  positions. 

In  the  liquid  state  the  molecules  have  no  fixed  positions.  They  can 
rotate  about  their  centres  of  gravity,  and  the  centre  of  gravity  itself  may 
move.  But  the  repellent  action  of  the  motion,  compared  with  the  mutual 
attraction  of  the  molecules,  is  not  sufficient  to  separate  the  molecules  from 
each  other.  A  molecule  no  longer  adheres  to  particular  adjacent  ones  ;  but 
it  does  not  spontaneously  leave  them  except  to  come  into  the  same  relation 
to  fresh  ones  as  to  its  previous  adjacent  ones.  Thus  in  a  liquid  there  is  a 
vibratory,  rotatory,  and  progressive  motion. 

In  the  gaseous  state  the  molecules  are  entirely  without  the  sphere  of  their 
mutual  attraction.  They  fly  forward  in  straight  lines  according  to  the  ordi- 
nary laws  of  motion,  until  they  impinge  against  other  molecules  or  against 
a  fixed  envelope  which  they  cannot  penetrate,  and  then  return  in  an  opposite 
direction,  with,  in  the  main,  their  original  velocity.  If  the  molecules  were  in 
space  where  no  external  force  could  act  upon  them,  they  would  fly  apart,  and 
disappear  in  infinity.  But  if  contained  in  any  vessel,  the  molecules  con- 
tinually impinge  in  all  directions  against  the  sides,  and  thus  arises  the  pres- 
sure which  a  gas  exerts  on  its  vessel. 

The  perfection  of  the  gaseous  state  implies  that  the  space  actually 
occupied  by  the  molecules  of  the  gas  be  infinitely  small  compared  with  the 
entire  volume  of  the  gas  ;  that  the  time  occupied  by  the  impact  of  a  mole- 
cule either  against  another  molecule,  or  against  the  sides  of  the  vessel,  be 
infinitely  small  in  comparison  with  the  interval  between  any  two  impacts ; 
and  that  the  influence  of  molecular  attraction  be  infinitely  small.  When 
these  conditions  are  not  fulfilled  the  gas  partakes  more  or  less  of  the  nature 
of  a  liquid,  and  exhibits  certain  deviations  from  Boyle's  law.  This  is  the 


262  On  Heat.  [292- 

case  with  all  gases  ;  to  a  very  slight  extent  with  the  less  easily  condensable 
gases,  but  to  a  far  greater  extent  with  vapours  and  the  more  condensable 
gases,  especially  near  their  points  of  liquefaction. 

293.  Dynamical  theory  of  gases.  —  We  have  seen  that  in  the  gaseous 
condition  the  particles  are  assumed  to  fly  about  in  right  lines  in  all  possible 
directions.  A  rough  illustration  of  this  condition  of  matter  is  afforded  by 
imagining  the  case  of  a  number  of  bees  inclosed  in  a  box. 

Let  us  suppose  a  cubical  vessel  to  be  filled  with  air  under  standard  con- 
ditions of  temperature  and  pressure.  Let  the  length  of  the  sides  be  a.  We 
will  for  the  present  suppose  that  each  particle  moves  freely  in  the  space 
without  striking  against  another  particle.  All  possible  motions  may  be  con- 
ceived to  be  resolved  into  motions  in  three  directions  which  are  parallel  to 
the  faces  of  the  cube.  Conceive  any  single  particle,  of  mass  m  ;  it  will  strike 
against  one  face  with  such  a  velocity,  u,  as  not  only  to  annul  its  own  motion, 
but  to  cause  it  to  rebound  in  the  opposite  direction  with  the  same  velocity  ; 
hence  the  measure  of  the  momentum  with  which  it  strikes  against  the  side 
will  be  imu.  Now  by  their  rapid  succession  and  their  uniform  distribu- 
tion, the  total  action  of  these  separate  impacts  is  to  produce  a  pressure 
against  the  sides  of  the  vessel  which  is  the  elastic  force  of  the  gas  ;  and  to 
measure  the  pressure  on  the  side,  we  must  multiply  the  momentum  of  each 
individual  impact  by  the  total  number  of  such  impacts. 

Since  the  length  of  the  side  is  a,  if  there  are  n  molecules  in  the  unit 

of  space,  there  will  be  ncP  in  the  volume  of  the  cube,  of  which—  will  be 

moving  in  a  direction  parallel  to  each  one  of  the  sides.  To  get  the  number 
of  impacts  on  one  face,  we  must  remember  that  they  succeed  each  other, 
after  the  interval  of  time  required  for  a  particle  to  fly  to  the  opposite  side 
and  back  again.  Hence,  u  being  the  velocity,  the  number  of  impacts  which 

each  particle  makes  in  the  unit  of  time,  a  second,  will  be  —  J  and  the  number 

of  all  such  which  strike  against  one  side  will  be  \ncr  U    =  %na*u. 

Now,  since  each  one  exerts  a  pressure  represented  by  2;//2/,  we  shall  have 
for  the  total  pressure  p  on  the  surface  a~ 

pa*  =  ^a-nmu?, 
and  therefore  the  pressure  on  the  unit  of  surface  will  be 


Now,  if  N  is  the  number  of  molecules  in  the  volume  v,  N  =  nv,  and 
therefore 

p  =  £*-mu*  ;  that  is,  pv  =  %Nmu\ 

But,  for  any  given  mass  of  gas,  N,  m,  and  u  are  constant  quantities,  and  the 
product  pv  must  therefore  also  be  constant  ;  this,  however,  is  only  one  form 
of  expressing  Boyle's  law  (180). 

294.  Molecular  velocity.  —  In  the  formula  p=>  £nmuz}  nm  represents  the 
mass  in  unit  volume  which  we  may  designate  as  the  density  p,  of  the   gas, 


-294]  Molecular  Velocity.  263 

referred  to  that  of  water,  and  which  can  be  directly  measured  ;  and  since  the 
pressure  p  is  also  capable  of  direct  measurement,  we  can  calculate  the  third 
magnitude  u  in  absolute  measure. 

The  pressure  p  on  a  gas  is  equal  to  the  action  of  gravity  on  a  column  of 
mercury  of  given  height  h  ;  so  that  if  8  is  the  density  of  mercury  =  I3'596, 
and  g  the  acceleration  of  gravity,  p  =  §gh  and 


P 

Now,  if  a-  be  the  specific  gravity  of  the  gas  as  compared  with  air,  which  is 
lighter  than  water,   px  773-3  =  0-,  or  p=~  cr    , 


773-3  773'3 

^  =  3  *  13-596x076x9-81  15x773-3 
cr 

which  gives  u  =  -^-j-  ;  that  is,  that  for  atmospheric  air  the  mean  velocity  of 

or 

the  particles  is  485  metres  in  a  second.     For  other  gases  we  have,  expressed 
in  the  same  units, 

0  =  461 


In  a  gas  the  velocities  of  the  particles  are  unequal  ;  since,  even  supposing 
that  they  were  all  originally  the  same,  it  is  not  difficult  to  see  that  they  would 
soon  alter.  For  imagine  a  particle  to  be  moving  parallel  to  one  side,  and  to 
be  struck  centrically  by  another  moving  at  right  angles  to  the  direction  of 
its  motion,  the  particle  struck  would  proceed  on  its  new  path  with  increased 
velocity,  while  the  striking  particle  would  rebound  in  a  different  direction 
with  a  smaller  velocity.  • 

Notwithstanding  the  accidental  character  of  the  velocity  of  any  individual 
particle  in  such  a  mass  of  gas  as  we  have  been  considering,  there  will,  at  any 
one  given  time,  be  a  certain  average  distribution  of  velocities.  Now,  from 
considerations  based  on  the  theory  of  probabilities,  it  follows  that  some 
velocities  will  be  more  probable  than  others  —  that  there  will,  indeed,  be  one 
velocity  which  is  more  probable  than  any  other.  This  is  called  the  most 
probable  velocity.  The  mean  velocity  of  the  particle,  as  found  above,  is 
not  this,  nor  is  it  the  same  as  the  arithmetical  mean  of  all  the  velocities  ;  it 
may  be  defined  to  be  that  velocity  which,  if  all  the  molecules  possessed  it, 
would  give  rise  to  the  same  mean  energy  of  the  molecular  impacts  against 
the  side  as  that  which  actually  exists.  This  mean  velocity  is  about  i  greater 
than  the  arithmetical  mean  velocity,  and  is  i£  that  of  the  most  probable 
single  velocity. 

Theoretical  as  well  as  experimental  observations  render  it  possible  to 
determine  with  great  probability  not  only  the  average  length  of  the  path 
which  a  molecule  traverses  before  it  encounters  another,  but  also  the  number 
of  impacts  in  a  given  time.  Thus,  in  air,  measured  under  standard  con- 
ditions, the  length  of  the  mean  path  of  a  molecule  is  calculated  to  be  0*000095 
mm.,  and  the  number  of  impacts  in  a  second  4,700  millions.  For  hydrogen 
these  numbers  are  0-0001855  mm.  for  the  length  of  path,  and  9,480  millions 


264  On  Heat.  [294- 

for  the  number  of  impacts.  Hence  it  is  that,  notwithstanding  these  enormous 
velocities,  gases  diffuse  but  slowly,  as  is  observed  in  the  case  of  those  with 
strong  odours. 

It  follows  from  the  above  equation  that 


that  is,  that  the  molecular  velocities  are  inversely  as  the  square  roots  of  the 
densities  or  the  molecular  weights.  This  is  confirmed  by  the  experiments 
on  diffusion  (190). 

295.  General  effects  of  beat.  —  The  general  effects  of  heat  upon  bodies 
may  be  classed  under  three  heads.  One  portion  is  expended  in  raising  the 
temperature  of  the  body  ;  that  is,  in  increasing  the  vis  viva  of  its  molecules. 
In  the  second  place,  the  molecules  of  bodies  have  a  certain  attraction  for 
each  other,  to  which  is  due  their  relative  position  ;  hence  a  second  portion 
of  heat  is  consumed  in  augmenting  the  amplitude  of  the  oscillations,  by 
which  an  increase  of  volume  is  produced,  or  in  completely  altering  the 
relative  positions  of  the  molecules,  by  which  a  change  of  state  is  effected. 
These  two  effects  are  classed  as  internal  work.  Thirdly,  since  bodies  are 
surrounded  by  atmospheric  air  which  exerts  a  certain  pressure  on  their  sur- 
face, this  has  to  be  overcome  or  lifted  through  a  certain  distance.  The  heat 
or  work  required  for  this  is  called  the  external  work. 

If  Q  units  of  heat  are  imparted  to  a  body,  and  if  A  be  the  quantity  of 
heat  which  is  equivalent  to  the  unit  of  work  ;  then  if  W  is  the  amount  of 
heat  which  serves  to  increase  the  temperature,  I  that  required  to  alter  the 
position  of  the  molecules,  and  if  L  be  that  expended  in  external  work,  then 


296.  Expansion.  —  All  bodies  expand  by  the  action  of  heat.    As  a  general 
rule,  gases  are  the  most  expansible,  then  liquids,  and  lastly  solids. 


Fig.  265. 

In  solids  which  have  definite  figures,  we  can  either  consider  the  expan- 
sion in  one  dimension,  or  the  linear  expansion  ;  in  two  dimensions,  the 
superficial  expansion  ;  or  in  three  dimensions,  the  cubical  expansion  or  the 
expansion  of  volume,  although  one  of  these  never  takes  place  without  the 
other.  As  liquids  and  gases  have  no  definite  figures,  the  expansions  of 
volume  have  in  them  alone  to  be  considered. 

To  show  the  linear  expansion  of  solids,  the  apparatus  represented  in  fig. 
265  may  be  used.  A  metal  rod,  A,  is  fixed  at  one  end  by  a  screw  B,  while 


-297] 


Temperature. 


2&S 


the  other  end  presses  against  the  short  arm  of  an  index,  K,  which  moves  on 
a  scale.  Below  the  rod  there  is  a  sort  of  cylindrical  lamp  in  which  alcohol 
is  burned.  The  needle  K  is  at  first  at  the  zero  point,  but  as  the  rod  becomes 
heated  it  expands,  and  moves  the  needle  along  the  scale: 

The  cubical  expansion  of  solids  is  shown  by  a  GravesandJs  ring.   This 


Fig.  266. 


Fig.  267. 


Fig.  268. 


consists  of  a  brass  ball  a  (fig.  266),  which  at  the  ordinary  temperature  passes 
freely  through  a  ring,  #2,  almost  of  the  same  diameter.  But  when  the  ball 
has  been  heated,  it  expands  and  no  longer  passes  through  the  ring. 

In  order  to  show  the  expansion  of  liquids,  a  large  glass  bulb  provided 
with  a  capillary  stem  is  used  (fig.  267).  If  the  bulb  and  a  part  of  the  stem 
contain  some  coloured  liquid,  the  liquid  rapidly  rises  in  the  stem  when  heat 
is  applied,  and  the  expansion  thus  observed  is  far  greater  than  in  the  case 
of  solids. 

The  same  apparatus  may  be  used  for  showing  the  expansion  of  gases. 
Being  filled  with  air,  a  small  thread  of  mercury  is  introduced  into  the  capillary 
tube  to  serve  as  index  (fig.  268).  When  the  globe  is  heated  in  the  slightest 
degree,  even  by  approaching  the  hand,  the  expansion  is  so  great  that  the 
index  is  driven  to  the  end  of  the  tube,  and  is  finally  expelled.  Hence,  even 
for  a  very  small  degree  of  heat,  gases  are  highly  expansible. 

In  these  different  experiments  the  bodies  contract  on  cooling,  and  when 
they  have  attained  their  former  temperature  they  resume  their  original 
volume.  Certain  metals,  however,  especially  zinc,  form  an  exception  to  this 
rule,  and  it  appears  to  be  also  the  case  with  some  kinds  of  glass. 


MEASUREMENT  OF  TEMPERATURE.      THERMOMETRY. 

297.  Temperature. — The  temperattire  or  hotness  of  a  body,  indepen- 
dently of  any  hypothesis  as  to  the  nature  of  heat,  may  be  defined  as  being 


266  On  Heat.  [297- 

the  greater  or  less  extent  to  which  it  tends  to  impart  sensible  heat  to  other 
bodies.  The  temperature  of  a  body  must  not  be  confounded  with  the  quan- 
tity of  heat  it  possesses  :  a  body  may  have  a  high  temperature  and  yet 
have  a  very  small  quantity  of  heat,  and  conversely  a  low  temperature  and  yet 
possess  a  large  amount  of  heat.  If  a  cup  of  water  be  taken  from  a  bucketful, 
both  will  indicate  the  same  temperature,  yet  the  quantities  they  possess  will 
be  different.  This  subject  of  the  quantity  of  heat  will  be  afterwards  more 
fully  explained  in  the  chapter  on  Specific  Heat. 

298.  Thermometers. — Thermometers   are    instruments    for    measuring 
temperatures.     Owing  to  the  imperfections  of  our  senses  we  are  unable  to 
measure  temperatures  by  the  sensation  of  heat  or  cold  which  they  produce 
in  us,  and  for  this  purpose  recourse  must  be  had  to  the  physical  actions  of 
heat  on  bodies.     These  actions  are  of  various  kinds,  but  the  expansion  of 
bodies  has  been  selected  as  the  easiest  to  observe.     But  heat  also  produces 
electrical  phenomena  in  bodies  ;  and  on  these  the  most  delicate  methods 
of  observing  temperatures  have  been  based,  as  we  shall  see  in  a  subsequent 
chapter. 

Liquids  are  best  suited  for  the  construction  of  thermometers — the  ex- 
pansion of  solids  being  too  small,  and  that  of  gases  too  great.  Mercury  and 
alcohol  are  the  only  liquids  used — the  former  because  it  only  boils  at  a  very 
high  temperature,  and  the  latter  because  it  does  not  solidify  at  the  greatest 
known  cold. 

The  mercurial  thermometer  is  the  most  extensively  used.  It  consists  of 
a  capillary  glass  tube,  at  the  end  of  which  is  blown  the  bulb,  a  cylindrical 
or  spherical  reservoir.  Both  the  bulb  and  a  part  of  the  stem  are  filled  with 
mercury,  and  the  expansion  is  measured  by  a  scale  graduated  either  on  the 
stem  itself,  or  on  a  frame  to  which  it  is  attached. 

Besides  the  manufacture  of  the  bulb,  the  construction  of  the  thermometer 
comprises  three  operations  :  the  calibration  of  the  tube,  or  its  division  into 
parts  of  equal  capacity,  the  introduction  of  the  mercury  into  the  reservoir, 
and  the  graduation. 

299.  Division  of  the  tube  Into  parts  of  equal  capacity.    Calibration. 
As  the  indications  of  the  thermometer  are  only  correct  when  the  divisions 
of  the  scale  correspond  to  equal  expansions  of  the  mercury  in  the  reservoir, 
the  scale  must  be  graduated,  so  as  to  indicate  parts  of  equal  capacity  in  the 
tube.     If  the  tube  were  quite  cylindrical,  and  of  the  same  diameter  through- 
out, it  would  only  be  necessary  to  divide  it  into  equal  lengths.     But  as  the 
diameter  of  glass  tubes  is  usually  greater  at  one  end  than  another,  parts  of 
equal  capacity  in  the  tube  are  represented  by  unequal  lengths  of  the  scale. 

In  order,  therefore,  to  select  a  tube  of  uniform  bore,  it  is  calibrated ;  for 
this  purpose,  a  thread  of  mercury  about  an  inch  long  is  introduced  into  the 
capillary  tube,  and  moved  in  different  positions  in  the  tube,  care  being  taken 
to  keep  it  at  the  same  temperature.  If  the  thread  is  of  the  same  length  in 
every  part  of  the  tube,  it  shows  that  the  capacity  is  everywhere  the  same  ; 
but  if  the  thread  occupies  different  lengths  the  tube  is  rejected,  and  another 
one  sought. 

300.  Filling-  the  thermometer. — In  order  to  fill  the  thermometer  with 
mercury,  a  small  funnel,  C  (fig.  269),  is  blown  on  at  the  top,  and  is  filled 
with  mercury  ;  the  tube  is  then  slightly  inclined,  and  the  air  in  the  bulb 


-302]    Determination  of  the  Fixed  Points  of  a  Thermometer.  267 

expanded  by  heating  it  with  a  spirit  lamp.  The  expanded  air  partially 
escapes  by  the  funnel,  and,  on  cooling,  the  air  which  remains  contracts,  and 
a  portion  of  the  mercury  passes  into  the  bulb  D.  The  bulb  is  then  again 
warmed,  and  allowed  to  cool,  a  fresh  quantity  of  mercury  enters,  and  so  on, 
until  the  bulb  and  part  of  the  tube  are  full  of 
mercury.  The  mercury  is  then  heated  to  boiling  ; 
the  mercurial  vapours  in  escaping  carry  with  them 
the  air  and  moisture  which  remain  in  the  tube. 
The  tube,  being  full  of  the  expanded  mercury  and 
of  mercurial  vapour,  is  hermetically  sealed  at  one 
end.  When  the  thermometer  is  cold,  the  mercury 
ought  to  fill  the  bulb  and  a  portion  of  the  stem. 

301.  Graduation   of  the   thermometer. — The 
thermometer  being  filled,  it  requires  to  be  gradu- 
ated ;  that  is,  to  be  provided  with  a  scale  to  which 
variations  of  temperature  can  be  referred.     And, 
first  of  all,  two  points  must  be  fixed  which  repre- 
sent identical  temperatures  and  which  can  always 
be  easily  reproduced. 

Experiment  has  shown  that  ice  constantly  melts 
at  the  same  temperature,  whatever  be  the  degree  of 
heat,  and  that  distilled  water  under  the  same  pres- 
sure and  in  a  vessel  of  the  same  kind  always  boils 
at  the  same  temperature.  Consequently,  for  the 
first  fixed  point,  or  zero,  the  temperature  of  melting 
ice  has  been  taken  :  and  for  a  second  fixed  point, 
the  temperature  of  boiling  water  in  a  metal  vessel 
under  the  normal  atmospheric  pressure  of  760 
millimetres. 

This  interval  of  temperature — that  is,  the  range 

from  zero  to  the  boiling  point — is  taken  as  the  unit  for  comparing  tempera- 
tures ;  just  as  a  certain  length,  a  foot  or  a  metre  for  instance,  is  used  as  a 
basis  for  comparing  lengths. 

302.  Determination   of  the    fixed   points. — To  obtain  zero,  snow  or 
pounded  ice  is  placed  in  a  vessel  in  the  bottom  of  which  is  an  aperture  by 
which  water  escapes  (fig.  270).     The  bulb  and  a  part  of  the  stem  of  the 
thermometer  are  immersed  in  this  for  about  a  quarter  of  an  hour,  and  a 
mark  made  at  the  level  of  the  mercury,  which  represents  zero. 

The  second  fixed  point  is  determined  by  means  of  the  apparatus  repre- 
sented in  the  figures  271  and  272,  of  which  272  represents  a  vertical  section. 
In  both,  the  same  letters  designate  the  same  parts.  The  whole  of  the 
apparatus  is  of  metal.  A  central  tube,  A,  open  at  both  ends,  is  fixed  on  a 
cylindrical  vessel  containing  water  ;  a  second  tube,  B,  concentric  with  the 
first,  and  surrounding  it,  is  fixed  on  the  same  vessel,  M.  In  this  second 
cylinder,  which  is  closed  at  both  ends,  there  are  three  tubulures,  «,  E,  D. 
A  cork,  in  which  is  the  thermometer  /,  fits  in  a.  To  E,  a  glass  tube,  con- 
taining mercury,  is  attached,  which  serves  as  a  manometer  for  measuring 
the  pressure  of  the  vapour  in  the  apparatus.  D  is  an  escape  tube  for  the 
vapour  and  condensed  water. 


269. 


268 


On  Heat. 


[302- 


The  apparatus  is  placed  on  a  furnace  and  heated  till  the  water  boils  ; 
the  vapour  produced  in  M  rises  in  the  tube  A,  and,  passing  through  the  two 
tubes  in  the  direction   of  the   arrows,  escapes  by  the   tubulure   D.     The 
thermometer  /  being  thus  surrounded  with  vapour,  the  mercury  expands,  and, 
when  it  has  become  stationary,  the  point  at  which 
it  stops  is  marked.     This  is  the  point  sought  for. 
The  object  of  the  second  case,  B,  is  to  avoid  the 
cooling  of  the  central  tubulure  by  its  contact  with 
the  air. 

The  determination  of  the  point  100  (see  next 
article)  would  seem  to  require  that  the  height  of 
the  barometer  during  the  experiment  should  be 
760  millimetres,  for  when  the  barometric  height  is 
greater  or  less  than  this  quantity,  water  boils  either 
above  or  below  100  degrees.  But  the  point  100 
may  always  be  exactly  obtained,  by  making  a 
suitable  correction.  For  every  27  millimetres 
difference  in  height  of  the  barometer  there  is  a 
difference  in  the  boiling  point  of  i  degree.  If, 
g,  for  example,  the  height  of  the  barometer  is  778 — 
that  is,  1 8  millimetres,  or  two-thirds  of  27,  above 
760 — water  would  boil  at  100  degrees  and  two- 
thirds.  Consequently  loof  would  have  to  be 
marked  at  the  point  at  which  the  mercury  stops. 
Gay-Lussac  observed  that  water  boils  at  a  somewhat  higher  temperature 


Fig.  270. 


Fig.  271. 


Fig.  272. 


in  a  glass  than  in  a  metal  vessel :  and  as  the  boiling  point  is  raised  by  any 
salts  which  are  dissolved,  it  has  been  assumed  that  it  was  necessary  to,  use 


-303]          Construction  of  the  Scale  of  a  Thermometer.  269 

a  metal  vessel  and  distilled  water  in  fixing  the  boiling  point.  Rudberg 
showed,  however,  that  these  latter  precautions  are  superfluous.  The  nature 
of  the  vessel  and  salts  dissolved  in  ordinary  water  influence  the  temperature 
of  boiling  water,  but  not  that  of  the  vapour  which  is  formed.  That  is  to 
say,  that  if  the  temperature  of  boiling  water  from  any  of  the  above  causes 
is  higher  than  100  degrees,  the  temperature  of  the  vapour  does  not  exceed 
100,  provided  the  pressure  is  not  more  than  760  millimetres. 
Consequently,  the  higher  point  may  be  determined  in  a  vessel  of 
any  material  provided  the  thermometer  is  quite  surrounded  by 
vapour,  and  does  not  dip  in  the  water. 

Even  with  distilled  water,  the  bulb  of  the  thermometer  must 
not  dip  in  the  liquid,  for,  strictly  speaking,  it  is  only  the  upper 
layer  that  really  has  the  temperature  of  100  degrees,  since  the 
temperature  increases  from  layer  to  layer  towards  the  bottom  in 
consequence  of  the  increased  pressure. 

303.  Construction  of  the  scale.  —  Just  as  the  foot-rule 
which  is  adopted  as  the  unit  of  comparison  for  length,  is  divided 
into  a  number  of  equal  divisions  called  inches  for  the  purpose  of 
having  a  smaller  unit  of  comparison,  so  likewise  the  unit  of  com- 
parison of  temperatures,  the  range  from  zero  to  the  boiling  point, 
must  be  divided  into  a  number  of  parts  of  equal  capacity  called 
degrees.  On  the  Continent,  and  more  especially  in  France,  this 
space  is  divided  into  100  parts,  and  this  division  is  called  the 
Centigrade  or  Celsius  scale ;  the  latter  being  the  name  of  the 
inventor.  The  Centigrade  thermometer  is  almost  exclusively 
adopted  in  foreign  scientific  works,  and,  as  its  use  is  gradually 
extending  in  this  country,  it  has  been  and  will  be  adopted  in 
this  book. 

The  degrees  are  designated  by  a  small  cypher  placed  a  little 
above  on  the  right  of  the  number  which  marks  the  temperature, 
and  to  indicate  temperatures  below  zero  the  minus  sign  is  placed 
before  them.  Thus,  -  15°  signifies  15  degrees  below  zero. 

In  accurate  thermometers  the  scale  is  marked  on  the  stem 
itself  (fig.  273).      It  cannot  be  displaced,  and  its  length  remains 
fixed,  as  glass  has  very  little  expansibility.      The  graduation  is 
effected  by  covering  the  stem  with  a  thin  layer  of  wax,  and  then 
marking  the  divisions  of  the  scale,  as  well  as  the  corresponding 
numbers,  with  a  steel  point.     The  thermometer  is  then  exposed       Fig.  273. 
for  about   ten  minutes  to    the  vapours   of  hydrofluoric    acid, 
which  attacks  the  glass  where  the  wax  has  been  removed.     The  rest  of  the 
wax  is  then  removed,  and  the  stem  is  found  to  be  permanently  etched. 

Besides  the  Centigrade  scale  two  others  are  frequently  used — Fahrenheifs 
scale  and  Reaumur's  scale. 

In  Reaumur's  scale  the  fixed  points  are  the  same  as  on  the  Centigrade 
scale,  but  the  distance  between  them  is  divided  into  80  degrees,  instead  of 
into  loo.  That  is  to  say,  80  degrees  Rdaumur  are  equal  to  100  degrees 
Centigrade  ;  one  degree  Reaumur  is  equal  to  ^°  or  f  of  a  degree  Centigrade, 
and  one  degree  Centigrade  equals  T85%  or  |  degrees  Reaumur.  Consequently 
to  convert  any  number  of  Reaumur's  degrees  into  Centigrade  degrees  (20,  for 


270  On  Heat.  [303- 

example),  it  is  merely  necessary  to  multiply  them  by  f  (which  gives  25). 
Similarly,  Centigrade  degrees  are  converted  into  Reaumur  by  multiplying 
them  by  f. 

The  thermometric  scale  invented  by  Fahrenheit  in  1714  is  still  much 
used  in  England,  and  also  in  Holland  and  North  America.  The  higher  fixed 
point  is,  like  that  of  the  other  scales,  the  temperature  of  boiling  water  ;  but 
the  null  point  of  zero  is  the  temperature  obtained  by  mixing  equal  weights 
of  sal-ammoniac  and  snow,  and  the  interval  between  the  two  points  is 
divided  into  212  degrees.  The  zero  was  selected  because  the  temperature 
was  the  lowest  then  known,  and  was  thought  to  represent  absolute  cold. 
When  Fahrenheit's  thermometer  is  placed  in  melting  ice  it  stands  at  32 
degrees,  and  therefore  100  degrees  on  the  Centigrade  scale  are  equal  to  180 
degrees  on  the  Fahrenheit  scale,  and  thus  i  degree  Centigrade  is  equal  to  \ 
of  a  degree  Fahrenheit,  and  inversely  I  degree  Fahrenheit  is  equal  to  f  of  a 
degree  Centigrade. 

If  it  be  required  to  convert  a  certain  number  of  Fahrenheit  degrees  (95, 
for  example)  into  Centigrade  degrees,  the  number  32  must  first  be  subtracted 
in  order  that  the  degrees  may  count  from  the  same  part  of  the  scale.  The  re- 
mainder in  the  example  is  thus  63,  and  as  I  degree  Fahrenheit  is  equal  to  f  of 
a  degree  Centigrade,  63  degrees  are  equal  to  6^  x  for  35  degrees  Centigrade. 

If  F  be  the  given  temperature  in  Fahrenheit  degrees  and  C  the  corre- 
sponding temperature  in  Centigrade  degrees,  the  former  may  be  converted 
into  the  latter  by  means  of  the  formula 


and  conversely,  Centigrade  degrees  may  be  converted  into  Fahrenheit  by 
means  of  the  formula 


These  formulas  are  applicable  to  all  temperatures  of  the  two  scales  pro- 
vided the  signs  are  taken  into  account.  Thus,  to  convert  the  temperature 
of  5  degrees  Fahrenheit  into  Centigrade  degrees  we  have 


In  like  manner  we  have,  for  con  verting  Rdaumur  into  Fahrenheit  degrees 
the  formula 


and  conversely,  for  changing  Fahrenheit  into  Reaumur  degrees,  the  formula 

(F-32)t-R. 

304.  Displacement  of  zero.  —  Thermometers,  even  when  constructed 
with  the  greatest  care,  are  subject  to  a  source  of  error  which  must  be  taken 
into  account  ;  that  is,  that  in  course  of  time  the  zero  tends  to  rise,  the  dis- 
placement sometimes  extending  to  as  much  as  two  degrees  ;  so  that  when 
the  thermometer  is  immersed  in  melting  ice  it  no  longer  sinks  to  zero. 

This  is  generally  attributed  to  a  diminution  of  the  volume  of  the  bulb  and 
also  of  the  stem,  occasioned  by  the  pressure  of  the  atmosphere.  It  is  usual 
with  very  accurate  thermometers  to  fill  them  two  or  three  years  before  they 


-307]          Conditions  of  tlie  Delicacy  of  a  Thermometer.  271 

are  graduated.  Joule  once  observed  that  even  after  twenty-five  years  a  deli- 
cate thermometer  indicated  a  displacement  of  zero. 

Besides  this  slow  displacement,  there  are  often  variations  in  the  position 
of  the  zero,  when  the  thermometer  has'  been  exposed  to  high  temperatures, 
caused  by  the  fact  that  the  bulb  and  stem  do  not  contract  on  cooling  to  their 
original  volume  (294),  and  hence  it  is  necessary  to  verify  the  position  of  zero 
when  a  thermometer  is  used  for  delicate  determinations. 

Regnault  noticed  that  some  mercurial  thermometers,  which  agree  at  o° 
and  at  100°,  differ  between  these  points,  and  that  these  differences  frequently 
amount  to  several  degrees.  Regnault  ascribed  this  to  the  unequal  expansion 
of  different  kinds  of  glass. 

305.  Limits  to  the   employment  of  mercurial  thermometers. — Of  all 
thermometers  in  which  liquids  are  used,  the  one  with  mercury  is  the  most 
useful,  because  this  liquid  expands  most  regularly,  and  is  easily  obtained 
pure,  and  because  its  expansion  between  —36°  and  100°  is  regular',  that  is, 
proportional  to  the  degree  of  heat.     It  also  has  the  advantage  of  having 
a  very  low  specific  heat.     But  for  temperatures  below  —  36°  C.  the  alcohol 
thermometer  must  be  used,   since  mercury   solidifies   at -40°   C.     Above 
100  degrees  the  coefficient  of  expansion  increases  and  the  indications  of 
the  mercurial  thermometer  are  only  approximate,  the   error  rising  some- 
times  to   several   degrees.     Mercury  thermometers   also   cannot   be  used 
for  temperatures  above  350°,  for  this  is  the  boiling  point  of  mercury. 

306.  Alcohol  thermometer. — The  alcohol  thermometer  differs  from  the 
mercury  thermometer   in  being  filled  with  coloured   alcohol.     But  as   the 
expansion  of  liquids  is  less  regular  in  proportion.as  they  are  near  the  boiling 
point,  alcohol,  which  boils  at  78°   C.,  expands   very   irregularly.     Hence, 
alcohol  thermometers  are  usually  graduated  by  placing  them  in  baths  at 
different  temperatures  together  with  a  standard  mercurial  thermometer,  and 
marking  on   the   alcohol  thermometer  the   temperature   indicated  by  the 
mercury  thermometer.     In  this  manner  the  alcohol  thermometer  is  compar- 
able with  the  mercury  one  ;  that  is  to  say,  it  indicates  the  same  temperatures 
under  the  same  conditions.     The  alcohol  thermometer  is  especially  used  for 
low  temperatures,  for  it  does  not  solidify  at  the  greatest  known  cold. 

307.  Conditions  of  the  delicacy  of  a  thermometer. — A  thermometer  may 
be  delicate  in  two  ways  : — i.  When  it  indicates  very  small  changes  of  tem- 
perature.    2.  When  it  quickly  assumes  the  temperature  of  the  surrounding 
medium. 

The  first  object  is  attained  by  having  a  very  narrow  capillary  tube  and  a 
very  large  bulb  ;  the  expansion  of  the  mercury  on  the  stem  is  then  limited 
to  a  small  number  of  degrees,  from  10  to  20  or  20  to  30  for  instance,  so  that 
each  degree  occupies  a  great  length  on  the  stem,  and  can  be  subdivided  into- 
very  small  fractions.  The  second  kind  of  delicacy  is  obtained  by  making 
the  bulb  very  small,  for  then  it  rapidly  assumes  the  temperature  of  the 
liquid  in  which  it  is  placed. 

A  good  mercury  thermometer  should  answer  to  the  following  tests  : — 
When  its  bulb  and  stem,  to  the  top  of  the  column  of  mercury,  are  immersed 
in  melting  ice,  the  top  of  the  mercury  should  exactly  indicate  o°  C. ;  and 
when  suspended  with  its  bulb  and  scale  immersed  in  the  steam  of  water 
boiling  in  a  metal  vessel  (as  in  fig.  271)  the  barometer  standing  at  760  mm.,. 


2/2 


On  Heat. 


[307- 


the  mercury  should  be  stationary  at  100°  C.  When  the  instrument  is 
inverted,  the  mercury  should  fill  the  tube,  and  fall  with  a  metallic  click,  thus 
showing  the  complete  exclusion  of  air.  The  value  of  the  degrees  should  be 
uniform  ;  to  ascertain  this  a  little  cylinder  of  mercury  may  be  detached  from 
the  column  by  a  slight  jerk,  and  on  inclining  the  tube  it  may  be  made  to 
pass  from  one  portion  of  the  bore  to  another.  If  the  scale  be  properly 
graduated,  the  column  will  occupy  an  equal  number  of  degrees  in  all  parts 
of  the  tube. 

308.  Differential  thermometer. — Sir  John  Leslie  constructed  a  ther- 


Fig.  274. 


Fig.  275. 


mometer  for  showing  the  difference  of  temperature  of  two  neighbouring 
places,  from  which  it  has  received  the  name  of  the  differential  thermometer. 

A  modified  form  of  it  is  that  devised  by  Matthiessen  (fig.  274),  which  has 
the  advantage  of  being  available  for  indicating  the  temperature  of  liquids. 
It  consists  of  a  bent  glass  tube,  each  end  of  which  is  bent  twice,  and 
terminates  in  a  bulb  ;  the  bulbs  being  pendent  can  be  readily  immersed  in 
a  liquid.  The  bend  contains  some  coloured  liquid,  and  in  a  tube  which 
connects  the  two  limbs  is  a  stopcock,  by  which  the  liquid  in  each  limb  is 
easily  brought  to  the  same  level.  The  whole  is  supported  by  a  frame. 

When  one  of  the  bulbs  is  at  a  higher  temperature  than  the  other,  the 
liquid  in  the  stem  is  depressed  and  rises  in  the  other  stem.  The  instru- 
ment is  now  only  used  as  a  thermoscope  ;  that  is,  to  indicate  a  difference 
of  temperature  between  the  two  bulbs,  and  not  to  measure  its  amount. 

309.  Bregruet's  metallic  thermometer. —  Breguet  invented  a  ther- 
mometer of  considerable  delicacy,  which  depends  on  the  unequal  expansion 
of  metals.  It  consists  of  three  strips  of  platinum,  gold,  and  silver,  which  are 
passed  through  a  rolling  mill  so  as  to  form  a  very  thin  metallic  ribbon.  This 
is  then  coiled  in  a  spiral  form,  as  seen  in  fig.  275,  and  one  end  being  fixed  to 


—310]  Rutherford's  Maximum  and  Minimum  Thermometers.  273 

a  support,  a  light  needle  is  fixed  to  the  other,  which  is  free  to  move  round  a 
graduated  scale. 

Silver,  which  is  the  most  expansible  of  the  metals,  forms  the  internal  face 
of  the  spiral,  and  platinum  the  external.  When  the  temperature  rises,  the 
silver  expands  more  than  the  gold  or  platinum,  the  spiral  unwinds  itself,  and 
the  needle  moves  from  left  to  right  of  the  above  figure.  The  contrary  effect 
is  produced  when  the  temperature  sinks.  The  gold  is  placed  between  the 
other  two  metals  because  its  expansibility  is  intermediate  between  that  of 
the  silver  and  the  platinum.  Were  these  two  metals  employed  alone,  their 
rapid  unequal  expansion  might  cause  a  fracture.  Breguet's  thermometer  is 
empirically  graduated  in  Centigrade  degrees,  by  comparing  its  indications 
with  those  of  a  standard  mercury  thermometer. 

On  this  principle  depend  several  forms  of  pocket  thermometers,  and  it  is 
also  applied  in  some  registering  thermometers. 

310.  Rutherford's  maximum  and  minimum  thermometers. — It  is 
necessary,  in  meteorological  observations,  to  know  the  highest  temperature 
of  the  day  and  the  lowest  temperature  of  the  night.  Ordinary  thermometers 
could  only  give  these  indications  by  a  continuous  observation,  which  would  be 
impracticable.  Several  instruments  have  accordingly  been  invented  for  this 
purpose,  the  simplest  of  which  is  Rutherford's.  On  a  rectangular  piece  of 
plate-glass  (fig.  276)  two  thermometers  are  fixed,  whose  stems  are  bent 


20 


Fig.  276. 

horizontally.  The  one,  A,  is  a  mercury,  and  the  other,  B,  an  alcohol 
thermometer.  In  A  there  is  a  minute  piece  of  iron  wire,  A,  moving  freely  in- 
the  tube,  which  serves  as  an  index.  The  thermometer  being  placed  hori- 
zontally, when  the  temperature  rises  the  mercury  pushes  the  index  before  it. 
But  as  soon  as  the  mercury  contracts,  the  index  remains  in  that  part  of  the 
tube  to  which  it  has  been  moved,  for  there  is  no  adhesion  between  the  iron 
and  the  mercury.  In  this  way  the  index  registers  the  highest  temperature 
which  has  been  attained  ;  in  the  figure  this  is  32°.  In  the  minimum  ther- 
mometer there  is  a  small  hollow  glass  tube  which  serves  as  index.  When  it 
is  at  the  end  of  the  column  of  liquid,  and  the  temperature  falls,  the  column 
contracts,  and  carries  the  index  with  it,  in  consequence  of  adhesion,  until  it 
has  reached  the  greatest  contraction.  When  the  temperature  rises  the  alcohol 
expands,  and,  passing  between  the  sides  of  the  tube  and  the  index,  does  not 
displace  B.  The  position  of  the  index  gives  therefore  the  lowest  temperature 
which  has  been  reached  ;  in  the  figure  this  is  9  degrees  below  zero. 

T 


274  On  Heat.  [311- 

* 

311.  Pyrometers. — The  name  pyrometers  is  given  to  instruments  for 
measuring  temperatures  so  high  that  mercurial  thermometers  could  not  be 
used.     The   older    contrivances   for   this   purpose — Wedgwood's,    Daniell's 
(which  in  principle  resembled  the  apparatus  in  fig.  265),  Brongniart's,  &c. — 
have  gone  entirely  out  of  use.     None  of  them  give  an  exact  measure  of  tem- 
perature.    The  arrangements  now  used  for  the  purpose  are  either  based  on 
the  expansion  of  gases  and  vapours,  or  on  the  electrical  properties  of  bodies, 
and  will  be  subsequently  described. 

312.  Different  remarkable  temperatures. — The  following  table  gives 
some  of  the  most  remarkable  points  of  temperature.     It  may  be  observed 
that  it  is  easier  to  produce  very  high  temperatures  than  very  low  degrees  of 
cold. 

Greatest  artificial  cold  produced  by  a  bath  of  bisulphide 

of  carbon  and  liquid  nitrous  acid        ....  -  140°  C. 

Greatest  cold  produced  by  ether  and  liquid  carbonic  acid  —  1 10 

Greatest  natural  cold  recorded  in  Arctic  expeditions         .  —    58*7 

Mercury  freezes          v'; -    39*4 

Mixture  of  snow  and  salt -    20 

Ice  melts    . ;  .  o 

Greatest  density  of  water .  .     +4 

Mean  temperature  of  London  .         .         .         .         .        v  *  9*9 

Blood  heat          .         .         .         .         .         .         .         .         .  36-6 

Water  boils 100 

Mercury  boils    .         .         ." 350 

Sulphur  boils     .         .         . 440 

Red  heat  (just  visible)       .       (Daniell)     ....  526 

Silver  melts        ...              „            ....  1000 

Zinc  boils  ....              ,,           ....  1040 

Cast  iron  melts ...              „  1 530 

Highest  heat  of  wind  furnace          ,,            .                  .         .  1800 

Platinum  melts  .         .         .         .         .         .         .                  .  2000 

Iridium        „                                ......  2700 


-314] 


Expansion  of  Solids. 


275 


CHAPTER    II. 

EXPANSION   OF   SOLIDS. 

313.  Linear    expansion    and    cubical    expansion.       Coefficients     of 
expansion. — It  has  been  already  explained  that  in  solid  bodies  the  expan- 
sion may  be  according  to  three  dimensions — -linear,  superficial,  and  cubical. 

The  coefficient  of  linear  expansion  is  the  elongation  of  the  unit  of  length 
of  a  body  when  its  temperature  rises  from  zero  t6  i  degree  ;  the  coefficient  of 
superficial  expansion  is  the  increase  of  the  surface  in  being  heated  from  zero 
to  i  degree,  and  the  coefficient  of  cubical  expansion  is  the  increase  of  the 
unit  of  volume  under  the  same  circumstances. 

These  coefficients  vary  with  different  bodies,  but  for  the  same  body  the 
.coefficient  of  cubical  expansion  is  three  times  that  of  the  linear  expansion,  as 
is  seen  from  the  following  considerations  : — Suppose  a  cube,  the  length  of 
whose  side  is  i  at  zero.  Let  k  be  the  elongation  of  this  side  in  passing  from 
zero  to  i  degree,  its  length  at  i  degree  will  be  i  +/£,  and  the  volume  of  the 
•cube,  which  was  i  at  zero,  will  be  (i  +£)3,  or  i  +  3^  +  3^  +  £3.  But  as  the 
elongation  k  is  always  a  very  small  fraction  (see  table,  Art.  316),  its  square 
vP,  and  still  more  its  cube  fc\  are  so  small  that  they  may  be  neglected, 
and  the  value  at  .1  degree  becomes  very  nearly  i  +  3/£.  Consequently,  the 
increase  of  volume  is  3/£,  or  thrice  the  coefficient  of  linear  expansion. 

In  the  same  manner  it  may  be  shown  that  the  coefficient  of  superficial 
expansion  is  double  the  coefficient  of  linear  expansion. 

314.  Measurement  of  the  coefficient  of  linear  expansion.    Lavoisier 
and  Laplace's  method. — The  apparatus  used  by  Lavoisier  and  Laplace  for 
determining  the  coefficients  of  linear  expansion  (fig.  277)  consists  of  a  brass 


Fig.  277. 

trough,  placed  on  a  furnace  between  four  stone  supports.  On  the  two  sup- 
ports on  the  right  hand  there  is  a  horizontal  axis,  at  the  end  of  which  is  a 
telescope ;  on  the  middle  of  this  axis,  and  at  right  angles  to  it,  is  fixed  a 
glass  rod,  turning  with  it,  as  does  also  the  telescope.  The  other  two  supports 

T  2 


276 


On  Heat. 


[314- 


are  joined  by  a  cross-piece  of  iron,  to  which  another  glass  rod  is  fixed,  also 
at  right  angles.  The  trough,  which  contains  oil  or  water,  is  heated  by  a 
furnace  not  represented  in  the  figure,  and  the  bar  whose  expansion  is  to  be 
determined  is  placed  in  it. 

Fig.  278  represents  a  section  of  the  apparatus  ;  G  is  the  telescope,  KH 
the  bar,  whose  ends  press  against  the  two  glass  rods  F  and  D.     As  the  rod 


i,   ,  

r  —  »^*- 

B 

\ 

LJI 

: 

H 

u 

Fig.  278. 

F  is  fixed,  the  bar  can  only  expand  in  the  direction  KH,  and  in  order  to 
eliminate  the  effects  of  friction  it  rests  on  two  glass  rollers.  Lastly,  the 
telescope  has  a  cross-wire  in  the  eyepiece,  which,  when  the  telescope  moves, 
indicates  the  depression  by  the  corresponding  number  of  divisions  on  a 
vertical  scale  AB,  at  a  distance  of  220  yards. 

The  trough  is  first  filled  with  ice,  and  the  bar  being  at  zero,  the  division 
on  the  scale  AB,  corresponding  to  the  wire  of  the  telescope,  is  read  off.  The 
ice  having  been  removed,  the  trough  is  filled  with  oil  or  water,  which  is 
heated  to  a  given  temperature.  The  bar  then  expands,  and  when  its  tempe- 
rature has  become  stationary,  which  is  determined  by  means  of  thermometers, 
the  division  of  the  scale,  seen  through  the  telescope,  is  read  off. 

•  From  these  data  the  elongation  of  the  bar  is  determined  ;  for  since  it  has 
become  longer  by  a  quantity,  CH,  and  the  optical  axis  of  the  telescope  has 
become  inclined  in  the  direction  GB,  the  two  triangles,  GHC  and  ABG, 
are  similar,  for  they  have  the  sides  at  right  angles  each  to  each,  so  that 

TT/~>  /"•  f-T 

-—-=——.  In  the  same  way,  if  HC'  were  another  elongation,  and  AB'  a 
AB  ACr 

T-TC"'     f  "FT 
corresponding  deviation,   there  would  still  be  —  —  =  —  -  ;    from   which   it 

X\.x5  .TTtVjr 

follows  that  the  ratio  between  the  elongation  of  the  bar  and  the  deflection 

f  T-T 
of  the  telescope  is  constant,  for  it  is  always  equal  to  --—  •  .     A  preliminary 

ACjr 


measurement  had  shown  that  this  ratio  was 


TT  /-• 

Consequently,  ——  =7—, 


that  is,  the  total  elongation  of  the  bar  is  obtained  by 


AB 
whence  HC  =  - 

744 

dividing  the  length  on  the  scale  traversed  by  the  cross-wire  by  744.  Divid- 
ing this  elongation  by  the  length  of  the  bar,  and  then  by  the  temperature  of 
the  bath,  the  quotient  is  the  dilatation  for  the  unit  of  length  and  for  a  single 
degree  —  in  other  words,  the  coefficient  of  linear  dilatation.  c^L^ 

315.  Roy  and  Ramsden's  method.  —  Lavoisier  and  Laplace's  method  is 
founded  on  an  artifice  which  is  frequently  adopted  in  physical  determinations, 
and  which  consists  in  amplifying  by  a  known  amount  dimensions  which,  in 
themselves,  are  too  small  to  be  easily  measured.  Unfortunately  this  plan  is 


-315]  Roy  and  Ramsderfs  Method.  277 

often  more  fallacious  than  profitable,  for  it  is  first  necessary  to  determine  the 
ratio  of  the  motion  measured  to  that  on  which  it  depends.  In  the  present 
case  it  is  necessary  to  know  the  lengths  of  the  arms  of  the  lever  in  the 
apparatus.  But  this  preliminary  operation  may  introduce  errors  of  such  im- 
portance as  partially  to  counterbalance  the  advantage  of  great  delicacy. 
The  following  method,  used  by  General  Roy  in  1787,  and  which  was  devised 
by  Ramsden,  depends  on  another  principle.  It  measures  the  elongations 
directly,  and  without  amplifying  them  ;  but  it  measures  them  by  means  of  a 
micrometric  telescope,  which  indicates  very  small  displacements. 

The  apparatus  (fig.  279)  consists  pf  three  parallel  metal  troughs  about  6 
feet  long.     In  the  middle  one  there  is  a  bar  of  the  body  whose  expansion  is 


Fig.  279. 

to  be  determined,  and  in  the  two  others  are  cast-iron  bars  of  exactly  the 
same  length  as  this  bar.  Rods  are  fixed  vertically  on  both  ends  of  these 
three  bars.  On  the  rods  in  the  troughs  A  and  B  there  are  rings  with  cross- 
wires  like  those  of  a  telescope.  On  the  rods  in  the  trough  C  are  small  tele- 
scopes, also  provided  with  cross-wires. 

The  troughs  being  filled  with  ice,  and  all  three  bars  at  zero,  the  points  of 
intersection  of  the  wires  in  the  disc,  and  of  the  wires  in  the  telescope,  are  all 
in  a  line  at  each  end  of  the  bar.  The  temperature  in  the  middle  trough  is 
then  raised  to  100°  C.  by  means  of  spirit  lamps  placed  beneath  the  trough  ; 
the  bar  expands,  but  as  it  is  in  contact  with  the  end  of  the  screw,  «,  fixed  on 
the  side,  all  the  elongation  takes  place  in  the  direction  nm,  and,  as  the  cross- 
wire  n  remains  in  position,  the  cross-wire  m  is  moved  towards  B  by  a  quantity 
equal  to  the  elongation.  But  since  the  screw  a  is  attached  to  the  bar,  by 
turning  it  slowly  from  right  to  left  the  bar  is  moved  in  the  direction  w«, 
and  the  cross-wire  m  regains  its  original  position.  To  effect  this,  the  screw 


On  Heat. 


[315- 


has  been  turned  by  a  quantity  exactly  equal  to  the  elongation  of  the  bar, 
and,  as  this  advance  of  the  screw  is  readily  deduced  from  the  number  of 
turns  of  \\stkr 6ad\l\\  the  total  expansion  of  the  bar  is  obtained,  which, 
divided  by  the  temperature  of  the  bath,  and  this  quotient  by  the  length  of 
the  bar  at  zero,  gives  the  coefficient  of  linear  expansion. 

316.  Coefficients  of  linear  expansion. — By  one  or  the  other  method 
the  following  results  have  been  obtained  : — 

Coefficients  of  linear  expansion  for  i°  between  o°  and  ioo°C. 


Pine     . 

0-000006080 

Bronze     . 

0-000018167 

Graphite 

0-000007860 

Brass 

0-000018782 

Marble     .    .      '  . 

0-000008490 

Silver 

0-000019097 

White  glass. 

0-000008613 

Tin 

0-000021730 

Platinum 

0-000008842 

Lead 

0-000028575 

Untempered  steel 

0-000010788 

Zinc 

0*000029417 

Cast  iron 

o-ooooi  1250 

Sodium  chloride       0-000040390 

Sandstone  . 

0-000011740 

Ice 

0-000052000 

Wrought  iron 

0-000012204 

Sulphur    . 

0-000064130 

Tempered  steel   . 

0-000012395 

Ebonite  (17° 

to  35°;  0-000080600 

Gold    . 

0*000014660 

Paraffine  . 

0-000278540 

Copper 

0-000017182 

From  what  has  been  said  about  the  linear  expansion  (311),  the  coefficients 
of  cubical  expansion  of  solids  are  obtained  by  multiplying  those  of  linear 
expansion  by  three. 

The  coefficients  of  the  expansion  of  the  metals  vary  with  their  physical 
condition,  being  different  for  the  same  metal  according  as  it  has  been  cast 
or  hammered  and  rolled,  hardened  or  annealed.  As  a  general  rule,  opera- 
tions which  increase  the  density  increase  also  the  rate  of  expansion.  But 
even  for  substances  in  apparently  the  same  condition,  different  observers 
have  found  very  unequal  amounts  of  expansion  ;  this  may  arise  in  the  case 
of  compound  substances,  such  as  glass,  brass,  or  steel,  from  a  want  of  uni- 
formity in  chemical  composition,  and  in  simple  bodies  from  slight  differences 
of  physical  state. 

The  expansion  of  amorphous  solids,  and  of  those  which  crystallise  in  the 
regular  system,  is  the  same  for  all  dimensions,  unless  they  are  subject  to  a 
strain  in  some  particular  direction.  A  fragment  of  such  a  substance  varies 
in  bulk,  but  retains  the  same  shape.  Crystals  not  belonging  to  the  regular 
system  when  heated,  exhibit  an  unequal  expansion  in  the  direction  of  their 
different  axes,  in  consequence  of  which  the  magnitude  of  their  angles,  and 
therefore  their  form,  is  altered.  In  the  dimetric  system  the  expansion  is  the 
same  in  the  direction  of  the  two  equal  axes,  but  different  in  the  third.  In 
crystals  belonging  to  the  hexagonal  system  the  expansion  is  the  same  in  the 
direction  of  the  three  secondary  axes,  but  different  from  that  according  to 
the  principal  one.  In  the  trimetric  system  it  is  different  in  all  three  directions. 

To  the  general  law  that  all  bodies  expand  by  heat  there  is  an  important 
exception  in  the  case  of  iodide  of  silver,  which  contracts  somewhat  when 
heated.  It  has  a  negative  coefficient  of  expansion,  the  value  of  which  is 
0-00000139  for  i°  C. 


-318]          Formula  relative  to  the  Expansion  of  Solids.  279 

Fizeau  determined  the  expansion  of  a  great  number  of  crystallised  bodies 
by  an  optical  method.  He  placed  thin  plates  of  the  substance  on  a  glass 
plate  and  let  yellow  light  pass  through  them.  He  thus  obtained  alternately 
yellow  and  dark  Newton's  rings  (g.v.)  On  heating,  the  plate  of  the  substance 
expanded,  the  thin  layer  of  air  became  thinner,  and  the  position  of  the  rings 
was  altered.  From  the  alteration  in  their  position  the  amount  of  the  expan- 
sion could  be  deduced.  Among  the  results  he  has  obtained  is  the  curious 
one  that  certain  crystallised  bodies,  such  as  diamond,  emerald  and  cupric 
oxide,  contract  on  being  cooled  to  a  certain  temperature,  but  as  the  cooling 
is  continued  below  this  temperature  they  expand.  They  have  thus  a  tem- 
perature of  maximum  density,  as  is  the  case  with  water  (329).  In  the  case 
of  emerald  and  cuprous  oxide  this  temperature  is  at  -4-2°,  in  the  case  of 
diamond  at  -42-3°. 

317.  The  coefficients  of  expansion  increase  with  the  temperature.  — 
According  to  Matthiessen,  who  determined  the  expansion  of  the  metals  and 
alloys  by  weighing  them  in  water  at  different  temperatures,  the  coefficients 
of  expansion  are  not  quite  regular  between  o°  and  100°.  He  found  the 
following  values  for  the  linear  expansion  between  o°  and  100°  :  — 

Zinc    ,  V  :     .  Lt  =•  L0  (i  +0-00002741  /  +  0-0000000235  *'} 

Lead  .  .    '  '  .  Lt  =  L0  (i  +  0-00002716  /  +  0-0000000074  f~) 

Silver.  .    "'•  .  Lt  =  L0  (i  +0*00001809  /+  0*0000000135  O 

Copper  /    .    .  Lt  =  L0  (i  +0-00001408  /  +  0-0000000264  r2) 

Gold  .  .»•"'..  Lt  =  L0  (i  +0-00001358  /H  0-0000000112  /j) 

Matthiessen  further  found  that  the  coefficients  of  expansion  of  an  alloy  are 
very  nearly  equal  to  the  mean  of  the  coefficients  of  expansion  of  the  volumes 

/of  the  metals  composing  it. 

i  318.  Formulae  relative  to  the  expansion  of  solids.  —  Let  /  be  the  length 
of  3,  bar  at  zero,  /'  its  length  at  the  temperature  t°  C.,  and  a  its  coefficient  of 
linear  expansion.  The  tables  usually  give  the  expansion  for  1°  between  o° 
and  100°  as  in  Art.  316,  or  for  100°  ;  in  this  latter  case  a  is  obtained  by 
dividing  the  number  by  100. 

The  relation  existing  between  the  above  quantities  is  expressed  by  a  few 
simple  formulae. 

The  elongation  corresponding  to  /  is  /  times  a  or  at  for  a  single  unit  of 
length,  or  atl  for  /  units.  The  length  of  the  bar  which  is  /  at  zero  is  /+  atl 
at  /,  consequently, 


This  formula  gives  the  length  of  a  body  /'  at  /°,  knowing  its  length  /  at 
zero,  and  the  coefficient  of  expansion  a  ;  and  by  simple  algebraical  transform- 
ations we  can  obtain  from  it  formulas  for  the  length  at  zero,  knowing  the 
length  /'  at  /°,  and  also  for  finding  #,  the  coefficient  of  linear  expansion, 
knowing  the  lengths  I'  and  /  at  /°  and  zero  respectively. 

The  formulae  for  cubical  expansion  are  entirely  analogous  to  the  preceding. 

The  following  are  examples  of  the  application  of  these  formulae  :  — 

(i.)  A  metal  bar  has  a  length  I'  at  /'°  ;  what  will  be  its  length  /  at  /°? 

From  the  above  formula  we  first  get  the  length  of  the  given  bar  at  zero, 


280  On  Heat.  [318- 

p 

which  is :  by  means  of  the  same  formula  we  pass  from  zero  to  f°  in 

i  +  af 

multiplying  by  i  +  at,  which  gives  for  the  desired  length  the  formula 


(ii.)  The  density  of  a  body  being  d  at  zero,  required  its  density  d'  at  t°. 

If  i  be  the  volume  of  the  body  at  zero,  and  D  its  coefficient  of  cubical 
expansion,  the  volume  at  jfwill  be  i  +  D/ ;  and  as  the  density  of  a  body  is  in 
inverse  ratio  of  the  volume  which  the  body  assumes  in  expanding,  we  get 
the  inverse  proportion, 

d'  :  d~  i     :     i  +  D/ 

d  =  7T~D/  '  °r  ^/=  F+D/' 

Consequently,  when  a  body  is  heated  from  o  to  /°,  its  density,  and  there- 
fore its  weight  for  an  equal  volume,  is  inversely  as  the  expression,  i  +  D/. 

319.  Applications  of  the  expansion  of  solids. — In  the  arts  we  meet 
with  numerous  examples  of  the  influence  of  expansion,  (i.)  The  bars  of 
furnaces  must  not  be  fitted  tightly  at  their  extremities,  but  must,  at  least,  be 
free  at  one  end,  otherwise  in  expanding  they  would  split  the  masonry,  (ii.) 
In  making  railways  a  small  space  is  left  between  the  successive  rails,  for,  if 
they  touched,  the  force  of  expansion  would  cause  them  to  curve  or  would 
break  the  chairs,  (iii.)  Water-pipes  are  fitted  to  one  another  by  means  of 
telescope  joints,  which  allow  room  for  expansion,  (iv.)  If  a  glass  is  heated 
or  cooled  too  rapidly  it  cracks ;  this  arises  from  the  fact  that  glass  is  a  bad 
conductor  of  heat,  the  sides  become  unequally  heated,  and  consequently 
unequally  expanded,  which  causes  a  fracture. 

When  bodies  have  been  heated  to  a  high  temperature,  the  force  pro- 
duced by  their  contraction  on  cooling  is  very  considerable  ;  it  is  equal  to 
the  force  which  is  needed  to  compress  or  expand  the  material  to  the  same 
extent  by  mechanical  means.  According  to  Barlow,  a  bar  of  malleable  iron 
a  square  inch  in  section  is  stretched  jo^ootn  °f  *ts  length  by  a  weight  of  a 
ton  ;  the  same  increase  is  experienced  by  about  9°  C.  A  difference  of  45° 
C.  between  the  cold  of  winter  and  the  heat  of  summer  is  not  unfrequently 
experienced  in  this  country.  In  that  range,  a  wrought-iron  bar  ten  inches 
long  will  vary  in  length  by  ^th  of  an  inch,  and  will  exert  a  strain,  if  its  ends 
are  securely  fastened,  of  fifty  tons.  It  has  been  calculated  from  Joule's  data 
that  the  force  exerted  by  heat  in  expanding  a  pound  of  iron  between  o°  and 
1 00°,  during  which  it  increases  about  ^  of  its  bulk,  is  equal  to  16,000 
foot-pounds  ;  that  is,  it  could  raise  a  weight  of  J  tons  through  a  height  of  one 
foot. 

(i.)  An  application  of  this  contractile  force  is  seen  in  the  mode  of  secur- 
ing tires  on  wheels.  The  tire  being  made  red-hot,  and  thus  considerably 
expanded,  is  placed  on  the  circumference  of  the  wheel  and  then  cooled. 
The  tire,  when  cold,  embraces  the  wheel  with  such  force  as  not  only  to 
secure  itself  on  the  rim  but  also  to  press  home  the  joints  of  the  spokes  into 
the  felloes  and  nave,  (ii.)  Another  interesting  application  was  made  in  the 
case  of  a  gallery  at  the  Conservatoire  des  Arts  et  Metiers  in  Paris,  the  walls 


-320] 


Compensation  Pendulum. 


2Sl 


of  which  had  begun  to  bulge  outwards.  Iron  bars  were  passed  across  the 
building  and  screwed  into  plates  on  the  outside  of  the  walls.  Each  alternate 
bar  was  then  heated  by  means  of  lamps,  and  when  the  bar  had  expanded 
it  was  screwed  up.  The  bars  being  then  allowed  to  cool  contracted,  and  in 
so  doing  drew  the  walls  together.  The  same  operation  was  performed  on 
the  other  bars. 

320.  Compensation   pendulum. — An  important  application  of  the  ex- 
pansion of  metals  has  been  made  in  the  compensation  pendulum.     This  is 
a  pendulum  in  which  the  elongation,  when  the 
temperature  rises,  is  so  compensated  that  the 
distance  between  the  centre  of  suspension  and 
the  centre  of  oscillation  (80)  remains  constant, 
which,  from  the  laws  of  the  pendulum  (81),  is 
necessary  for  isochronous  oscillations,  and  in 
order  that  the  pendulum  may  be   used   as   a 
regulator  of  clocks. 

In  fig.  280,  which  represents  the  gridiron 
pendulum,  one  of  the  commonest  forms  of  com- 
pensation pendulum,  the  ball,  L,  instead  of 
being  supported  by  a  single  rod,  is  supported 
by  a  framework,  consisting  of  alternate  rods  of 
steel  and  brass.  In  the  figure,  the  shaded  rods 
represent  steel  ;  including  a  small  steel  rod,  b, 
which  supports  the  whole  of  the  apparatus, 
there  are  six  of  them.  The  rest  of  the  rods, 
four  in  number,  are  of  brass.  The  rod  z,  which 
.supports  the  ball,  is  fixed  at  its  upper  end  to  a 
horizontal  cross-piece  ;  at  its  lower  end  it  is 
free,  and  passes  through  the  two  circular  holes 
in  the  lower  horizontal  cross-pieces. 

Now  it  is  easy  to  see  from  the  manner  in 
which  the  vertical  rods  are  fixed  to  the  cross- 
pieces,  that  the  elongation  of  the  steel  rods  can 
•only  take  place  downward,  and  that  of  the 
brass  rods  upward.  Consequently,  in  order 
that  the  pendulum  may  remain  of  the  same 
length,  it  is  necessary  that  the  elongation  of 
the  brass  rods  shall  tend  to  make  the  ball 
rise,  by  exactly  the  same  quantity  that  the 
elongation  of  the  steel  rod  tends  to  lower  it  ; 
when  the  sum  of  the  lengths  of  the  steel  rods  A  is  to  the  sum  of  the  lengths 
of  the  brass  rods  B  in  the  inverse  ratio  of  the  coefficients  of  expansion  of 
steel  and  brass,  a  and  b  ;  that  is,  in  the  proportion  A  :  B  =  b  :  a. 

The  elongation  of  the  rod  may  also  be  compensated  for  by  means  of 
.compensating  strips.  These  consist  of  two  blades  of  copper  and  iron 
soldered  together  and  fixed  to  the  pendulum  rod,  as  represented  in  fig.  281. 
The  copper  blade,  which  is  more  expansible,  is  below  the  iron.  When  the 
temperature  sinks,  the  pendulum  rod  becomes  shorter,  and  the  ball  rises.  But 
at  the  same  time  the  compensating  strips  become  curved,  as  seen  in  fig.  282, 


Fig.  280. 

a  result  which  is  attained 


282  On  Heat.  [320- 

in  consequence  of  the  copper  contracting  more  than  the  iron,  and   two 
metallic  balls  at  their  extremities  become  lower.    If  they  have  the  proper  size 


Fig.  281. 


Fig.  282. 


Fig.  283. 


in  reference  to  the  pendulum  ball,  the  parts  which  tend  to  approach  the 
centre  of  suspension  compensate  those  which  tend  to  remove  from  it,  and  the 
centre  of  oscillation  is  not  displaced.  If  the  temperature  rises,  the  pendu- 
lum ball  descends ;  but  at  the  same  time  the  small  balls  ascend,  as  shown  in 
fig.  283,  so  that  there  is  always  compensation. 

One  of  the  most  simple  compensating  pendulums  is  the  mercury  pendu- 
lum, invented  by  an  English  watchmaker,  Graham.  The  ball  of  the  pendu- 
lum, instead  of  being  solid,  consists  of  a  glass  cylinder,  containing  pure 
mercury,  which  is  placed  in  a  sort  of  stirrup,  supported  by  a  steel  rod. 
When  the  temperature  rises  the  rod  and  stirrup  become  longer,  and  thus 
lower  the  centre  of  gravity  ;  but  at  the  same  time  the  mercury  expands,  and, 
rising  in  the  cylinder,  produces  an  inverse  effect,  and  as  mercury  is  much 
more  expansible  than  steel,  a  compensation  may  be  effected  without  making 
the  mercurial  vessel  of  undue  dimensions. 

The  same  principle  is  applied  in  the  compensating  balances  of  chronometers 
(fig.  284).  The  motion  here  is  regulated  by  a  balance  or  wheel,  furnished  with 
a  spiral  spring  not  represented  in  the  figure,  and  the  time 
of  the  chronometer  depends  on  the  force  of  the  spring,  the 
mass  of  the  balance,  and  on  its  circumference.  Now 
when  the  temperature  rises  the  circumference  increases, 
and  the  chronometer  goes  slower  ;  and  to  prevent  this 
part  of  the  mass  must  be  brought  nearer  the  axis.  The 
circumference  of  the  balance  consists  of  compensating 
strips  BC,  pf  which  the  more  expansible  metal  is  on  the 
outside,  and  towards  the  end  of  these  are  small  masses 
of  metal  D,  which  play  the  same  part  as  the  balls  in  the  above  case.  When 
the  radius  is  expanded  by  heat,  the  small  masses  are  brought  nearer  the 
centre  in  consequence  of  the  curvature  of  the  strips  ;  and  as  they  can  be 
fixed  in  any  position,  they  are  easily  arranged  so  as  to  compensate  for  the 
expansion  of  the  balance.  It  may,  however,  here  be  observed  that  the  chief 
action  of  heat  on  chronometers  is  to  expand  and  soften  the  spring,  and 
thereby  lessen  its  elasticity  ;  this  action  produces  five  times  the  effect  that 
the  expansion  of  the  balance-wheel  does. 


Fig.  284. 


-322]      Coefficient  of  the  Absolute  Expansion  of  Mercury.         283. 


CHAPTER    III. 

EXPANSION   OF   LIQUIDS. 

»  321.  Apparent  and  real  expansion. — If  a  flask  of  thin  glass,  provided 
with  a  narrow  stem,  the  flask  and  part  of  the  stem  being  filled  with  some 
coloured  liquid,  be  immersed  in  hot  water 
(fig.  285),  the  column  of  liquid  in  the  stem  at 
first  sinks  from  b  to  a,  but  then  immediately 
after  rises,  and  continues  to  do  so  until  the 
liquid  inside  has  the  same  temperature  as  the 
hot  water.  This  first  sinking  of  the  liquid  is 
not  due  to  its  contraction  ;  it  arises  from  the 
expansion  of  the  glass,  which  becomes  heated 
before  the  heat  can  reach  the  liquid  ;  but  the 
expansion  of  the  liquid  soon  exceeds  that  of 
the  glass,  and  the  liquid  ascends. 

Hence  in  the  case  of  liquids  we  must  dis- 
tinguish between  the  apparent  and  the  real 
or  absolute  expansion.  The  apparent  expan- 
sion is  that  which  is  actually  observed  when 
liquids  contained  in  vessels  are  heated ;  the 
absolute  expansion  is  that  which  would  be 
observed  if  the  vessel  did  not  expand  ;  or,  as 
this  is  never  the  case,  it  is  the-  apparent  ex- 
pansion corrected  for  the  simultaneous  expansion  of  the  containing  vessel. 

As  has  been  already  stated,  the  cubical  expansion  of  liquids  is  alone 
considered  ;  and  as  in  the  case  of  solids,  the  coefficient  of  expansion  of  a 
liquid  is  the  increase  of  the  unit  of  volume  for  a  single  degree  ;  but  a 
distinction  is  here  made  between  the  coefficient  of  absolute  expansion  and  the 
coefficient  of  apparent  expansion.  Of  the  many  methods  which  have  been 
employed  for  determining  these  two  coefficients,  we  shall  describe  that  of 
Dulong  and  Petit. 

^  322.  Coefficient  of  the  absolute  expansion  of  mercury. — In  order  to 
determine  the  coefficient  of  the  absolute  expansion  of  mercury,  the  influence 
of  the  envelope  must  be  eliminated.  Dulong  and  Petit's  method  depends  on 
the  hydrostatical  principle  that,  in  two  communicating  vessels,  the  heights 
of  two  columns  of  liquid  in  equilibrium  are  inversely  as  their  densities  (108), 
a  principle  independent  of  the  diameters  of  the  vessels,  and  therefore  of 
their  expansions. 

The  apparatus  consists  of  two  glass  tubes,  A  and  B  (fig.  286),  joined  by  a 
capillary  tube  and  kept  vertical  on  an  iron  support,  KM,  the  horizontally 
of  which  is  adjusted  by  means  of  two  levelling  screws  and  two  spirit-levels,. 


284 


On  Heat. 


[322- 


m  and  n.  Each  of  the  tubes  is  surrounded  by  a  metal  case,  of  which  the 
smaller,  D,  is  filled  with  ice  ;  the  other,  E,  containing  oil,  can  be  heated  by 
the  furnace,  which  is  represented  in  section  so  as  to  show  the  case.  Mercury 
is  poured  into  the  tubes  A  and  B  ;  it  remains  at  the  same  level  in  both,  as 


Fig.  286. 

long  as  they  are  at  the  same  temperature,  but  rises  in  B  in  proportion  as  it 
is  heated,  and  expands. 

Let  h  and  d  be  the  height  and  density  of  the  mercury  in  the  leg  A,  at  the 
temperature  zero,  and  h'  and  d'  the  same  quantities  in  the  leg  B.  From  the 
hydrostatical  principle  previously  cited  we  have  had  hd  =  h'd'.  Now  from 

the  problem  in  Art.   318,  d'  =  ,    D  being  the  coefficient  of  absolute 

expansion  of  mercury ;   substituting  this  value  of  d'  in   the  equation,  we 


have 


h'd_ 
D/ 


hd,  from  which  we  get  D 


-h 
~ht 


The  coefficient  of  absolute  expansion  of  mercury  is  obtained  from  this 
formula,  knowing  the  heights  h'  and  h,  and  the  temperature  /  of  the  bath  in 
which  the  tube  B  is  immersed.  In  Dulong  and  Petit's  experiment  this 
temperature  was  measured  by  a  weight  thermometer,  P  (323),  the  mercury  of 
which  overflowed  into  the  basin,  C,  and  by  means  of  an  air  thermometer,  T 
(331)  ;  the  heights  h'  and  h  were  measured  by  a  cathetometer,  K  (89). 

Dulong  and  Petit  found  by  this  method  that  the  coefficient  of  absolute 
expansion  of  mercury  between  o°  and  100°  C.  is  5^.  But  they  found  that 
the  coefficient  increased  with  the  temperature.  Between  100°  and  200° 
it  is  ^25,  and  between  200°  and  300°  it  is  ^Q.  The  same  observation 
has  been  made  in  reference  to  other  liquids,  showing  that  their  expansion 
is  not  regular.  It  has  been  found  that  this  expansion  is  less  regular  in 
proportion  as  liquids  are  near  a  change  in  their  state  of  aggregation  ;  that 


-325]  Coefficient  of  the  Expansion  of  Glass.  285 

is,  approach  their  freezing  or  boiling  points.  Dulong  and  Petit  found  that 
the  expansion  of  mercury  between  -36°  and  ioo°is  practically  quite  uniform. 

Regnault,  who  determined  this  important  physical  constant,  found  that 
the  mean  coefficient  between  o°  and  100°  is  5^,  between  100°  and  200°, 
5^,  and  between  200°  and  300°,  ^—. 

323.    Coefficient  of  the   apparent  expansion   of  mercury. — The  co- 
efficient of  apparent  expansion  of  a  liquid  varies  with  the  nature  of  the 
envelope.    That  of  mercury  in  glass 
was   determined  by  means  of  the 
apparatus  represented  in   fig.  287. 
It   consists   of  a  glass  cylinder  to 
which   is  joined  a    bent    capillary   ; 
glass  tube,  open  at  the  end. 

The  apparatus  is  weighed  first 
empty,  and  then  when  filled   with  Fig>  287- 

mercury   at    zero :     the    difference 

gives  the  weight  of  the  mercury,  P.  It  is  then  raised  to  a  known  temperature., 
t ;  the  mercury  expands,  a  certain  quantity  passes  out,  which  is  received  in 
the  capsule  and  weighed.  If  the  weight  of  this  mercury  be  /,  that  of  the 
mercury  remaining  in  the  apparatus  will  be  P  —p. 

When  the  temperature  is  again  zero,  the  mercury  in  cooling  produces  an 
empty  space  in  the  vessel,  which  represents  the  contraction  of  the  weight  of 
mercury  P  —p,  from  f  to  zero,  or,  what  is  the  same  thing,  the  expansion 
of  the  same  weight  from  o  to  *°  ;  that  is,  the  weight  p  represents  the  ex- 
pansion of  the  weight  P  —p,  for  f.  If  this  weight  expands  in  glass  by  a 

quantity  p  for  /°,  a  single  unit  of  weight  would  expand  -— • %-  -  for    /°,    and 
P.       for  a  single   degree ;  consequently,  for  D',  the  coefficient  of  ap- 
parent  expansion  of  mercury   in  glass,  we  have  D'  =  ..*__.         Dulong 
and  Petit  found  the  coefficient  of  apparent  expansion  of  mercury  in  glass  to 

\    be    C^SO- 

*  324.  Weight  thermometer. — The  apparatus  represented  in  fig.  287  is 
called  the  weight  thermometer,  because  the  temperature  can  be  deduced 
from  the  weight  of  mercury  which  overflows. 

The  above  experiments  have  placed  the  coefficient  of  apparent  expansion 

at  g^  ;  we  have  therefore  the  equation  -••-  --..,,  =  eiio'  fr°m  which  we  get 
/  =  4  °P^  a  formuia  which  gives  the  temperature  t  when  the  weights  P  and 

\p  are  known. 

^  325.  Coefficient  of  the  expansion  of  glass. — As  the  absolute  expansion 
of  a  liquid  is  the  apparent  expansion,///^  the  expansion  due  to  the  envelope, 
the  coefficient  of  the  cubical  expansion  of  glass  is  obtained  by  taking  the 
difference  between  the  coefficient  of  absolute  expansion  of  mercury  in  glass 
and  that  of  its  apparent  expansion.  That  is,  the  coefficient  of  cubical  expan- 
sion of  glass  is 

6 fee  -  esVs  =  3sfoo  =  0-00002 584. 


286  On  Heat.  [325- 

Regnault  found  that  the  coefficient  of  expansion  varies  with  different 
kinds  of  glass,  and  further  with  the  shape  of  the  vessel.  For  ordinary 
chemical  glass  tubes,  the  coefficient  is  0*0000254. 

326.  Coefficients  of  expansion  of  various  liquids. — The  coefficient  of 
'  apparent  expansion  of  liquids  may  be  determined  by  means  of  an  application 
of  the  principle  of  the  weight  thermometer,  and  the  absolute  expansion  is 
obtained  by  adding  to  this  coefficient  the  expansion  of  the  glass. 

Mean  coefficients  of  absolute  expansion  of  liquids  for  i°  C. 

Mercury  .         .         .  0*00018  Fixed  oils  .         .         .  0*00080 

Water  saturated  with  Nitric  acid          .         .  0*00110 

salt  .         .  0*00050  Alcohol       .         .         .  o'ooic>4 

Sulphuric  acid          .  0*00063  Bisulphide  of  carbon  .  0-00114 

Oil  of  turpentine       .  0*00090  Chloroform          .         .  0*00111 

Ether        .         .         .  0*00015  Bromine      .         .         .  0*00104 

The  numbers  here  given  only  hold  for  moderate  temperatures.  The  co- 
•efficient  of  expansion  of  almost  all  liquids  increases  gradually  from  zero,  and 
can  only  be  expressed  with  accuracy  by  a  somewhat  complicated  formula 

V/  =  V0  (I  +  at  +  fit*  +  y/3) 

in  which  /  is  the  temperature,  and  «,  /3,  and  y  are  constants  specially  deter- 
mined for  each  liquid.  The  expansion  of  mercury  is  practically  constant 
between  —36°  and  100°  C.,  while  water  contracts  from  zero  to  4°,  and  then 
expands. 

For  many  physical  experiments  a  knowledge  of  the  exact  expansion  of 
water  is  of  great  importance.     This  physical  constant  was  determined  with 
great  care  by  Matthiessen,  who  found  that  between  4°  and  30°  it  may  be 
expressed  by  the  formula 
V/=  i  -0*00000253  (/-4)  +0*0000008389  (t-tf  +0*00000007173  (V-4)3; 

and  between  30  and  100  by  V/  =  0*999695  +  0*00000 547 24^  +  0*00000001 126/3. 
Many  liquids,  with  low  boiling  points,  especially  condensed  gases,  have  very 
high  coefficients  of  expansion.  Thilorier  found  that  liquid  carbonic  acid 
•expands  four  times  as  much  as  air.  Drion  confirmed  this  observation  and 
has  obtained  analogous  results  with  chloride  of  ethyle,  liquid  sulphurous 

.  acid,  and  liquid  hyponitrous  acid. 

4  327.  Correction  of  the  barometric  height. —  It  has  been  already  ex- 
plained under  the  barometer  (164),  that,  in  order  to  make  the  indications  of 
this  instrument  comparable  in  different  places  and  at  different  times,  they 
must  be  reduced  to  a  uniform  temperature,  which  is  that  of  melting  ice.  The 
correction  is  made  in  the  following  manner  : — 

Let  H  be  the  barometric  height  at  /°,  and  //  its  height  at  zero,  d  the 
density  of  mercury  at  zero,  and  d'  its  density  at  /°.  The  heights  H  and  h 

are  inversely  as  the  densities  dTand  d' ;  that  is,  w  =    ,-     If  we  call   one   the 

volume  of  mercury  at  zero,  its  volume  at  f  will  be  i  +  D/,  D  being  the  co- 
efficient of  absolute  expansion  of  mercury.  But  these  volumes,  i  +  D/.and  i, 

are  inversely  as  the  densities  of  d  and  d' ',  that  is    —  =  —   - .  Consequently, 


/330] 


Maximum  Density  of  Water.  287 


— I      ,  whence  h  =      H     .     Replacing   D    by  its  value   W^,   we   have 
H     i  +  \Jt  I  +  Di 


/,._       H       _ 

'T^Jl'sW^ 
5508 

In  this  calculation,  the  coefficient  of  absolute  expansion  of  mercury  is 
taken,  and  not  that  of  apparent  expansion  ;  for  the  value  H  is  the  same  as 
if  the  glass  did  not  expand,  the  barometric  height  being  independent  of  the 
diaprte'ter  of  the  tube,  and  therefore  of  its  expansion. 

/  328.  Correction  of  thermometric  readings. — If  the  whole  column  of 
mercury  of  a  thermometer  is  not  immersed  in  the  space  whose  temperature 
is  to  be  determined,  it  is  necessary  to  make  a  correction,  which  in  the 
accurate  determination  of  boiling  points,  for  instance,  is  of  great  import- 
ance, in  order  to  arrive  at  the  true  temperature  which  the  thermometer 
should  show.  That  part  of  the  stem  which  projects  will  have  a  tempera- 
ture which  must  be  estimated,  and  which  may  roughly  be  taken  as  some- 
thing over  that  of  the  surrounding  air. 

Supposing,  for  instance,  the  actual  reading  is  160°  and  that  the  whole  of 
the  part  over  80°  is  outside  the  vessel,  while  the  temperature  of  the  surround- 
ing air  is  15°.  We  will  assume  that  the  mean  temperature  of  the  stem  is" 2 5°, 
and  that  a  length  of  i6o°-8o°  is  to  be  heated  through  160-25  =  135°  ;  this 

gives  Sox  JLM.  r=  1-66   (taking   the   coefficient   of  apparent  expansion   of 

6480 

mercury)  ;  so  that  the  true  reading  is  i6r66. 

329.  Force  exerted  by  liquids  in  expanding. — The  force  which  liquids 
exert  in  expanding  is  very  great,  and  equal  to  that  which  would  be  required 
in  order  to  bring  the  expanded  liquid  back  to  its  original  volume.  Now  we 
know  what  an  enormous  force  is  required  to  compress  a  liquid  to  even  a 
very  small  extent  (98).  Thus  between  o°  and  10°,  mercury  expands  by 
0-0015790  of  its  volume  at  o°  ;  its  compressibility  is  0-00000295  of  its  volume 
for  one  atmosphere  ;  hence  a  pressure  of  more  than  600  atmospheres  would 
be  requisite  to  prevent  mercury  expanding  when  it  is  heated  from  o°  to  10°. 
v  330.  Maximum  density  of  water. — Water  presents  the  remarkable 
phenomenon  that  when  its  temperature  sinks  it  contracts  up  to  4°  ;  but 
from  that  point,  although  the  cooling  continues,  it  expands  up  to  the  freezing 
point,  so  that  4°  represent  the  point  of  greatest  contraction  of  water. 

Many  methods  have  been  used  to  determine  the  maximum  density  of 
water.  Hope  made  the  following  experiment  : — He  took  a  deep  vessel 
perforated  by  two  lateral  apertures,  in  which  he  fixed  thermometers,  and 
having  filled  the  vessel  with  water  at  o°,  he  placed  it  in  a  room  at  a  tem- 
perature of  1 5°.  As  the  layers  of  liquid  at  the  sides  of  the  vessel  became 
heated  they  sank  to  the  bottom,  and  the  lower  thermometer  marked  4°  while 
the  upper  one  was  still  at  zero.  Hope  then  made  the  inverse  experiment  ; 
having  filled  the  vessel  with  water  at  15°,  he  placed  it  in  a  room  at  zero. 
(The  lower  thermometer  having  sunk  to  4°  remained  stationary  for  some 
time,  while  the  upper  one  cooled  down  until  it  reached  zero.  Both  these 
experiments  prove  that  water  is  heavier  at  4°  that  at  o°,  for  in  both  cases  it 
sinks  to  the  lower  part  of  the  vessel. 


288  ,        On  Heat.  [330^- 

This  last  experiment  may  be  adapted  for  lecture  illustration  by  using  a 
cylinder  containing  water  at  15°  C,  partially  surrounded  by  a  jacket  contain- 
ing bruised  ice  (fig.  288). 

Hallstrom  made  a  determination  of  the  maximum  density  of  water  in  the 
following  manner  : — He  took  a  glass  bulb,  loaded  with  sand,  and  weighed  it 

in  water  of  different  temperatures.  Allow- 
ing for  the  expansion  of  glass,  he  found 
that  4*1°  was  the  temperature  at  which  it 
lost  most  weight,  and  consequently  this 
was  the  temperature  of  the  maximum 
density  of  water. 

Despretz  arrived  at  the  temperature 
4°  by  another  method.  He  took  a  water 
thermometer — that  is  to  say,  a  bulbed 
tube  containing  water— and,  placing  it  in 
a  bath,  the  temperature  of  which  was  in- 
dicated by  an  ordinary  mercury  thermo- 
meter, found  that  the  water  contracted  to 
the  greatest  extent  at  4°,  and  that  this 
therefore  is  the  point  of  greatest  density. 
This  phenomenon  is  of  great  import- 
ance in  the  economy  of  nature.  In  winter 
the  temperature  of  lakes  and  rivers  falls, 
from  being  in  contact  with  the  cold  air 
and  from  other  causes,  such  as  radiation. 
The  cold  water  sinks  to  the  bottom,  and 
a  continual  series  of  currents  goes  on  until  the  whole  has  a  temperature  of 
4°.  The  cooling  on  the  surface  still  continues,  but  the  cooled  layers  being 
lighter  remain  on  the  surface,  and  ultimately  freeze.  The  ice  formed  thus 
protects  the  water  below,  which  remains  at  a  temperature  of  4°,  even  in  the 
most  severe  winters,  a  temperature  at  which  fish  and  other  inhabitants  of 
the  water  are  not  destroyed. 

The  following  table  of  the  density  of  water  at  various  temperatures  is 
based  on  several  sets  of  observations  : — • 

Density  of  water  between  o°  and  30°. 


Fig.  288. 


Tempe- 
ratures 

Densities 

Tempe- 
ratures 

Densities 

Tempe- 
ratures 

Densities 

0 

0-99988 

II 

0-99965 

22 

0-99785 

I 

0-99993 

12 

0-99955 

23 

0-99762 

•o 

0-99997 

13 

0-99943 

24 

0-99738 

3 

0-99999 

14 

0-99930 

25 

0-99704 

4 

i  -ooooo 

15 

0-99915 

26 

0-99089 

5 

0-99999 

16 

0-99900 

27 

0-99662 

6 

0-99997 

i? 

0-99884 

28 

0-99635 

7 

0-99994 

18 

0-99800 

29 

0*99607 

8 

0-99988 

19 

0-99847 

30 

0-99579 

9 

0-99982 

20 

0-99807 

10 

0-99974 

21 

0-99806 

-331]  Gay-Lussads  Method.  289 


CHAPTER  IV. 

EXPANSION   AND   DENSITY  OF   GASES 

331.  Gay-lussac's  method. — Gases  are  the  most  expansible  of  all 
tiodies,  and  at  the  same  time  the  most  regular  in  their  expansion.  The  co- 
efficients of  expansion,  too,  of  the  several  gases  differ  only  by  very  small 
quantities.  The  cubical  expansion  of  gases  need  alone  be  considered. 

Gay-Lussac  first  determined  the  coefficient  of  the  expansion  of  gases  by 
means  of  the  apparatus  represented  in  fig.  289. 

In  a  rectangular  metal  bath,  about  16  inches  long,  was  fitted  an  air 
thermometer,  which  consisted  of  a  capillary  tube,  AB,  with  a  bulb,  A,  at  one 
end.  The  tube  was  divided  into  parts  of  equal  capacity,  and  the  contents  of 
the  bulb  ascertained  in  terms  of  these  parts.  This  was  effected  by  weighing 
the  bulb  and  tube  full  of  mercury  at  zero,  and  then  heating  slightly  to  ex- 
pel a  small  quantity  of  mercury,  which  was  weighed.  The  apparatus  being 


Fig.   2 


again  cooled  down  to  zero,  the  vacant  space  in  the  tube  corresponded  to  the 
weight  of  mercury  which  had  overflowed  ;  the  volume  of  mercury  remaining 
in  the  apparatus,  and  consequently  the  volume  of  the  bulb,  was  determined 
by  calculations  analogous  to  those  made  for  the  piezometer  (98). 

In  order  to  fill  the  thermometer  with  dry  air  it  was  first  filled  with 
mercury,  which  was  boiled  in  the  bulb  itself.  A  tube,  C,  filled  with  chloride 
of  calcium,  was  then  fixed  on  to  its  end  by  means  of  a  cork.  A  fine  platinum 
wire  having  then  been  introduced  into  the  stem  AB,  through  the  tube  C,  and 
•the  apparatus  being  slightly  inclined  and  agitated  from  time  to  time,  air 
entered,  having  been  previously  well  dried  by  passing  through  the  chloride  of 
calcium  tube.  The  whole  of  the  mercury  was  displaced,  with  the  exception 
of  a  small  thread,  which  remained  in  the  tube  AB  as  an  index. 

U 


290  On  Heat.  [331- 

The  air  thermometer  was  then  placed  in  the  box  filled  with  melting  ice, 
the  index  moved  towards  A,  and  the  point  was  noted  at  which  it  became 
stationary.  This  gave  the  volume  of  air  at  zero  ;  for  the  capacity  of  the 
bulb  was  known.  Water  or  oil  was  then  substituted  for  the  ice,  and  the 
bath  successively  heated  to  different  temperatures.  The  air  expanded  and 
moved  the  index  from  A  towards  B.  The  position  of  the  index  in  each  case 
was  noted,  and  the  corresponding  temperature  was  indicated  by  means  of 
the  thermometers  D  and  E. 

Assuming  that  the  atmospheric  pressure  did  not  vary  during  the  experi- 
ment, and  neglecting  the  expansion  of  the  glass  as  being  small  in  comparison 
with  that  of  the  air,  the  total  expansion  of  the  air  is  obtained  by  subtracting 
from  its  volume  at  a  given  temperature,  its  volume  at  zero.  Dividing  this  by  a 
given  temperature,  and  then  by  the  number  of  units  contained  in  the  volume 
at  zero,  the  quotient  is  the  coefficient  of  expansion  for  a  single  unit  of  volume 
and  a  single  degree;  that  is,  the  coefficient  of  expansion.  It  will  be  seen, 
further  on,  how  corrections  for  pressure  and  temperature  may  be  introduced. 

By  this  method  Gay-Lussac  found  that  the  coefficient  of  expansion  of  air 
was  0-00375  ;  the  two  following  laws  hold  in  reference  to  the  expansion  of 
gases  :— 

I.  All  gases  have  the  same  coefficient  of  expansion  as  air. 

I 1.  This  coefficient  is  the  same  whatever  be  the  pressure  supported  by  the  gas. 
These  simple  laws  are  not,  however,  rigorously  exact  (333) ;  they  only 

express  the  expansion  of  gases  in  an  approximate  manner.  These  laws  were 
discovered  independently  by  Dalton  and  by  Gay-Lussac,  and  are  usually 
ascribed  to  them.  The  first  discoverer  of  the  former  law. was,  however,, 
Charles. 

332.  Problems  on  the  expansion  of  gases. — Many  of  the  problems 
relative  to  the  expansion  of  gases  are  similar  to  those  on  the  expansion  of 
liquids.  With  obvious  modifications,  they  are  solved  in  a  similar  manner. 
In  most  cases  the  pressure  of  the  atmosphere  must  be  taken  into  account  in 
considering  the  expansion  of  gases.  The  following  is  an  example  of  the 
manner  in  which  this  correction  is  made  : — 

i.  The  volume  of  a  gas  at  /°,  and  under  the  pressure  H,  is  V;  what  will 
be  the  volume  V  of  the  same  gas  at  zero,  and  under  the  normal  pressure 
760  millimetres  ? 

Here  there  are  two  corrections  to  be  made  ;  one  relative  to  the  tempera- 
ture, and  the  other  to  the  pressure.  It  is  quite  immaterial  which  is  taken 
first.  If  a  be  the  coefficient  of  cubical  expansion  for  a  single  degree,  by 
reasoning  similar  to  that  in  the  case  of  linear  expansion  (318),  the  volume  of 

the  gas  at  zero,  but  still  under  the  pressure  H,  will  be  -  —  .    This  pressure 

is  reduced  to  the  pressure  760  in  accordance  with  Boyle's  law  (180),  by 

V  VXH 

putting  V  x  760  = x  H  ;    whence   V 


i+at  760(1  +  at) 

ii.  A  volume  of  gas  weighs  P'  at  t° ;  what  will  be  its  weight  at  zero? 
Let  P'  be  the  desired  weight,  a  the  coefficient  of  expansion  of  the  gas, 
df  its  density  at  /°,  and  d  its  density  at  zero.    As  the  weights  of  equal 

P'     d' 
volumes  are  proportional  to  the  densities,  we  have  --  »— .     If  I  be  the 


-333] 


Regnaulfs  Method. 


291 


volume  of  a  gas  at  zero,  its  volume  at  t  will  be  i  +  at :  but  as  the  densities 

are  inversely  as  the  volumes       = , 

d     i  -t-  at 

P/  T 

and  therefore       =        -  ;  whence  P  ••=  P'  (i  +  at}. 

r        I  +  at 

p 

From  this    equation  we   get    P'  = which   gives   the    weight   at   /, 

I  -t-  at 

knowing  the  weight  at  zero,  and  which  further  shows  that  the  weight  P'  is 
inversely  as  the  binomial  of  expansion  i  +  at. 

333.  Regnault's  method. — Regnault  used  successfully  four  different 
methods  for  determining  the  expansion  of  gases.  In  some  of  them  the 
pressure  was  constant  and  the  volume  variable,  as  in  Gay-Lussac's  method  ; 
in  others  the  volume  remained  the  same  while  the  pressure  varied.  The 
first  method  will  be  described.  It  is  the  same  as  that  used  by  Rudberg  and 
Dulong,  but  is  distinguished  by  the  care  with  which  all  sources  of  error  are 
avoided. 

The  apparatus  consisted  of  a  pretty  large  cylindrical  reservoir,  B  (fig. 
290),  terminating  in  a  bent  capillary  tube.  In  order  to  fill  the  reservoir  with 


Fig.  290. 

dry  air,  it  was  placed  in  a  hot-water  bath,  and  the  capillary  tube  connected 
by  a  caoutchouc  tube  with  a  series  of  drying  tubes.  These  tubes  were 
joined  to  a  small  air-pump,  P,  by  which  a  vacuum  could  be  produced  in  the 
reservoir  while  at  a  temperature  of  100°.  The  reservoir  was  first  exhausted, 
and  air  afterwards  admitted  slowly  \  this  operation  was  repeated  a  great 
many  times,  so  that  the  air  in  the  reservoir  became  quite  dry,  for  the  mois- 
ture adhering  to  the  sides  passed  off  in  vapour  at  100°,  and  the  air  which 
entered  became  dry  in  its  passage  through  the  U  tubes. 

The  reservoir  was  then  kept  for  half  an  hour  at  the  temperature  of  boil- 
ing water  ;  the  air-pump  having  been  detached,  the  drying  tubes  were  then 
disconnected,  and  the  end  of  the  tube  hermetically  sealed,  the  height  H  of 
the  barometer  being  noted.  When  the  reservoir  B  was  cool,  it  was  placed 

u  2 


292 


On  Heat. 


[333- 


in  the  apparatus  represented  in  fig.  291.     It  was  there  quite  surrounded 
with  ice,  and  the  end  of  the  tube  dipped  in  the  mercury  bath,  C.     After  the 

air  in  the  reservoir  B  had  sunk  to  zero,  the 
point  b  was  broken  off  by  means  of  a  forceps  ; 
the  air  in  the  interior  became  condensed  by 
atmospheric  pressure,  the  mercury  rising  to  a 
height  oG.  In  order  to  measure  the  height  of 
this  column,  Go,  which  will  be  called  h,  a  mov- 
able rod,  go,  was  lowered  until  its  point,  o,  was 
flush  with  the  surface  of  the  mercury  in  the 
bath  ;  the  distance  between  the  point  o  and  the 
level  of  the  mercury  G  was  measured  by  means 
of  the  cathetometer.  The  point  b  was  finally 
closed  with  wax  by  means  of  the  spoon  a,  and 
the  barometric  pressure  noted  at  this  moment. 
If  this  pressure  be  H',  the  pressure  in  the  reser- 
voir is  H'  —  h. 

The  reservoir  was  now  weighed  to  ascertain 
P,  the  weight  of  the  mercury  which  it  con- 
tained. It  was  then  completely  filled  with  mer- 
cury at  zero,  in  order  to  have  the  weight  P'  of 
the  mercury  in  the  reservoir  and  in  the  tube. 

If  5  be   the   coefficient  of  the  cubical  ex- 

pansion of  glass,  and  D  the  density  of  mercury  at  zero,  the  coefficient  a 
of  the  cubical  expansion  of  air  is  determined  in  the  following  manner  :  — 

P' 

The  volume  of  the  reservoir  and  of  the  tube  at  zero  is  —  ,  from  the  formula 


Fig.  291. 


P  =  VD  (126)  ;  consequently  this  volume  is 


— 


(0 


at  the  temperature  /°,  assuming,  as  is  the  case,  that  the  reservoir  and  tube 

expand  as  if  they  were  solid  glass.     But  from  the  formula  P  =  VD,  the  volume 

p/ p 

of  air  in  the  reservoir  at  zero,  and  under  the  pressure  H'  -  /?,  is  —       .       At 

the  same  pressure,  but  at  /°,  its  volume  would  be 
P'-P,          } 
D    ( 

and  by  Boyle's  law  (180),  at  the  pressure  H,  at  which  the  tube  was  sealed, 
this  volume  must  have  been 


7-?)  (l+a/)  (H'- 
DH 


(2) 


Now  the  volumes  represented  by  these  formulae,  (i)  and  (2),  are  each 
equal  to  the  volume  of  the  reservoir  and  the  tube  at  f  ;  they  are  therefore 
equal.  Removing  the  denominators,  we  have 


from  which  the  value  of  a  is  deduced. 


-334]  Air  Thermometer.  293 

The  means  of  a  great  number  of  experiments  between  zero  and  100°  and 
for  pressure  between  300  millimetres  and  500  millimetres,  gave  the  following 
numbers  for  the  coefficients  of  expansion  for  a  single  degree  : — 

Air     ....  0-003667  Carbonic  acid .  .  0-003710 

Hydrogen.         .         .  0*003661  Nitrous  oxide  .  .  0-003719 

Nitrogen    .         .         .  0-003661  Cyanogen         .  .  0-003877 

Carbonic  oxide .         .  0-003667  Sulphurous  acid  .  0-003903 

These  numbers,  with  which  the  results  obtained  by  Magnus  closely  agree, 
show  that  the  coefficients  of  expansion  of  the  permanent  gases  differ  very 
little  ;  but  that  they  are  somewhat  greater  in  the  case  of  the  more  easily 
condensible  gases,  such  as  carbonic  and  sulphurous  acids.  Regnault  has 
further  found  that,  at  the  same  temperature,  the  coefficient  of  expansion  of 
any  gas  increases  with  the  pressure  which  it  supports.  Thus,  while  the 
coefficient  of  expansion  of  air  under  a  pressure  of  no  mm.  is  0-003648,  under 
a  pressure  of  3655  mm.,  or  nearly  five  atmospheres,  it  is  0-003709. 

The  number  found  by  Regnault  for  the  coefficient  of  the  expansion  of 
air,  0-003667,  is  equal  to  ^-  =  ^  nearly  ;  and  if  we  take  the  coefficient  of  ex- 
pansion at  0-0036666  ...  it  may  be  represented  by  the  fraction  -3^ 
which  is  convenient  for  purposes  of  calculation. 

The  small  difference  in  the  expansibility  of  various  gases  may  be  ascribed 
to  the  circumstance  that  when  a  gas  is  heated  the  relative  positions  of  the 
atoms  in  the  molecules  are  thereby  altered  ;  and  a  certain  amount  of  internal 
work  is  required  for  this,  which  is  different  for  different  gases. 

334.  Air  thermometer. — The  air  thermometer  is  based  on  the  expan- 
sion of  air.  When  it  is  used  to  measure  small  differences  of  temperature,  it 
has  the  same  form  as  the  tube  used  by  Gay-Lussac  in  determining  the  ex- 
pansion of  air  (fig.  289),  that 'is,  a  capillary  tube  with  a  bulb  at  the  end.  The 
reservoir  being  filled  with  dry  air,  an  index  of  coloured  sulphuric  acid  is 
passed  into  the  tube  ;  the  apparatus  is  then  graduated  in  Centigrade  degrees 
by  comparing  the  positions  of  the  index  with  the  indications  of  a  mercurial 
thermometer.  Of  course  the  end  of  the  tube  must  remain  open  ;  otherwise, 
the  air  above  the  index  condensing  or  expanding  at  the  same  time  as  that  in 
the  bulb,  the  index  would  remain  stationary.  A  correction  must  be  made 
at  each  observation  for  the  atmospheric  pressure. 

When  considerable  variations  of  temperature  are  to  be  measured,  the 
tube  has  a  form  like  that  used  in  Regnault's  experiments  (figs.  290  and  291). 
By  experiments  made  as  described  in  article  333,  P,  P',  H,  H',  and  h  may 
be  found,  and  the  coefficients  a  and  8  being  known,  the  temperature  /  to 
which  the  tube  has  been  raised  is  readily  reduced  from  the  equation  (3).  / 

Regnault  found  that  the  air  and  the  mercurial  thermometer  agree  up  /> 
260°,  but  above  that  point  mercury  expands  relatively  more  than  air.  In 
cases  where  very  high  temperatures  are  to  be  measured,  the  reservoir  is 
made  of  platinum.  The  use  of  an  air  thermometer  is  seen  in  Dulong  and 
Petit's  experiment  (322);  it  was  by  such  an  apparatus  that  Pouillet  measured 
the  temperature  corresponding  to  the  colours  which  metals  take  when  heated 
in  a  fire,  and  found  them  to  be  as  follows  : — 


294 


Incipient  red 
Dull  red 
Cherry  red    . 


On  Heat. 

525°  C.      Dark  orange  . 

700  White     . 

900  Dazzling  white 


[334- 


iioo°C. 

1300 

1500 


A' 


In  the  measurement  of  high  temperatures  Deville  and  Troost  used  with 
advantage  the  vapour  of  iodine  instead  of  air,  and,  as  platinum  has  been 
found  to  be  permeable  to  gases  at  high  temperatures,  they  employed  porce- 
lain instead  of  that  metal. 

The  expansion  of  gases  has  been  determined  by  Jolly  by  means  of  a 
form  of  apparatus  which  is  also  a  convenient  form  of  air  thermometer  (fig. 
292).  A  quadrangular  post  rests  on  a  tripod  ;  on  one  side 
of  this  post  is  a  graduated  glass  scale,  while  in  the  two 
others  are  grooves  in  which  screw-blocks  A  and  A  can 
be  slid  up  and  down  and  adjusted  at  any  height. 

A  glass  bulb  a  is  prolonged  in  a  tube  bent  twice,  the 
end  of  which  is  provided  with  a  stopcock,  not  shown  in 
the  figure,  and  in  which  can  be  fitted  a  glass  tube  R  sup- 
ported by  the  block  A.  This  again  is  fitted  to  a  flexible 
india-rubber  tube,  at  the  other  end  of  which  is  an  open 
glass  tube  R/  fixed  to  the  block  A/.  This  tube  contains 
mercury. 

The  bulb  a  having  been  filled  with  dry  air>  the  stopcock 
is  closed,  the  tube  R  fixed,  and  the  stopcock  opened 
The  bulb  a  is  then  immersed  to  the  stem  in  melting  ice, 
and  when  it  is  supposed  that  the  temperature  is  stationary, 
the  tube  Rx  is  moved  up  and  down  until  the  mercury  in 
the  other  limb  is  at  a  mark  S.  The  difference  between 
the  levels  of  the  mercury  at  S  and  at  R'  is  noted.  If  the 
latter  is  higher  the  difference  is  added  to,  and  if  lower 
subtracted  from,  the  barometric  height  at  the  time,  to  give 
the  pressure  h  in  the  vessel  a. 

The  bulb  a  is  then  placed  in  a  space  at  -any  constant 
temperature,  and  the  same  operation  repeated  to  get  the 
.     pressure  hr     From  the  ratio  of  the  total  pressures   in  the  two  cases  we 
get  the  coefficient    of  expansion  from  the  formula  h  :  hl  =  I  +  at  :  i  +  at' . 
By  means  of  this  apparatus  Jolly  found  0-00366957  for  the  value  of  a. 
/      335-    Density   of  gases. — The  relative  density  of  a  gas,  or  its  specific 
/gravity,  is  the  ratio  of  the  weight  of  a  certain  volume  of  the  gas  to  that  of 
\    the  same  volume  of  air  ;  both  the  gas  and  the  air  being  at  zero  and  under  a 
\  pressure  of  760  millimetres. 

\  In  order,  therefore,  to  find  the  specific  gravity  of  a  gas,  it  is  necessary  to 
d^ermine  the  weight  of  a  certain  volume  of  this  gas  at  a  pressure  of  760 
millimetres,  and  a  temperature  of  zero,  and  then  the  weight  of  the  same 
volume  of  air  under  the  same  conditions.  For  this  purpose  a  large  globe  of 
about  two  gallons'  capacity  is  used,  the  neck  of  which  is  provided  with  a 
stopcock,  which  can  be  screwed  to  the  air-pump.  The  globe  is  first  weighed 
empty,  and  then  full  of  air,  and  afterwards  full  of  the  gas  in  question.  The 
weights  of  the  gas  and  of  the  air  are  obtained  by  subtracting  the  weight  of 
the  exhausted  globe  from  the  weight  of  the  globes  filled,  respectively,  with 


Fig.  292. 


-336]  Density  of  Gases.  295 

air  and  gas.  The  quotient,  obtained  by  dividing  the  latter  by  the  former, 
gives  the  specific  gravity  of  the  gas.  It  is  difficult  to  make  these  determina- 
tions at  the  same  temperature  and  pressure,  and  therefore  all  the  weights 
are  reduced  to  zero  and  the  normal  pressure  of  760  millimetres. 

The  gases  are  dried  by  causing  them  to  pass  through  drying  tubes  before 
they  enter  the  globe,  and  air  must  also  be  passed  over  potash  to  free  it  from 
carbonic  acid.  And  as  even  the  best  air-pumps  never  produce  a  perfect 
vacuum,  it  is  necessary  to  exhaust  the  globe  until  the  manometer  in  each 
case  marks  the  same  pressure. 

The  globe  having  been  exhausted,  dried  air  is  allowed  to  enter,  and  the 
process  is  repeated  several  times  until  the  globe  is  perfectly  dried.  It  is  then 
finally  exhausted  until  the  residual  pressure,  in  millimetres,  is  e.  The  weight 
of  the  exhausted  globe  is^.  Air,  which  has  been  dried  and  purified  by  passing 
through  potash  and  chloride  of  calcium  tubes,  is  then  allowed  to  enter 
slowly.  The  weight  of  the  globe  full  of  air  is  P.  If  H  is  the  barometric 
height  in  millimetres,  and  t°  the  temperature  at  the  time  of  weighing,  P  -p  is 
the  weight  of  the  air  in  the  globe  at  the  temperature  /,  and  the  pressure  H  -  e. 

To  reduce  this  weight  to  the  pressure  760  millimetres  and  the  tempera- 
ture zero,  let  a  be  the  coefficient  of  the  expansion  of  air,  and  8  the  coefficient 
of  the  cubical  expansion  of  glass.  From  Boyle's  law  the  weight,  which  is 

P  —  p  at  t°  and  a  pressure  of  H  -  £,  would  be  *  —  'IJLL    —  under  the  pressure 

760  milimetres  and  at  the  same  temperature  /°.  If  the  temperature  is  oc, 
the  capacity  of  the  globe  will  diminish  in  the  ratio  i  +  §/  to  i,  while  the 
weight  of  the  gas  increases  in  the  ratio  i  :  i  +  a/,  as  follows  from  the  problems 
in  Art.  332.  Consequently,  the  weight  of  the  air  in  the  globe  at  o°  and  at  the 
pressure  760  millimetres  will  be 


(i) 


Further,  let  a'  be  the  coefficient  of  expansion  of  the  gas  in  question  ;  let 
P'  be  the  weight  of  the  globe  full  of  gas  at  the  temperature  t'  and  the  pres- 
sure H',  and  let  p'  be  the  weight  of  the  globe  when  it  is  exhausted  to  the 
pressure  e  ;  the  weight  of  the  gas  in  the  globe  at  the  pressure  760  and  the 
temperature  zero  will  be 


Dividing  the  latter  formula  by  the  former  we  obtain  the  density 

D  =  (P'-^HH-gHi+a'QCi+M) 

"(P-/)  (H'-*)  (i  +a/)  (i  +d*'j"  / 

If  the  temperature  and  the  pressure  do  not  vary  during  the  experiment, 
H  =  H'  and  /  =  f  ;  whence  D  =  (^'  ~^Jl±^  ,  and  if  a  =  a',  D  = 


, 

(P-/)  (I  +a/)  P-/ 


336.    Regnault's    method    of   determining:   the    density    of 

Regnault  so  modified  the  above  method  that  many  of  the  corrections  may 
be  dispensed  with.     The  globe  in  which  the  gas  is  weighed  is  suspended 


296 


On  Heat. 


[336- 


from  one  pan  of  a  balance,  and  is  counterpoised  by  means  of  a  second  globe 
of  the  same  dimensions,  and  hermetically  sealed,  suspended  from  the  other. 
These  two  globes,  expanding  at  the  same  time,  always  displace  the  same 
quantity  of  air,  and  consequently  variations  in  the  temperature  and  pressure 
of  the  atmosphere  do  not  influence  the  weighing.  The  globe,  too,  is  filled 
with  the  air  or  with  the  gas,  at  the  temperature  of  zero.  This  is  effected  by 
placing  it  in  a  vessel  full  of  ice,  as  shown  in  fig.  293.  It  is  then  connected 
with  a  three-way  cock,  A,  by  which  it  may  be  connected  either  with  an  air- 
pump,  or  with  the  tubes  M  and  N,  which  are  connected  with  the  reservoir 
of  gas.  The  tubes  M  and  N  contain  substances  which  by  their  action  on 
the  gas  dry  and  also  purify  it. 

The  stopcock  A  being  so  turned  that  the  globe  is  only  connected  with 
the  air-pump,  a  vacuum  is  produced ;  by  means  of  the  same  cock,  the  con- 
nection with  the  pump  being  cut  off,  but  established  between  M  and  N,  the 


Fig.  293- 

gas  soon  fills  the  globe.  But  as  the  exhaustion  could  not  have  been  com- 
plete, and  some  air  must  have  been  left,  the  globe  is  again  exhausted  and 
the  gas  allowed  to  enter,  and  the  process  is  repeated  until  it  is  thought  all 
air  is  removed.  The  vacuum  being  once  more  produced,  a  differential 
barometer  (fig.  142),  connected  with  the  apparatus  by  the  tube  E,  indicates 
the  pressure  of  the  residual  rarefied  gas  e.  Closing  the  cock  B  and  de- 
taching A,  the  globe  is  removed  from  the  ice,  and  after  being  cleaned  is 
weighed. 

This  gives  the  weight  of  the  empty  globe  p  ;  it  is  again  replaced  in  the 
ice,  the  stopcock  A  adjusted,  and  the  gas  allowed  to  enter,  care  being  taken- 
to  leave  the  stopcocks  open  long  enough  to  allow  the  gas  in  the  globe  to  ac- 
quire the  pressure  of  the  atmosphere,  H,  which  is  marked  by  the  barometer.. 
The  stopcock  B  is  then  closed,  A  removed,  and  the  globe  weighed  with  the 
same  precautions  as  before.  This  gives  the  weight  P'  of  the  gas. 


-337]  Density  of  Gases  which  Attack  Metals.  297 

The  same  operations  are  then  repeated  on  this  globe  with  air,  and  two 
corresponding  weights  p  and  P  are  obtained.  The  only  correction  necessary 
is  to  reduce  the  weights  in  the  two  cases  to  the  standard  pressure  by  the 
method  described  in  the  preceding  paragraph.  The  correction  for  temperature 
is  not  needed,  as  the  gas  is  at  the  temperature  of  melting  ice.  The  ratio  of 
the  weight  of  the  gas  to  that  of  the  air  is  thus  obtained  by  the  formula 

P'-  # 


P-J» 

337.  Density  of  gases  which  attack  metals. — For  gases  which  attack 
the  ordinary  metals,  such  as  chlorine,  a  metal  stopcock  cannot  be  used,  and 
vessels  with  ground-glass  stoppers  are  substituted.  The  gas  is  introduced 
by  a  bent  glass  tube,  the  vessel  being  held  either  upright  or  inverted,  accord- 
ing as  the  gas  is  heavier  or  lighter  than  air  ;  when  the  vessel  is  supposed  to 
be  full,  the  tube  is  withdrawn,  the  stopper  inserted,  and  the  weight  taken- 
This  gives  the  weight  of  the  vessel  and  gas.  If  the  capacity  of  the  vessel 
be  measured  by  means  of  water,  the  weight  of  the  air  which  it  contains  is 
deduced,  for  the  density  of  air  at  o°  C.  and  760  millimetres  pressure  is  ^ 
that  of  distilled  water  under  the  same  circumstances.  The  weight  of  the 
vessel  full  of  air,  less  the  weight  of  the  contained  air,  gives  the  weight  of  the 
vessel  itself.  From  these  three  data — the  weight  of  the  vessel  full  of  the  gas,, 
the  weight  of  the  air  which  it  contains,  and  the  weight  of  the  vessel  alone — 
the  specific  gravity  of  the  gas  is  readily  deduced,  the  necessary  corrections 
being  made  for  temperature  and  pressure. 

Density  of  gases  at  zero  and  at  a  pressure  ofj6o  millimetres •,  that  of  air 
being  taken  as  unity. 

Air      Y'''v-  /«  .  roooo  Sulphuretted  hydrogen  -1912 

Hydrogen    .         .  .  0-0693  Hydrochloric  acid        .  -2540 

Ammoniacal  gas  .  .  0-5367  Protoxide  of  nitrogen  .  -5270 

Marsh  gas    .         .  .  0-5590  Carbonic  acid       .         .  "5291 

Carbonic  oxide     .  .  0-9670  Cyanogen     .         .         .  -8600 

Nitrogen       .         .  .  0-9714  Sulphurous  acid  .         .  2-2474 

Binoxide  of  nitrogen  .  1-0360  Chlorine       .         .         .  3-4400 

Oxygen         .         .  .  1*1057  Hydriodic  acid     .         .  4*4430 

Regnault  made  the  following  determinations  of  the  weight  of  a  litre  of  the 
most  important  gases  at  o°  C.  and  760  mm.  : — 

Air.        .         .     1-293187  grms.         Nitrogen          .     1-256157  grms. 
Oxygen  .         .     1-429802     „  Carbonic  acid     1-977414      „ 

Hydrogen       .     0-089578     „ 


298  On  Heat.  [338- 


CHAPTER  V. 

CHANGES   OF   CONDITION.      VAPOUR. 

338.  Fusion.  Its  laws. — The  only  phenomena  of  heat  with  which  we 
have  hitherto  been  engaged  have  been  those  of  expansion.  In  the  case  of 
solids  it  is  easy  to  see  that  this  expansion  is  limited.  For  in  proportion  as 
a  body  absorbs  a  larger  quantity  of  heat,  the  vis  viva  of  the  molecules  is 
increased,  and  ultimately  a  point  is  reached  at  which  the  molecular  attraction 
is  not  sufficient  to  retain  the  body  in  the  solid  state.  A  new  phenomenon  is 
then  produced  ;  melting  at  fusion  takes  place  ;  that  is,  the  body  passes  from 
the  solid  into  the  liquid  state. 

Some  substances,  however,  such  as  paper,  wood,  wool,  and  certain  salts, 
do  not  fuse  at  a  high  temperature,  but  are  decomposed.  Many  bodies  have 
long  been  considered  refractory — that  is,  incapable  of  fusion  ;  but,  in  pro- 
portion as  it  has  been  possible  to  produce  higher  temperatures,  their  number 
has  diminished.  Gaudin  succeeded  in  fusing  rock  crystal  by  means  of  a 
lamp  fed  by  a  jet  of  oxygen  ;  and  Despretz,  by  combining  the  effects  of  the 
sun,  the  voltaic  battery,  and  the  oxy-hydrogen  blow-pipe,  melted  alumina 
and  magnesia,  and  softened  carbon  so  as  to  be  flexible,  which  is  a  condition 
near  that  of  fusion. 

It  has  been  found  experimentally  that  the  fusion  of  bodies  is  governed  by 
the  two  following  laws  : — 

I.  Every  substance  begins  to  fuse  at  a   certain  temper  attire,  which  is 
invariable  for  each  substance,  if  the  pressure  be  constant. 

II.  Whatever  be  the  intensity  of  the  source  of  heat,  from  the  moment, 
fusion  begins,  the  temperature  of  the  body  ceases  to  rise,  and  remains  constant 

until  the  fusion  is  comj. 


Melting  points  of  certain  substances. 

Mercury     .         .  .  .-38-8°  Stearine    ....       60° 

Oil  of  Turpentine  .  .  —  27  White  wax        ...       65 

Bromine     .         .  .  .-12  Wood's  fusible  metal         .       68 

Ice     .         ,  ;      .  .  .  .     o  Stearic  acid       .        ,        .       70 

Butter         .         .  .  .  +  33  Sodium     ....       90 

Rubidium  .         .  .  -39  Rose's  fusible  metal .         .       94 

Phosphorus         .  .  .44  Sulphur     .         .         .         .114 

Spermaceti          .  .  -49  Indium      .         .         .         .176 

Potassium  .         .  .  -55  Tin    .         ...         .     228 

Margaric  acid    .  .  -57  Bismuth    .         .         .         .     264 


-339]  Influence  of  Pressure  on  the  Melting  Point. 


299 


Cadmium  . 
Lead 
Zinc                • 

.         .     321° 

•     335 

422 

Gold 
Copper 

.  1035' 
.  1054 
.  1  500 

Antimony 
Silver 

.   450 

•     954 

Platinum  . 
Iridium 

•  1775 
.  1950 

Fig.  294. 


Some  substances  pass  from  the  solid  to  the  liquid  state  without  showing 
any  definite  melting  point ;  for  example,  glass  and  iron  become  gradually 
softer  and  softer  when  heated,  and  pass  by  imperceptible  stages  from  the 
solid  to  the  liquid  condition.  This  intermediate  condition  is  spoken  of  as 
the  state  of  vitreous  fusion.  Such  substances  may  be  said  to  melt  at  the 
lowest  temperature  at  which  perceptible  softening  occurs,  and  to  be  fully 
melted  when  the  further  elevation  of  temperature  does  not  make  them  more 
fluid  ;  but  no  precise  temperature  can  be  given  as  their 
melting  points. 

The  determination  of  the  melting  point  of  a  body  is 
a  matter  of  considerable  importance  in  fixing  the  identity 
of  many  chemical  compounds,  and  is  moreover  a  point 
of  frequent  practical  application  in  determining  the  com- 
mercial value  of  tallow  and  other  fats. 

It  is  done  as  follows  : — A  portion  of  the  substance  is 
melted  in  a  watch-glass,  and  a  small  quantity  of  it  sucked 
into  a  fine  capillary  tube,  AC,  the  end  of  which  is  then 
sealed.  This  tube  is  then  placed  in  a  bath*  of  clear  water 
(fig.  294)  in  which  is  a  thermometer,  and  the  tempera- 
ture of  the  bath  is  gradually  raised  until  the  substance 
is  completely  melted,  which  from  its  small  mass  is  very 
easily  observed.  The  bath  is  then  allowed  to  cool,  and 
the  solidifying  point  noted  ;  and  the  mean  of  the  two  is  taken  as  the  true 
melting  point. 

339.  Influence  of  pressure  on  the  melting-  point. — Thomson  and 
Clausius  have  deduced  from  the  principles  of  the  mechanical  theory  of  heat 
that,  with  an  increase  of  pressure,  the  melting  point  of  a  body  must  be  raised. 
All  bodies  which  expand  on  passing  from  the  solid  to  the  liquid  state  have 
to  perform  external  work— namely,  to  raise  the  pressure  of  the  atmosphere 
by  the  amount  of  this  expansion.  Under  ordinary  circumstances,  the 
amount  of  external  work  which  solids  and  liquids  thus  perform  is  so  small 
that  it  may  be  neglected.  But  if  the  external  pressure  be  increased,  the 
power  of  overcoming  it  can  only  be  obtained  by  an  increase  of  vis  viva  of  the 
molecules.  This  increase  can  do  more  work  ;  the  temperature  of  fusion  as 
well  as  the  heat  of  fusion  are  both  increased.  Bunsen  examined  the  influence 
of  pressure  on  the  melting  point  by  means  of  the  apparatus  represented  in 
fig.  295,  in  which  acb  is  a  thick  tube  about  the  thickness  of  a  straw  in  the 
clear,  in  the  parts  ca  and  the  bent  part  b.  The  whole  tube  having  been  filled 
with  mercury,  it  was  sealed  at  «,  and  then  a  small  quantity  was  driven  out  at 
b  and  some  of  the  substance  introduced  ;  the  end  b  was  then  sealed  and  a 
opened,  and  the  whole  tube  gently  warmed  so  as  to  expel  some  mercury,  upon 
which  a  was  again  hermetically  sealed. 

When  the  tube  was  placed  in  a  bath  of  warm  water  a  little  above  the 


300 


On  Heat. 


[339- 


melting  point  ol  the  body,  the  mercury  expanded  and  a  pressure  resulted'. 
which  could  be  accurately  measured  from  the  diminution  in  volume  of  the- 
air  in  ca,  which  was  carefully  calibrated  for  this  purpose.  By 
carefully  raising  or  lowering  the  instrument  in  the  water,  the 
pressure  could  be  increased  or  diminished  at  will.  It  only  then 
remained  to  observe  the  temperature  at  which  the  substance 
solidified  and  the  corresponding  pressure  at  that  moment.  In 
this  way  Bunsen  found  that  spermaceti,  Vhich  melts  at  48° 
under  a  pressure  of  i  atmosphere,  melts  at  51°  under  a  pressure 
of  156  atmospheres.  Hopkins  found  that  spermaceti  melted  at 
60°  under  a  pressure  of  519  atmospheres,  and  at  80°  under  792 
atmospheres  ;  the  melting-point  of  sulphur  under  these  pres- 
sures was  respectively  135°  and  141°. 

But  in  the  case  of  those  bodies  which  contract  on  passing 
from  the  solid  to  the  liquid  state,  and  of  which  water  is  the  best 
example,  the  reverse  is  the  case.  Melting  ice  has  no  external 
work  to  perform,  since  it  has  no  external  pressure  to  raise  ,- 
on  the  contrary,  in  melting,  it  assimilates  external  work,  which, 
transformed  into  heat,  renders  a  smaller  quantity  of  heat  neces- 
sary ;  the  external  work  acts  in  the  same  direction  as  the  internal 
heat — namely,  in  breaking  up  the  crystalline  aggregates.  Yet 
these  differences  of  temperature  must  be  but  small,  for  the 
molecular  forces  in  solids  preponderate  far  over  the  external 
pressure  ;  the  internal  work  is  far  greater  than  the  external. 
Fig.  295.  Sir  W.  Thomson  found  that  pressures  of  8*1  and  16-8  atmo- 

spheres lowered  the  melting  point  of  ice  by  0-059°  and  0-126° 
respectively.  These  results  justify  the  theoretical  previsions  of  Prof.  J. 
Thomson,  according  to  which  an  increase  of  pressure  of  n  atmospheres 
lowers  the  melting  point  of  ice  by  0-0074^°  C,  so  that  a  pressure  of  135 
atmospheres,  or  about  2,000  pounds  to  the  square  inch,  would  lower  the 
melting  point  i°  C. 

340.  Alloys.  Fluxes. — Alloys  are  generally  more  fusible  than  any  of 
the  metals  of  which  they  are  composed  ;  for  instance,  an  alloy  of  5  parts  of 
tin  and  I  of  lead  fuses  at  194°.  The  alloy  known  as  Rose's  fusible  metal^ 
which  consists  of  4  parts  of  bismuth,  I  part  of  lead,  and  I  of  tin,  melts  at 
94°,  and  an  alloy  of  I  or  2  parts  of  cadmium  with  2  parts  of  tin,  4  parts  of 
lead,  and  7  or  8  parts  of  bismuth,  known  as  Wood's  fusible  metal,  melts 
between  66°  and  71°  C.  Fusible  alloys  are  of  extended  use  in  soldering  and 
in  taking  casts.  Steel  melts  at  a  lower  temperature  than  iron,  though  it 
contains  carbon,  which  is  almost  completely  infusible. 

Mixtures  of  the  fatty  acids  melt  at  lower  temperatures  than  the  pure  acids. 
A  mixture  of  the  chlorides  of  potassium  and  of  sodium  fuses  at  a  lower  tem- 
perature than  either  of  its  constituents  ;  the  same  is  the  case  with  a  mixture 
of  the  carbonates  of  potassium  and  sodium,  especially  when  they  are  mixed 
in  the  proportion  of  their  chemical,  equivalents. 

An  application  of  this  property  is  met  with  in  the  case  o>i fluxes,  which  are 
much  used  in  metallurgical  operations.  They  consist  of  substances  which, 
when  added  to  an  ore,  partly  by  their  chemical  action,  help  the  reduction  of 


-343]  Solidification.  301 

the   substance  to  the  metallic   state,  and,  partly,  by  presenting  a  readily 
fusible  medium,  promote  the  formation  of  a  regulus. 

341.  Latent  beat. — Since,  during  the  passage  of  a  body  from  the  solid 
to  the  liquid  state,  the  temperature  remains  constant  until  the  fusion  is  com- 
plete, whatever  be  the  intensity  of  the  source  of  heat,  it  must  be  concluded 
that,  in  changing  their  condition,  bodies  absorb  a  considerable  amount  of 
heat,  the  only  effect  of  which  is  to  maintain  them  in  the  liquid  state.     This 
iheat,  which  is  not  indicated  by  the  thermometer,  is  called  latent  heat  or 
.latent  heat  of  fusion,  an  expression  which,  though  not  in  strict  accordance 
with  modern  ideas,  is  convenient  from  the  fact  of  its  universal  recognition 
,and  employment  (461). 

An  idea  of  what  is  meant  by  latent  heat  may  be  obtained  from  the  follow- 
ing experiment : — If  a  pound  of  water  at  80°  is  mixed  with  a  pound  of  water 
at  zero,  the  temperature  of  the  mixture  is  40°.  But  if  a  pound  of  pounde 
at  zero  is  mixed  with  a  pound  of  water  at  80°,  the  ice  melts  and  two 
of  water  at  zero  are  obtained.  Consequently  the  mere  change  of  a  poi 
ice  to  a  pound  of  water  at  the  same  temperature  requires  as  much  heat 
will  raise  a  pound  of  water  through  80°.  This  quantity  of  heat  represents 
the  latent  heat  of  the  fusion  of  ice,  or  the  latent  heat  of  water. 

Every  liquid  has  its  own  latent  heat,  and  in  the  chapter  on  Calorimetry 
Ave  shall  show  how  this  is  determined. 

342.  Solution. — A  body  is  said  to  dissolve  when  it  becomes  liquid  in  con- 
sequence of  an  attraction  between  its  molecules  and  those  of  a  liquid.     Gum 
arabic,  sugar,  and  most  salts  dissolve  in  water.     The  weight  dissolved  gene- 
rally increases  with  the  temperature.     When  a  liquid  has  dissolved  as  much 
-as  it  can  at  a  particular  temperature  it  is  said  to  be  saturated. 

During  solution,  as  well  as  during  fusion,  a  certain  quantity  of  heat  always 
becomes  latent,  and  hence  it  is  that  the  solution  of  a  substance  usually 
produces  a  diminution  of  temperature.  In  certain  cases,  however,  instead 
•of  the  temperature  being  lowered,  it  actually  rises,  as  when  caustic  potash  is 
dissolved  in  water.  This  depends  upon  the  fact  that  two  simultaneous 
and  contrary  phenomena  are  produced.  The  first  is  the  passage  from  the 
solid  to  the  liquid  condition,  which  always  lowers  the  temperature.  The 
second  is  the  chemical  combination  of  the  body  dissolved  with  the  liquid, 
and  which,  as  in  the  case  of  all  chemical  combinations,  produces  an  increase 
•  of  temperature.  Consequently,  as  the  one  or  the  other  of  these  effects  pre- 
dominates, or  as  they  are  equal,  the  temperature  either  rises  or  sinks,  or 
remains  constant. 

343.  Solidification. — Solidification   or   congelation  is  the  passage  of  a 
body  from  the  liquid  to  the  solid  state.     This  phenomenon  is  regulated  by 
the  two  following  laws  : — 

I.  Every  body,  under  the  same  pressure,  solidifies  at  a  fixed  temperature, 
which  is  the  same  as  that  of  fusion. 

II.  From  the  commencement  to  the  end  of  the  solidification,  the  tempera- 
ture of  a  liquid  remains  constant. 

Certain  bodies,  more  especially  some  of  the  fats,  present  an  exception  to 
the  first  law,  in  so  far  that  by  repeated  fusions  they  seem  to  undergo  a 
molecular  change  which  alters  their  melting  point. 


302  On  Heat.  [343- 

The  second  law  is  the  consequence  of  the  fact  that  the  latent  heat  ab- 
sorbed during  fusion  becomes  free  at  the  moment  of  solidification. 

Many  liquids,  such  as  alcohol,  ether,  and  bisulphide  of  carbon,  do  not 
solidify  even  at  the  lowest  known  temperature.  Despretz,  by  the  cold  pro- 
duced by  a  mixture  of  liquid  protoxide  of  nitrogen,  solid  carbonic  acid,  and 
ether,  reduced  alcohol  to  such  a  consistence  that  the  vessel  containing  it 
could  be  inverted  without  losing  the  liquid. 

344.  Crystallisation. — Generally   speaking,   bodies  which    pass    slowly 
from  the  liquid  to  the  solid  state  assume  regular  geometrical  forms,  such  as 
the  cube,  prisms,  rhombohedra,  £c.  ;  these  are  called  crystals.     If  the  crys- 
tals are  formed  from  a  body  in  fusion,  such  as  sulphur  or  bismuth,  the 
crystallisation  is  said  to  take  place  by  the  dry  way.     The  crystallisation  is 
said  to  be  by  the  moist  way  when  it  takes  place  owing  to  the  slow  evapo- 

of  a  solution  of  a  salt,  or  when  a  solution  saturated  at  a  higher 
,  is  allowed  to  cool  slowly.     Snow,  ice,  and  many  salts  present 
of  crystallisation. 

345.  Retardation  of  the  point  of  solidification. — The  freezing  point  of 
pure  water  can  be  diminished  by  several  degrees,  if  the  water  be  previously 

freed  from  air  by  boiling  and  be  then  kept  in  a  perfectly  still 
place.  In  fact,  it  may  be  cooled  to  -15°  C.,  and  even  lower,  with- 
out freezing.  But  when  it  is  slightly  agitated,  the  liquid  at  once 
solidifies.  This  may  be  conveniently  shown  by  means  of  the 
apparatus  represented  in  fig.  296,  which  consists  of  a  delicate 
thermometer  round  the  bulb  of  which  is  a  wider  one  containing 
some  water.  Before  sealing  at  a  the  whole  outside  bulb  was 
filled  with  water,  which  was  then  boiled  out  and  sealed  so  that 
over  the  water  the  space  is  quite  empty. 

The  vessel  is  placed  in  snow  at  o°  and  then  in  alcohol  cooled 
to  -6°  or  -8°.  The  thermometer  sinks  a  few  degrees,  but  at 
once  rises  to  zero  when  the  water  in  the  bulb  solidifies.  The 
smaller  the  quantity  of  liquid,  the  lower  is  the  temperature  to  which 
it  can  be  cooled,  and  the  greater  the  mechanical  disturbance  it 
supports  without  freezing.  Fournet  has  observed  the  frequent 
occurrence  of  mists  formed  of  particles  of  liquid  matter  suspended 
in  an  atmosphere  whose  temperature  was  10°  or  even  15°  below 
zero. 

A  very  rapid   agitation    also   prevents    the   formation  of  ice. 
The   same   is    the    case   with   all    actions    which,    hindering   the 
molecules  in  their  movements,  do  not  permit  them  to  arrange 
themselves   in   the    conditions    necessary   for    the    solid    state. 
Despretz  was  able  to  lower  the  temperature  of  water  contained  in 
fine    capillary   tubes   to    -20°   without    their   solidifying.      This 
experiment   shows   how  it  is  that  plants  in   many  cases  do  not 
become  frozen  even  during  severe  cold,  as  the  sap  is  contained 
in  very  fine  capillary  vessels.     Finally,  Mousson  found  that  a 
powerful   pressure   not   only   retards   the  freezing  of  water,  but 
Fig.  296.      prevents  its   complete  solidification.     In  this  case   the  pressure 
opposes  the  tendency  of  the  water  to  expand  on  freezing,  and  thus  virtu- 
ally lowers  the  point  of  solidification. 


-346]  Change  of  Volume  on  Solidification  and  Liquefaction.     303 

If  water  contains  salts,  or  other  foreign  bodies,  its  freezing  point  is 
lowered.  Sea  water  freezes  at  —2-5°  to  -3°  C.  ;  the  ice  which  forms  is  quite 
pure,  and  a  saturated  solution  remains.  In  Finland  advantage  is  taken  of 
this  property  to  concentrate  sea  water  for  the  purpose  of  extracting  salt 
from  it.  If  water  contains  alcohol,  precisely  analogous  phenomena  are 
observed ;  the  ice  formed  is  pure,  and  practically  all  the  alcohol  is  con- 
tained in  the  residue. 

Dufour  has  observed  some  very  curious  cases  of  liquids  cooled  out  of 
contact  with  solid  bodies.  His  mode  of  experimenting  was  to  place  the 
liquid  in  another  of  the  same  specific  gravity  but  of  lower  melting  point,  and 
in  which  it  is  insoluble.  Drops  of  water,  for  instance,  suspended  in  a 
mixture  of  chloroform  and  oil,  usually  solidified  between  —4°  and  -  12°, 
while  still  smaller  globules  cooled  down  to  -  18°  or  -20°.  Contact  with  a 
fragment  of  ice  immediately  set  up  congelation.  Globules  of  sulphur  (which 
solidifies  at  115°)  remained  liquid  at  40°;  and  globules  of  phospj 
(solidifying  point  42°.)  at  20°. 

When  a  liquid  solidifies  after  being  cooled  below  its  normal  freezing  point, 
the  solidification  takes  place  very  rapidly,  and  is  accompanied  by  a  disen- 
gagement of  heat,  which  is  sufficient  to  raise  its  temperature  from  the  point 
at  which  solidification  begins  up  to  its  ordinary  freezing  point.  This  is  well 
seen  in  the  case  of  hyposulphite  of  sodium,  which  melts  in  its  own  water  of 
crystallisation  at  45°,  and  when  carefully  cooled  will  remain  liquid  at  the 
ordinary  temperature  of  the  atmosphere.  If  it  then  be  made  to  solidify  by 
agitation,  or  by  adding  a  small  fragment  of  the  solid  salt,  the  rise 
of  temperature  is  distinctly  felt  by  the  hand.  In  this  case  the  heat 
which  had  become  latent  in  the  process  of  liquefaction,  again 
becomes  free,  and  a  portion  of  the  substance  remains  melted  ;  for 
it  is  kept  liquid  by  the  heat  of  solidification  of  that  which  has 
solidified. 

346.  Change  of  volume  on  solidification  and  liquefaction. — 
The  rate  of  expansion  of  bodies  generally  increases  as  they  ap- 
proach their  melting  points,  and  is  in  most  cases  followed  by 
a  further  expansion  at  the  moment  of  liquefaction,  so  that  the 
liquid  occupies  a  greater  volume  than  the  solid  from  which  it  is 
formed.  The  apparatus  represented  in  fig.  297  is  well  adapted 
for  exhibiting  this  phenomenon.  It  consists  of  a  glass  tube,  ab, 
containing  water  or  some  other  suitable  liquid,  to  which  is  care- 
fully fitted  a  cork  with  a  graduated  glass  tube  c.  This  forms,  in 
fact,  a  thermometer,  and  the  values  of  the  degrees  on  the  tube  c 
are  determined  in  terms  of  the  capacity  of  the  whole  apparatus.  A 
known  volume  of  the  substance  is  placed  in  the  tube  aa  and  the 
cork  inserted  ;  the  apparatus  is  then  placed  in  a  space  at  a  known 
temperature  very  little  below  the  melting  point  of  the  body  in 
question,  until  it  has  acquired  its  temperature,  and  the  position  of 
the  liquid  in  c  is  noted.  The  temperature  is  then  allowed  to  rise 
slowly,  and  the  position  noted  when  the  melting  is  complete. 
Knowing  then  the  difference  in  the  two  readings  and  the  volume 
of  the  substance  under  experiment,  and  making  a  correction  for  the  expan- 
sion of  the  liquid  and  of  the  glass,  it  is  easy  to  deduce  the  increase  due  to 


Fig.  297. 


304  On  Heat.  [346- 

the  melting  alone.  Phosphorus,  for  instance,  increases  about  3*4  per  cent, 
on  liquefaction  ;  that  is,  100  volumes  of  solid  phosphorus  at  44°  (the  melting 
point)  become  103-4  at  the  same  temperature  when  melted.  Sulphur 
expands  about  5  per  cent,  on  liquefying,  and  stearic  acid  about  n  per 
cent. 

Water  presents  a  remarkable  exception  ;  it  expands  at  the  moment  of 
solidifying,  or  contracts  on  melting,  by  about  10  per  cent.  One  volume  of 
ice  at  o°  gives  0-9178  of  water  at  o°,  or  i  volume  of  water  at  o°  gives 
1*102  of  ice  at  the  same  temperature.  In  consequence  of  this  expansion, 
ice  floats  on  the  surface  of  water.  According  to  Dufour,  the  specific 
gravity  of  ice  is  0-9178  ;  Bunsen  found  for  ice  which  had  been  freed  from 
water  by  boiling  the  somewhat  smaller  number  0-91674. 

The  increase  of  volume  in  the  formation  of  ice  is  accompanied  by  an 
expansive  force  which  sometimes  produces  powerful  mechanical  effects,  of 
the  bursting  of  water-pipes  and  the  breaking  of  jugs  containing  water 

familiar  examples.  The  splitting  of  stones,  rocks,  -and  the  swelling  up 
of  moist  ground  during  frost,  are  caused  by  the  fact  that  water  penetrates 
into  the  pores  and  there  becomes  frozen  ;  in  short,  the  great  expansion  of 
water  on  freezing  is  the  most  active  and  powerful  agent  of  disintegration  on 
the  earth's  surface. 

The  expansive  force  of  ice  was  strikingly  shown  by  some  experiments  of 
Major  Williams,  in  Canada.  Having  quite  filled  a  1 3-inch  iron  bomb-shell 
with  water,  he  firmly  closed  the  touch-hole  with  an  iron  plug  weighing  three 
pounds  and  exposed  it  in  this  state  to  the  frost.  After  some  time  the  iron 
plug  was  forced  out  with  a  loud  explosion,  and  thrown  to  a  distance  of  41 5  feet, 
and  a  cylinder  of  ice  8  inches  long  issued  from  the  opening  (fig.  298).  In 
another  case  the  shell  burst  before  the  plug  was  driven  out,  and  in  this  case 
a  sheet  of  ice  spread  out  all  round  the  crack.  It  is  probable  that  under  the 
great  pressure  some  of  the  water  still  remained  liquid  up  to  the  time  at 
which  the  resistance  was  overcome ;  that  it  then  issued 
from  the  shell  in  a  liquid  state,  but  at  a  temperature 
below  o°,  and  therefore  instantly  began  to  solidify  when 
the  pressure  was  removed,  and  thus  retained  the  shape 
of  the  orifice  whence  it  issued. 

Cast-iron,  bismuth,  and  antimony  expand  on  solidi- 
Fig  298  fymg>  like  water,  and  can  thus  be  used  for  casting ;  but 

gold,  silver,  and   copper  contract,  and   hence   coins   of 
these  metals  cannot  be  cast,  but  must  be  stamped  with  a  die. 

347.  Freezing-  mixtures. — The  absorption  of  heat  in  the  passage  of 
bodies  from  the  solid  to  the  liquid  state  has  been  used  to  produce  artificial 
cold.  This  is  effected  by  mixing  together  bodies  which  have  an  affinity  for 
each  other,  and  of  which  one  at  least  is  solid,  such  as  water  and  a  salt,  ice 
and  a  salt,  or  an  acid  and  a  salt.  Chemical  affinity  accelerates  the  fusion  : 
the  portion  which  melts,  robs  the  rest  of  the  mixture  of  a  large  quantity  of 
sensible  heat,  which  thus  becomes  latent.  In  many  cases  a  very  consider- 
able diminution  of  temperature  is  produced. 

The  following  table  gives  the  names  of  the  substances  mixed,  their  pro- 
portions, and  the  corresponding  diminutions  of  temperature  : — 


-348]  Gut /trie's  Researches.  305 

Parts  Reduction  of 

Substances  by  weight  temperature 

Sulphate  of  sodium  8  |  0  .  o 

r  1  1     1  •  •     1  /  ~h     IO         tO       "~~    I/ 

Hydrochloric  acid  .         .         .         .         5  ' 
Pounded  ice  or  snow       .  2  • 

„  ,  >  +  IO    tO  —  Io 

Common  salt I 

Sulphate  of  sodium         ...  3 

Dilute  nitric  acid    ....  2 

Sulphate  of  sodium         .         .         .  6  \ 

Nitrate  of  ammonium     .         .         .  5^  +io°to-26° 

Dilute  nitric  acid    .         .         .         .  4 ' 

Phosphate  of  sodium      .         .         .  g{  +  io°to-2Q0 

Dilute  nitric  acid    .         .         .         .  4  | 

If  the  substances  taken  be  themselves  previously  cooled  down,  a  still 
more  considerable  diminution  of  temperature  is  occasioned. 

Freezing  mixtures  are  frequently  used  in  chemistry,  in  physics,  and  in 
domestic  economy.  One  form  of  the  portable  ice-making  machines  which 
have  come  into  use  during  the  last  few  years  consists  of  a  cylindrical 
metallic  vessel  divided  into  four  concentric  compartments.  In  the  central 
•one  is  placed  the  water  to  be  frozen  ;  in  the  next  there  is  the  freezing 
mixture,  which  usually  consists  of  sulphate  of  sodium  and  hydrochloric  acid  ; 
6  pounds  of  the  former  and  5  of  the  latter  will  make  5  to  6  pounds  of  ice  in 
an  hour.  The  third  compartment  also  contains  water,  and  the  outside  one 
^contains  some  badly-conducting  substance,  such  as  cotton,  to  cut  off  the 
influence  of  the  external  temperature.  The  best  effect  is  obtained  when 
pretty  large  quantities  (2  or  3  pounds)  of  the  mixture  are  used,  and  when 
they  are  intimately  mixed.  It  is  also  advantageous  to  use  the  machines  for 
a  series  of  successive  operations. 

348.  Guthrie's  researches. — It  appears  from  recent  experiments  of 
•Guthrie,  that  what  are  called  freezing  mixtures  may  be  divided  into  two 
classes,  namely  those  in  which  one  of  the  constituents  is  liquid  and  those  in 
which  both  are  solid.  The  temperature  indicated  by  the  thermometer 
placed  in  a  freezing  mixture  is,  of  course,  due  to  the  loss  of  heat  by  the 
thermometer  to  the  liquefying  freezing  mixture,  and  is  measured  by  the  rate 
of  such  loss.  The  quantity  of  heat  absorbed  by  the  freezing  mixture  is 
obviously  the  heat  required  to  melt  the  constituents,  together  with  ( + )  the 
heat  of  combination  of  the  constituents.  When  one  constituent  is  liquid, 
as  when  hydrochloric  acid  is  added  to  ice,  then  a  lower  temperature  is  got 
by  previously  cooling  the  hydrochloric  acid.  There  is  no  advantage  in 
cooling  the  ice.  But  when  both  constituents  are  solid,  as  in  the  case  of  the 
ice-salt  freezing  mixture,  there  is  no  advantage  to  be  gained  by  cooling  one 
or  both  constituents.  Within  very  wide  limits  it  is  also  in  the  latter  case  a 
matter  of  indifference  as  to  the  ratio  between  the  constituents.  Nor  does  it 
matter  whether  the  ice  be  finely  powdered  as  snow  or  in  pieces  as  large  as 
a  pea. 

The  different  powers  of  various  salts  when  used  in  conjunction  with  ice 
as  freezing  mixtures,  appear  to  have  remained  unexplained  until  Guthrie 
showed  that,  with  each  salt,  there  is  always  a  minimum  temperature  below 
which  it  is  impossible  for  an  aqueous  solution  of  any  strength  of  that  salt  to 

X 


3o6  On  Heat.  [348- 

exist  in  the  liquid  form  ;  that  there  is  a  certain  strength  of  solution  for  each 
salt  which  resists  solidification  the  longest,  that  is,  to  the  lowest  temperature. 
Weaker  solutions  give  up  ice  on  being  cooled,  stronger  solutions  give  up  the 
salt  either  in  the  anhydrous  state  or  in  combination  with  water.  That 
particular  strength  of  a  particular  salt,  which  resists  solidification  to  the 
lowest  temperature,  is  called  by  Guthrie  a  cryohydrate.  It  is  of  such  a 
strength  that  when  cooled  below  o°  C.  it  solidifies  as  a  whole  ;  that  is,  the 
ice  and  the  salt  solidify  together  and  form  crystals  of  constant  composition 
and  constant  melting  and  the  same  solidifying  temperatures.  The  liquid 
portion  of  a  freezing  mixture,  as  long  as  the  temperature  is  at  its  lowest,  is, 
indeed,  a  melted  cryohydrate.  The  slightest  depression  of  temperature  below 
this  causes  solidification  of  the  cryohydrate,  and  hence  the  temperature  can 
never  sink  below  the  solidifying  temperature  of  the  cryohydrate. 

Guthrie  has  also  shown  that  colloid  bodies,  such  as  gum  and  gelatine, 
neither  raise  the  boiling  point  of  water  nor  depress  the  solidifying  point,  nor 
can  they  act  as  elements  in  freezing  mixtures. 

VAPOURS.      MEASUREMENT   OF  THEIR  TENSION. 

349.  Vapours. — We  have  already  seen  (146)  that  vapours  are  the  aeriform 
fluids   into   which  volatile    substances,  buch   as   ether,  alcohol,  water,  and 
mercury,  are  changed  by  the  absorption; of  heat.      Volatile  liqitids  are  those 
which  thus  possess  the  property  of  passing  into  the  aeriform  state,  andy^mf 
liquids  are  those  which  do  not  form  vapours  at  any  temperature  without  under- 
going chemical  decomposition,  such  as  the  fatty  oils.     There  are  many  solids, 
such   as   ice,  arsenic,  camphor,  and  in  general  all  odoriferous   solid   sub- 
stances, which  can  directly  form  vapours  without  first  becoming  liquid. 

Vapours  are  transparent  like  gases,  and  generally  colourless  ;  there  are- 
only  a  few  coloured  liquids  which  also  give  coloured  vapours. 

350.  Vaporisation. — The  passage  of  a  liquid  into  the  gaseous  state  is- 
designated  by  the  general  term  vaporisation ;  the  term  evaporation  espe- 
cially refers  to  the  slow  production  of  vapour  at  the  free  surface  of  a  liquid, 
and  boiling  to  its  rapid  production  in  the  mass  of  the  liquid  itself.     We  shall 
presently  see  (356)  that  at  the  ordinary  atmospheric  pressure,  ebullition,  like 
fusion,  takes  place   at  a  definite  temperature.     This  is  not   the   case  with 
evaporation,  which  takes  place  even  with  the  same  liquid  at  very  different  tem- 
peratures, although  the  formation  of  a  vapour  seems  to  cease  below  a  certain 
point.     Mercury,  for  example,  gives  no  vapour  below  — 10°,  nor  sulphuric 
acid  below  30°. 

351.  Elastic   force   of  vapour.— Like  gases,  vapours   have  a  certain 
elastic  force,  in  virtue  of  which  they  exert  pressures  on  the  sides  of  vessels  in 
which  they  are  contained.     The  elastic  force  of  vapour  may  be  demonstrated 
by  the  following  experiment : — A  quantity  of  mercury  is  placed  in  a  bent 
glass  tube  (fig.  299),  the  shorter  leg  of  which  is  closed  ;  a  few  drops  of  ether 
are  then  passed  into  the  closed  leg  and  the  tube  immersed  in  a  water  bath  at 
a  temperature  of  about  45°.     The  mercury  then  sinks  slowly  in  the  short 
branch,  and  the  space  ab  is  filled  with  a  gas  which  has  all  the  appearance  of 
air  and  whose  elastic  force  counterbalances  the  pressure  of  the  column  of 
mercury  cd^  and  the  atmospheric  pressure  on  d.     This  gas  is  the  vapour  of 


-353] 


Saturated  Vapour.     Maximum  of  Tension. 


30; 


ether.  If  the  water  be  cooled,  or  if  the  tube  be  removed  from  the  bath,  the 
vapour  which  fills  the  space  ab  disappears,  and  the  drop  of  ether  is  reproduced. 
If,  on  the  contrary, 
the  bath  be  heated  still 
higher,  the  level  of  the 
mercury  descends  be- 
low />,  indicating  an 
increase  in  the  elastic 
force  of  the  vapour. 
V/^352.  Formation  of 
vapour  in  a  vacuum. 
— In  the  previous  ex- 
periment the  liquid 
changed  very  slowly 
into  the  vaporous  con- 
dition ;  the  same  is 
the  case  when  a  liquid 
is  freely  exposed  to 
the  air.  In  both  cases 
the  atmosphere  is  an 
obstacle  to  the  vapori- 
sation. In  a  vacuum 
there  is  no  resistance,  vVk^JI 

and  the   formation    of 
vapours     is     instanta- 
neous,   as   is    seen    in      fj 
the    following    experi- 
ment :  — Four      baro-  Fig.  299.  Fig.  300. 
meter  tubes,  filled  with 

mercury,  are  immersed  in  the  same  trough,  fig.  300.  One  of  them,  A, 
serves  as  a  barometer,  and  a  few  drops  of  water,  alcohol,  and  ether  are  re- 
spectively introduced  into  the  tubes  B,  C,  D.  When  the  liquids  reach  the 
vacuum,  a  depression  of  the  mercury  is  at  once  produced.  And  as  this 
depression  cannot  be  produced  by  the  weight  of  the  liquid,  which  is  an 
extremely  small  fraction. of  the  weight  of  the  displaced  mercury,  it  must  be 
due  to  the  formation  of  some  vapour  whose  elastic  force  has  depressed  the 
column  of  mercury. 

The  experiment  also  shows  that  the  depression  is  not  the  same  in  all  the 
tubes  ;  it  is  greater  in  the  case  of  alcohol  than  of  water,  and  greater  with 
ether  than  with  alcohol.  We  consequently  obtain  the  two  following  laws  of 
the  formation  of  vapours  : — 

I.  In  a  vacuum  all  volatile  liquids  are  instantaneously  converted  into 
vapour. 

II.  At  the  same  temperature  the    vapours  of  different  liquids   have 
different  elastic  forces. 

For  example,  at  20°  the  tension  of  ether  vapour  is  25  times  as  great  as 
that  of  aqueous  vapour. 

>/  353.  Saturated  vapour.  Maximum  of  tension. — When  a  very  small 
quantity  of  a  volatile  liquid,  such  as  ether,  is  introduced  into  a  barometer 

x  2 


308 


On  Heat. 


[353- 


tube,  it  is  at  once  completely  vaporised,  and  the  mercurial  column  is  not 
depressed  to   its   full  extent  ;    for  if  some  more   ether  be   introduced   the 
depression  increases.     By  continuing  the  addition  of  ether,  it  finally  ceases 
to  vaporise,  and  remains  in  the  liquid  state.     There  is,  therefore,  for  a  cer- 
tain temperature,  a  limit  to  the  quantity  of  vapour 
which  can  be  formed  in  a  given  space.    This  space 
is  accordingly  said  to  be  saturated.    Further,  when 
the  vaporisation  of  the  ether  ceases,  the  depression 
of  the  mercurial  column  stops.     And  hence  there 
is  a  limit  to  the   tension  of  the  vapour,  a  limit 
which,  as  we  shall  presently  see  (354),  varies  with 
the  temperature. 

To  show  that,  in  a  closed  space,  saturated  with 
vapour  and  containing  liquid  in  excess,  the  tempera- 
ture remaining  constant,  there  is  a  maximum  of 
tension  which  the  vapour  cannot  exceed,  a  baro- 
metric tube  is  used  which  dips  in  a  deep  bath 
(fig.  301).  This  tube  is  filled  with  mercury,  and 
then  so  much  ether  is  added  as  to  be  in  excess 
after  the  Torricellian  vacuum  is  saturated.  The 
height  of  the  mercurial  column  is  next  noted  by 
means  of  the  scale  graduated  on  the  tube  itself. 
Now,  whether  the  tube  be  depressed,  which  tends 
to  compress  the  vapour,  or  whether  it  be  raised, 
which  tends  to  expand  it,  the  height  of  the  mercurial 
column  is  constant.  The  tension  of  the  vapour 
remains  constant  in  the  two  cases,  for  the  depres- 
sion neither  increases  nor  diminishes  it.  Hence  it 
is  concluded  that  when  the  saturated  vapour  is 
compressed,  a  portion  returns  to  the  liquid  state  ; 
that  when,  on  the  other  hand,  the  pressure  is 
diminished,  a  portion  of  the  excess  of  liquid  vapor- 
ises, and  the  space  occupied  by  the  vapour  is  again 
saturated  ;  but  in  both  cases  the  tension  and  the 
density  of  the  vapour  remain  constant. 
\T  354.  ITnsaturated  vapours. — From  what  has  been  said,  vapours  pre- 
sent two  very  different  states,  according  as  they  are  saturated  or  not.  In 
the  first  case,  where  they  are  saturated  and  in  contact  with  the  liquid,  they 
differ  completely  from  gases,  since  for  a  given  temperature  they  can  neither 
be  compressed  nor  expanded ;  their  elastic  force  and  their  density  remain 
constant. 

In  the  second  case,  on  the  contrary,  where  they  are  not  saturated,  they 
exactly  resemble  gases.  For  if  the  experiments  (fig.  301)  be  repeated,  only  a 
small  quantity  of  ether  being  introduced,  so  that  the  vapour  is  not  saturated, 
and  if  the  tube  be  then  slightly  raised,  the  level  of  the  mercury  is  seen  to  rise, 
which  shows  that  the  elastic  force  of  the  vapour  has  diminished.  Similarly, 
by  immersing  the  tube  still  more,  the  level  of  the  mercury  sinks.  The  vapour 
consequently  behaves  just  as  a  gas  would  do,  its  tension  diminishes  when  the 
volume  increases,  and  vice  versa ;  and  as  in  both  cases  the  volume  of  the 


Fig.  301. 


-356]  Tension  of  Aqueous  Vapour  below  Zero.  309 

vapour  is  inversely  as  the  pressure,  it  is  concluded  that  unsaturated  vapours 
obey  Boyle's  laiv. 

When  an  unsaturated  vapour  is  heated,  its  volume  increases  like  that  of 
a  gas  ;  and  the  number  0-00366,  which  is  the  coefficient  of  the  expansion  of 
air,  may  be  taken  for  that  of  vapours. 

Hence  we  see  that  the  physical  properties  of  unsaturated  vapours  are 
comparable  with  those  of  gases,  and  that  the  formulae  for  the  compressibility 
and  expansibility  of  gases  (182  and  332)  also  apply  to  unsaturated  vapours. 

355.  Tension  of  aqueous  vapour  below  zero.— In  order  to  measure 
the  elastic  force  of  aqueous  vapour  below  zero,  Gay-Lussac  used  two  baro- 
meter tubes  filled  with  mercury,  and  placed  in 
the  same  bath  (fig.  302).  The  straight  tube,  A, 
serves  as  a  barometer  ;  the  other,  C,  is  bent,  so 
that  part  of  the  Torricellian  vacuum  can  be  sur- 
rounded by  a  freezing  mixture  B  (347)-  When 
a  little  water  is  admitted  into  the  bent  tube,  the 
level  of  the  mercury  sinks  below  that  in  the 
tube  A,  to  an  extent  which  varies  with  the  tem- 
perature of  the  freezing  mixture. 

At       o°  the  depression  is  .  4-54  millimetres 


„  -   3 

„-    5C 
„-   f 

O 

',!~20C 

,,-3oc 


•  2-67 
.  2-08 
.  0.84 

•  0-36 


Fig.  302. 


These  depressions,  which  must  be  due  to 
the  tension  of  aqueous  vapour  in  the  space  BC, 
show  that  even  at  very  low  temperatures  there 
is  always  some  aqueous  vapour  in  the  atmo- 
sphere. 

Although  in  the  above  experiment  the  part  B 
and  the  part  C  are  not  both  immersed  in  the 
freezing  mixture,  we  shall  presently  see  that 
when  two  communicating  vessels  are  at  different 
temperatures,  the  tension  of  the  vapour  is  the 
same  in  both,  and  always  corresponds  to  that  of  the  lowest  temperature. 

That  water  evaporates  even  below  zero  follows  from  the  fact  that  wet  linen 
exposed  to  the  air  during  frost  becomes  first  stiff  and  then  dry,  showing  that  the 
particles  of  water  evaporate  even  after  the  latter  has  been  converted  into  ice. 
\j  356.  Tension  of  aqueous  vapour  between  zero  and  one  hundred 
degrees. — i.  Daltorts  method.  Dalton  measured  the  elastic  force  of  aqueous 
vapour  between  o°  and  100°  by  means  of  the  apparatus  represented  in  fig. 
303.  Two  barometer  tubes,  A  and  B,  are  filled  with  mercury,  and  inverted 
in  an  iron  bath  full  of  mercury,  and  placed  on  a  furnace.  The  tube  A  con- 
tains a  small  quantity  of  water.  The  tubes  are  supported  in  a  cylindrical 
vessel  full  of  water,  the  temperature  of  which  is  indicated  by  the  thermometer. 


3io 


On  Heat. 


[356- 


The  bath  being  gradually  heated,  the  water  in  the  cylinder  becomes  heated 
too  ;  the  water  which  is  in  the  tube  A  vaporises,  and  in  proportion  as  the 
tension  of  its  vapour  increases,  the  mercury  sinks.  The  depressions  of  the 
mercury  corresponding  to  each  degree  of  the  thermometer  are  indicated  on 
the  scale  E,  and  in  this  manner  a  table  of  the  elastic  forces  between  zero  and 
\ioo°  has  been  constructed. 

ii.  RegnauWs  method.—  Dalton's  method  is  wanting  in  precision,  for  the 
liquid  in  the  cylinder  has  not  everywhere  the  same  temperature,  and  con- 
sequently the  exact  temperature  of  the  aqueous  vapour  is  not  shown. 


Fig.  303- 


Fig.  304. 


Regnault's  apparatus  is  a  modification  of  that  of  Dalton.  The  cylindrical 
vessel  is  replaced  by  a  large  cylindrical  zinc  drum,  MN  (fig.  304),  in  the 
bottom  of  which  are  two  tubulures.  The  tubes  A  and  B  pass  through  these 
tubulures,  and  are  fixed  by  caoutchouc  collars.  The  tube  containing  vapour, 
B,  is  connected  with  a  flask,  #,  by  means  of  a  brass  three-way  tube,  O.  The 
third  limb  of  this  tube  is  connected  with  a  drying  tube,  D,  containing 
pumice  charged  with  sulphuric  acid,  which  is  connected  with  the  air-pump. 
When  the  flask  a  contains  some  water,  a  small  portion  is  distilled  into  B 
by  gently  heating  the  flask.  Exhausting,  then,  by  means  of  the  air-pump, 


—357]        Tension  of  Aqueous  Vapour 'above  100  degrees.  311 

the  water  distils  continuously  from  the  flask  and  from  the  barometric  tube 
towards  D,  which  condenses  the  vapour.  After  having  vaporised  some 
quantity  of  water,  and  when  it  is  thought  that  the  air  in  the  tube  is  withdrawn, 
the  capillary  tube  which  connects  B  with  the  three-way  tube  is  sealed.  The 
tube  B  being  thus  closed,  it  is  experimented  with  as  in  Dalton's  method. 

The  drum,  MN,  being  filled  with  water,  is  gently  heated  by  a  spirit  lamp, 
which  is  separated  from  the  tubes  by  a  wooden  screen.  By  means  of  a 
stirrer,  K,  all  parts  of  the  liquid  are  kept  at  the  same  temperature.  In  the 
side  of  the  drum  is  a  glass  window,  through  which  the  height  of  the  mercury 
in  the  tubes  can  be  read  off  by  means  of  a  cathetometer  ;  from  the  difference 
in  these  heights,  reduced  to  zero,  the  tension  of  vapour  is  deduced.  'By 
means  of  this  apparatus,  the  elastic  force  of  vapour  between  o°  and  50°  has 
been  determined  with  accuracy. 


Fig.  305- 

357-  Tension  ot  aqueous  vapour  above  one  hundred  degrees. — Two 

methods  have  been  employed  for  determining  the  tension  of  aqueous  vapour 
at  temperatures  above  iooc  ;  the  one  by  Dulong  and  Arago,  in  1830,  and  the 
other  by  Regnault,  in  1 844. 

Fig.  305  represents  a  vertical  section  of  the  apparatus  used  by  Dulong 
and  Arago.  It  consisted  of  a  copper  boiler,  k,  with  very  thick  sides,  and  of 
about  20  gallons'  capacity.  Two  gun-barrels,  a,  of  which  only  one  is  seen  in 
the  drawing,  were  firmly  fixed  in  the  sides  of  the  boiler,  and  plunged  in  the 
water.  The  gun-barrels  were  closed  below,  and  contained  mercury,  in  which 
were  placed  thermometers,  /,  indicating  the  temperature  of  the  water  and  of 
the  vapour.  The  tension  of  the  vapour  was  measured  by  means  of  a  mano- 
meter with  compressed  air,  m,  previously  graduated  (184)  and  fitted  into  an 
iron  vessel,  d,  filled  with  mercury.  In  order  to  see  the  height  of  the  mercury 
in  the  vessel,  it  was  connected  above  and  below  with  a  glass  tube,  #,  in  which 
the  level  was  always  the  same  as  in  the  bath.  A  copper  tube,  z,  connected 


312  On  Heat.  [357- 

the  upper  part  of  the  vessel,  dt  with  a  vertical  tube,  c,  fitted  in  the  boiler. 
The  tube  i  and  the  upper  part  of  the  bath  d  were  filled  with  water,  which 
was  kept  cool  by  means  of  a  current  of  cold  water  flowing  from  a  reservoir, 
and  circulating  through  the  tube  b. 

The  vapour  which  was  disengaged  from  the  tube  c  exerted  a  pressure 
on  the  water  of  the  tube  i ;  this  pressure  was  transmitted  to  the  water  and 
to  the  mercury  in  the  bath  d,  and  the  mercury  rose  in  the  manometer.  By 
noting  on  the  manometer  the  pressures  corresponding  to  each  degree  of  the 
thermometer,  Dulong  and  Arago  were  able  to  make  a  direct  measurement 
of  the  tension  up  to  24  atmospheres,  and  the  tension  from  thence  to  50 
atmospheres  was  determined  by  calculation. 

358.  Tension  of  vapour  below  and  above  one  hundred  degrees. — 
Regnault  devised  a  method  by  which  the  tension  of  vapour  may  be 


Fig.  306. 

measured  at  temperatures  either  below  or  above  100°.  It  depends  on  the 
principle  that  when  a  liquid  boils,  the  tension  of  the  vapour  is  equal  to  the. 
pressure  it  supports  (363).  If,  therefore,  the  temperature  and  the  corre- 
sponding pressure  are  known,  the  question  is  solved,  and  the  method  merely 
consists  in  causing  water  to  boil  in  a  vessel  under  a  given  pressure,  and 
measuring  the  corresponding  temperature. 

The  apparatus  consists  of  a  copper  retort,  C  (fig.  306),  hermetically  sealed 
and  about  two-thirds  full  of  water.  In  the  cover  there  are  four  thermometers, 
two  of  which  just  dip  into  the  water,  and  two  descend  almost  to  the  bottom. 
By  means  of  a  tube,  AB,  the  retort  C  is  connected  with  a  glass  globe,  M,  of 


-358] 


Table  of  Tensions  of  Aqueous  Vapour. 


313 


about  6  gallons'"  capacity,  and  full  of  air.  The  tube  AB  passes  through  a 
metal  cylinder,  D,  through  which  a  current  of  cold  water  is  constantly 
flowing  from  the  reservoir  E.  To  the  upper  part  of  the  globe  a  tube  with 
two  branches  is  attached,  one  of  which  is  connected  with  a  manometer,  O  ; 
the  other  tube,  HH',  which  is  of  lead,  can  be  attached  either  to  an  exhaust- 
ing or  a  condensing  air-pump,  according  as  the  air  in  the  globe  is  to  be  rare- 
fied or  condensed.  The  reservoir  K,  in  which  is  the  globe,  contains  water  at 
the  temperature  of  the  surrounding  air. 

If  the  elastic  force  of  aqueous  vapour  below  100°  is  to  be  measured,  the 
end  H'  of  the  lead  pipe  is  connected  with  the  plate  of  the  air-pump,  and 
the  air  in  the  globe  M,  and  consequently  that  in  the  retort  C,  is  rarefied. 
The  retort  being  gently  heated,  the  water  begins  to  boil  at  a  temperature 
below  100°,  in  consequence  of  the  diminished  pressure.  And  since  the  vapour 
is  condensed  in  the  tube  AB,  which  is  always  cool,  the  pressure  originally 
indicated  by  the  manometer  does  not  increase,  and  therefore  the  tension  of 
the  vapour  during  ebullition  remains  equal  to  the  pressure  on  the  liquid. 

A  little  air  is  then  allowed  to  enter  ;  this  alters  the  pressure,  and  the 
liquid  boils  at  a  new  temperature  ;  both  these  are  read  off,  and  the  experi- 
ment repeated  as  often  as  desired  up  to  100°. 

In  order  to  measure  the  tension  above  100°,  the  tube  H'  is  connected 
with  a  condensing  pump,  by  means  of  which  the  air  in  the  globe  M  and  that 
in  the  vessel  C  are  exposed  to  successive  pressures,  higher  than  the  atmo- 
sphere. The  ebullition  is  retarded  (367),  and  it  is  only  necessary  to  observe 
the  difference  in  the  height  of  the  mercury  in  the  two  tubes  of  the  mano- 
meter O,  and  the  corresponding  temperature,  in  order  to  obtain  the  tension 
for  a  given  temperature. 

The  following  tables  by  Regnault  give  the  tension  of  aqueous  vapour 
from  -10°  to  104°  : — 

Tensions  of  aqueous  vapour  from  —  10°  to  104°  C. 


Tempe- 
ratures 

Tensions  in 
millimetres 

Tempe-      Tensions  in 
ratures       millimetres 

Tempe- 
ratures 

Tensions  in 
millimetres 

Tempe- 
ratures 

Tensions  in 
millimetres 

-10° 

2-078 

12°           10-457 

29° 

29782 

90° 

525-45 

8 

2-456 

13             II-062 

30 

3^548 

91 

54578 

6           2-890 

14             II  -906 

31 

33-405 

92 

566-76 

4           3-387 

15              I2-699 

32 

35*359 

93 

588-41 

2 

3-955 

16          13-635 

33 

37-4IO 

94 

61074 

o           4  -6oo 

17          14-421 

34 

39-565 

95 

63378 

+    i            4  -940 

18          15-357 

35 

4I-827 

96 

657'54 

2            5-302 

19          16-346 

40 

54-906 

97 

682-03 

3 

5-687 

20              I7-39I 

45 

7I-39I 

98 

707-26 

4 

6-097 

21               I8-495 

50 

91*982 

98-5 

720-I5 

5 

6-534 

22             I9-659 

55 

II7-479 

99-0 

733-9I 

6 

0-998 

23         20-888 

60 

148-791 

99'5 

746-50 

7 

7-492 

24         22-184 

65 

186-945 

I  OO'O 

760-00 

8 

8-017 

25       23-550 

70 

233-093 

100-5 

773-71 

9 

8-574 

26        24-998 

75 

288-5I7 

ioro 

787-63 

10 

9-165 

27         26-505 

80 

354^43 

IO2"O 

8I6-I7 

ii 

9-792 

28         28-101 

85 

433-4I 

104-0 

875^9 

On  Heat. 


[358- 


Tensions  in  atmospheres  from  100°  to  230-9°. 


Number 

Number 

Number 

Number 

Temperatures 

of  atmo- 

Temperatures 

of  atmo- 

Temperatures 

of  atmo- 

Temperatures 

of  atmo- 

spheres 

spheres 

spheres  ! 

spheres 

100-0° 

I 

170-8° 

8 

198-8° 

15 

21  7-9° 

22 

II2'2 

4       175-8 

9 

201'9 

16 

220-3 

23 

I2O'6 

•           ! 

2 

180-3 

10 

204-9 

17 

222-5 

24 

I33-9 

3 

184-5 

ii 

207-7 

18 

224-7 

25 

144-0            4 

188-4 

12 

2IO-4 

19 

226-8 

26 

152-2            5 

I92-I 

13 

2I3-0 

20 

228-9 

27 

156-2            6 

I95-5 

14 

215-5 

21 

230-9 

28 

165-3            7 

In  the  second  table  the  numbers  were  obtained  by  direct  observation 
up  to  24  atmospheres  ;  the  others  were  calculated  by  the  aid  of  a  formula  of 
interpolation. 

This  table  and  the  one  next  following  show  that  the  elastic  force  increases 
much  more  rapidly  than  the  temperature.  It  has  been  attempted  to  express 
the  relation  between  them  by  formulae,  but  none  of  the  formulae  seems  to  have 
the  simplicity  which  characterises  a  true  law. 

359.  Tension  of  the  vapours  of  different  liquids, — Regnault  deter- 
mined the  elastic  force,  at  various  temperatures,  of  a  certain  number  of 
liquids  which  are  given  in  the  following  table  : — 


Liquids 

Tempera- 
tures 

Tensions  in     !             T  .      .  , 
millimetres     jj             Liquids 

'    Tempera- 
tures 

/ 

0° 

0-02 

(\       -20° 

Mercury  .       J         50° 

13 

o 

IOO 

0-74 

i    6o 

f          ° 

1  3 

IOO 

Alcohol    .      J  i       50 

I  ;     loo 

220 
1695 

Sulphurous 
acid 

-          ~  2Q 

1     ' 

—  20 

43 

\  j            OO 

Bisulphide 

0 

132 

f:   -30 

of  carbon     •" 

60 

1164         Ammonia 

1 

IOO 

3329 

30 

Tensions  in 
millimetres 

68 

182 

1728 

4950 

479 
1165 
8124 

876 
3163 
8832 


360.  Tension  of  the  vapours  of  mixed  liquids. — Regnault's  experiments 
on  the  tension  of  the  vapour  of  mixed  liquids  prove  that  (i.)  when  two  liquids 
exert  no  solvent  action  on  each  other — such  as  water  and  bisulphide  of  carbon, 
or  water  and  benzole — the  tension  of  the  vapour  which  rises  from  them  is 
nearly  equal  to  the  sum  of  the  tensions  of  the  two  separate  liquids  at  the 
same  temperature  ;  (ii.)  with  water  and  ether,  which  partially  dissolve  each 
other,  the  tension  of  the  mixture  is  much  less  than  the  sum  of  the  tensions  of 
the  separate  liquids,  being  scarcely  equal  to  that  of  the  ether  alone  ;  (iii.) 
when  two  liquids  dissolve  in  all  proportions,  as  ether  and  bisulphide  of  carbon, 
or  water  and  alcohol,  the  tension  of  the  vapour  of  the  mixed  liquids  is  inter- 
mediate between  the  tensions  of  the  separate  liquids. 


—362]  Evaporation.     Causes  which  Accelerate  it.  315 

Wiillner  has  shown  that  the  tension  of  aqueous  vapour  emitted  from  a 
saline  solution,  as  compared  with  that  of  pure  water,  is  diminished  by  an 
amount  proportional  to  the  quantity  of  anhydrous  salt  dissolved,  when  the 
salt  crystallises  without  water  or  yields  efflorescent  crystals  :  when  the  salt  is 
deliquescent,  or  has  a  powerful  attraction  for  water,  the  reduction  of  tension 
is  proportional  to  the  quantity  of  crystallised  salt. 

361.  Tension  in  two  communicating  vessels  at  different  temperatures. 
When  two  vessels  containing  the  same  liquid,  but  at  different  temperatures, 
.are  connected  with  each  other,  the  elastic  force  is  not  that  corresponding  to 
the  mean  of  the  two  temperatures,  as  would  naturally  be  supposed.  Thus, 
if  there  are  two  globes  (fig.  307),  one,  A,  containing  water  kept  at  zero  by 


Fig.  307. 

means  of  melting  ice,  the  other,  B,  containing  water  at  100°,  the  tension,  as 
long  as  the  globes  are  not  connected,  is  4  to  6  millimetres  in  the  first,  and 
760  millimetres  in  the  second.  But  when  they  are  connected  by  opening  the 
stopcock  C,  the  vapour  in  the  globe  B,  from  its  greater  tension,  passes  into 
the  other  globe,  and  is  there  condensed,  so  that  the  vapour  in  B  can  never 
reach  a  higher  pressure  than  that  in  the  globe  A.  The  liquid  simply 
distils  from  B  towards  A  without  any  increase  of  tension. 

From  this  experiment  the  general  principle  may  be  deduced  that  when 
two  vessels  containing  the  same  liquid,  but  at  different  temperatures,  are  con- 
nected, the  pressure  is  identical  in  both  vessels,  and  is  the  same  as  that  corre- 
sponding to  the  lower  temperature.  An  application  of  this  principle  has  been 
made  by  Watt  in  the  condenser  of  the  steam-engine. 

362.  Evaporation.  Causes  which  accelerate  it. — Evaporation,  as  has 
l^een  already  stated  (349),  is  the  slow  production  of  vapour  at  the  surface  of 
a  liquid.  It  is  in  consequence  of  this  evaporation  that  wet  clothes  dry  when 
exposed  to  the  air,  and  that  open  vessels  containing  water  become  empty. 
The  vapours  which,  rising  in  the  atmosphere,  condense,  and  becoming  clouds, 
fall  as  rain,  are  due  to  the  evaporation  from  the  seas,  lakes,  rivers,  and  the 
soil. 

Four  causes  influence  the  rapidity  of  the  evaporation  of  a  liquid  :  i.  the 


On  Heat.  [362- 

temperature  ;  ii.  the  quantity  of  the  same  vapour  in  the  surrounding  atmo- 
sphere ;  iii.  the  renewal  of  this  atmosphere  ;  iv.  the  extent  of  the  surface  of 
evaporation. 

Increase  of  temperature  accelerates  the  evaporation  by  increasing  the 
elastic  force  of  the  vapours. 

In  order  to  understand  the  influence  of  the  second  cause,  it  is  to  be  ob- 
served that  no  evaporation  could  take  place  in  a  space  already  saturated 
with  vapour  of  the  same  liquid,  and  that  it  would  reach  its  maximum  in 
air  completely  freed  from  this  vapour.  It  therefore  follows  that  between 
these  two  extremes,  the  rapidity  of  evaporation  varies  according  as  the 
surrounding  atmosphere  is  already  more  or  less  charged  with  the  same 
vapour. 

The  effect  of  the  renewal  of  this  atmosphere  is  similarly  explained  ;  for 
if  the  air  or  gas,  which  surrounds  the  liquid,  is  not  renewed,  it  soon  becomes 
saturated,  and  evaporation  ceases.  Dalton  found  that  the  ratios  of  the 
evaporation  in  a  feeble,  medium,  and  strong  draught  were  respectively  as 
270  :  347  :  424.  He  also  observed  that  the  quantity  evaporated  in  perfectly 
dry,  almost  still  air  at  a  temperature  of  20°,  was  equivalent  to  o'l  of  a  gramme 
on  a  square  decimetre  of  surface  in  a  minute. 

The  influence  of  the  fourth  cause  is  self-evident. 

Vegetation  exercises  a  great  influence  on  evaporation.  Schiibler  found 
that  the  evaporation  from  a  space  covered  with  meadow  grass,  in  the  most 
vigorous  stage  of  its  growth,  was  thrice  as  rapid  as  that  from  an  adjacent 
surface  of  water.  As  the  plants  ripened  the  evaporation  diminished. 

\(  363.  Laws  of  ebullition. — Ebullition* 
or  boiling,  is  the  rapid  production  of 
elastic  bubbles  of  vapour  in  the  mass  of 
a  liquid  itself. 

When  a  liquid,  water  for  example,  is, 
heated  at  the  lower  part  of  a  vessel,  the 
first  bubbles  are  due  to  the  disengagement 
of  air  which  had  previously  been  absorbed. 
Small  bubbles  of  vapour  then  begin  to 
rise  from  the  heated  parts  of  the  sides, 
but  as  they  pass  through  the  upper  layers,, 
the  temperature  of  which  is  lower,  they 
condense  before  reaching  the  surface.  The 
formation  and  successive  condensation  of 
these  first  bubbles  occasion  the  singing' 
noticed  in  liquids  before  they  begin  to 
boil.  Lastly,  large  bubbles  rise  and  burst 
on  the  surface,  and  this  constitutes  the 
phenomenon  of  ebullition  (fig.  308). 

The  laws  of  ebullition  have  been 
determined  experimentally,  and  are  as. 
follows  : — 

I.  The   temperature  of  ebtdlition  or  the  boiling  point  increases  with  the- 
pressure. 

II.  For  a  given  pressure  ebullition  begins  at  a  certain  temperature,  whicJc 


Fig.  308. 


-364]  Theoretical  Explanation  of  Evaporation  and  Ebullition.  317 

varies  in  different  liquids,  but  which,  for  equal  pressures,  is  always  the  same 
in  the  same  liquid. 

III.  Whatever  be  the  intensity  of  the  source  of  heat,  as  soon  as  ebullition 
begins  the  temperature  of  the  liquid  remains  stationary. 

Boiling  points  tmder  the  pressure  of  760  millimetres. 

Nitrous  oxide         .         .  —92°  Acetic  acid      .         .         .117° 

Carbonic  acid         .  —  80  Amylic  alcohol*       .         .       131 

Ammonia       .         .  -  39  Propionic  acid         .         .        137 

Chloride  of  methyle        .  -23  Butyric  acid   .         .         .156 

Cyanogen       .         .  -  20  Turpentine      .         .         .157 

Sulphurous  acid     .         .  -  10  Aniline    .         .         .         .182 

Chloride  of  ethyl e  .  +  II  Iodine     ....       200 

Aldehyde        .         .         .  21  Phosphorus     .         .         .       290 

Ether     ....  37  Strong  sulphuric  acid      .       318 

Bisulphide  of  carbon      .  47  Mercury           .         .         .       358 

Acetone          .  56  Sulphur  ....       448 

Bromine         ...  58  Phosphorus  pentasulphide    530 

Methylic  alcohol    .         .  66  Selenium         .         .         .       665 

Alcohol ....  78  Cadmium        .'        .         .       720 

Benzole ....  80  Zinc         ....     1040 

Distilled  water       .         .  100 

Kopp  has  pointed  out  that  in  homologous  chemical  compounds  the  same 
difference  in  chemical  composition  frequently  involves  the  same  difference 
of  boiling  points  ;  and  he  has  shown  that  in  a  very  extensive  series  of 
compounds,  the  fatty  acids  for  instance,  the  difference  of  CH2  is  attended  by 
a  difference  of  19°  C.  in  the  boiling  point.  In  other  series  of  homologous 
compounds  the  corresponding  difference  in  the  boiling  point  is  30°,  and  in 
others  again  24°. 

364.  Theoretical  explanation  of  evaporation  and  ebullition. — From 
what  has  been  said  about  the  nature  of  the  motion  of  the  molecules  in  liquids 
(292),  it  may  readily  be  conceived  that  in  the  great  variety  of  these  motions, 
the  case  occurs  in  which,  by  a  fortuitous  concurrence  of  the  progressive, 
vibratory,  and  rotatory  motions,  a  molecule  is  projected  from  the  surface  of 
the  liquid  with  such  force  that  it  overleaps  the  sphere  of  the  action  of  its  cir- 
cumjacent molecules,  before,  by  their  attraction,  it  has  lost  its  initial  velocity ; 
and  that  it  then  flies  into  the  space  above  the  liquid. 

Let  us  first  suppose  this  place  limited  and  originally  vacuous,  it  gradu- 
ally fills  with  the  propelled  molecules,  which  act  like  a  gas  and  in  their 
motion  are  driven  against  the  sides  of  the  envelope.  One  of  these  sides, 
however,  is  the  surface  of  the  liquid  itself,  and  a  molecule  when  it  strikes 
against  this  surface  will  not  in  general  be  repelled,  but  will  be  retained  by  the 
attraction  which  the  adjacent  ones  exert.  Equilibrium  will  be  established 
when  as  many  molecules  are  dispersed  in  the  surrounding  space  as,  on  the 
average,  impinge  against  the  surface  and  are  retained  by  it  in  the  unit  of 
time.  This  state  of  equilibrium  is  not,  however,  one  of  rest,  in  which  eva- 
poration has  ceased,  but  a  condition  in  which  evaporation  and  condensation, 
which  are  equally  strong,  continually  compensate  each  other. 


3i8  On  Heat.  [364- 

The  density  of  a  vapour  depends  on  the  number  of  molecules  which  are 
repelled  in  a  given  time,  and  this  manifestly  depends  on  the  motion  of  the 
molecules  in  the  liquid,  and  therefore  on  the  temperature. 

What  has  been  said  respecting  the  surface  of  the  liquid  clearly  applies  to- 
the  other  sides  of  the  vessel  within  which  the  vapour  is  formed  ;  some  vapour 
is  condensed,  this  is  subject  to  evaporation,  and  a  condition  ultimately  occurs 
in  which  evaporation  and  condensation  are  equal.  The  quantity  of  vapour 
necessary  for  this  depends  on  the  density  of  vapour  in  the  closed  space,  on 
the  temperature  of  the  vapour,  and  of  the  sides  of  the  vessel,  and  on  the  force 
with  which  this  attracts  the  molecules.  The  maximum  will  be  reached  when 
the  sides  are  covered  with  a  layer  of  liquid,  which  then  acts  like  the  free- 
surface  of  a  liquid. 

In  the  interior  of  a  liquid  it  may  happen  that  the  molecules  repel  each 
other  with  such  force  as  to  momentarily  destroy  the  coherence  of  the  mass. 
The  small  vacuous  space  which  is  thereby  formed  is  entirely  surrounded  by 
a  medium  which  does  not  allow  of  the  passage  of  the  repelled  molecules. 
Hence  it  cannot  increase  and  maintain  itself  as  a  bubble  of  vapour,  unless  so- 
many  molecules  are  projected  from  the  inner  sides  that  the  internal  pressure 
which  thereby  results  can  balance  the  external  pressure  which  tends  to- 
condense  the  bubble.  The  expansive  force  of  the  enclosed  vapour  must 
therefore  be  so  much  the  greater,  the  greater  the  external  pressure  on  the 
liquid,  and  thus  we  see  the  dependence  of  pressure  on  the  temperature  of 
boiling. 

365.  Influence  of  substances  in  solution  on  the  boiling:  point.— The 
ebullition  of  a  liquid  is  the  more  retarded  the  greater  the  quantity  of  any 
substance  it  may  contain  in  solution,  provided  that  the  substance  be  not 
volatile,  or,  at  all  events,  be  less  volatile  than  the  liquid  itself.  Water,  which 
boils  at  100°  when  pure,  boils  at  the  following  temperatures  when  saturated 
with  different  salts  : — 

Water  saturated  with  common  salt         .         .  boils  at  102° 

„             „             nitrate  of  potassium  „       116 

„             „             carbonate  of  potassium  „      135 

„             „             chloride  of  calcium  „       179 

Acids  in  solution  present  analogous  results ;  but  substances  merely 
mechanically  suspended,  such  as  earthy  matters,  bran,  wooden  shavings,  &c., 
do  not  affect  the  boiling  point. 

Dissolved  air  exerts  a  very  marked  influence  on  the  boiling  point  of 
water.  Deluc  first  observed  that  water  freed  from  air  by  ebullition,  and 
placed  in  a  flask  with  a  long  neck,  could  be  raised  to  112°  without  boiling. 
M.  Donny  examined  this  phenomenon  by  means  of  the  apparatus  depicted  in 


Fig.  309. 

figure  309.     It  consists  of  a  glass  tube  CAB,  bent  at  one  end  and  closed  at 
C,  while  the  other  is  blown  into  a  pear-shaped  bulb,  B,  drawn  out  to  a 


-366]    Influence  of  Nature  of  Vessel  on  the  Boiling  Point.        319 

point.  The  tube  contains  water  which  is  boiled  until  all  air  is  expelled,  and 
the  open  end  is  hermetically  sealed.  By  inclining  the  tube  the  water  passes 
into  the  bent  end  CA  ;  this  end  being  placed  in  a  bath  of  chloride  of  calcium, 
the  temperature  may  be  raised  to  130°  without  any  signs  of  boiling.  At  138° 
the  liquid  is  suddenly  converted  into  steam  and  the  water  is  thrown  over 
into  the  bulb,  which  is  smashed  if  not  sufficiently  strong. 

Boiled  out  water,  covered  with  a  layer  of  oil,  may  be  raised  to  120°  with- 
out boiling,  but  above  this  temperature  it  suddenly  begins  to  boil,  and  with 
almost  explosive  violence. 

When  a  liquid  is  suspended  in  another  of  the  same  specific  gravity,  but  of 
higher  boiling  point,  with  which  it  does  not  mix,  it  may  be  raised  far  beyond 
its  boiling  point  without  the  formation  of  a  trace  of  vapour.  Dufour  has 
made  a  number  of  valuable  experiments  on  this  subject ;  he  used  in  the  case 
of  water  a  mixture  of  oil  of  cloves  and  linseed  oil,  and  placed  in  it  globules 
of  water,  and  then  gradually  heated  the  oil ;  in  this  way  ebullition  rarely  set 
in  below  110°  or  115°;  very  commonly  globules  of  10  millimetres'  diameter 
reached  a  temperature  of  120°  or  130°,  while  very  small  globules  of  i  to  3 
millimetres  reaches  the  temperature  of  175°,  a  temperature  at  which  the 
tension  of  vapour  on  a  free  surface  is  8  or  9  atmospheres. 

At  these  high  temperatures  the  contact  of  a  solid  body,  or  the  production 
of  gas  bubbles  in  the  liquid,  occasioned  a  sudden  vaporisation  of  the  globule,, 
accompanied  by  a  sound  like  the  hissing  of  a  hot  iron  in  water.. 

Saturated  aqueous  solutions  of  sulphate  of  copper,  chloride  of  sodium,, 
&c.,  remain  liquid  at  a  temperature  far  beyond  their  boiling  point,  when 
immersed  in  melted  stearic  acid.  In  like  manner,  globules  of  chloroform 
(which  boils  at  61°),  suspended  in  a  solution  of  chloride  of  zinc,  could  be 
heated  to  97°  or  98°  without  boiling. 

It  is  a  disputed  question  as  to  what  is  the  temperature  of  the  vapour 
from  boiling  saturated  saline  solutions.  It  has  been  stated  by  Rudberg  to 
be  that  of  pure  water  boiling  under  the  same  pressure.  The  most  recent 
experiments  of  Magnus  seem  to  show,  however,  that  this  is  not  the  case,  but 
that  the  vapour  of  boiling  solutions  is  hotter  than  that  of  pure  water ;  and 
that  the  temperature  rises  as  the  solutions  become  more  concentrated,  and 
therefore  boil  at  higher  temperatures.  Nevertheless,  the  vapour  was  always, 
found  somewhat  cooler  than  the  mass  of  the  boiling  solution,  and  the  differ- 
ence was  greater  at  high  than  at  low  temperatures. 

The  boiling  point  of  a  liquid  is  usually  lowered  when  it  is  mixed  with  a 
more  volatile  liquid  than  itself,  but  raised  when  it  contains  one  which  is  less, 
volatile.  Thus  a  mixture  of  two  parts  alcohol  and  one  of  water  boils  at  83°, 
a  mixture  of  two  parts  of  bisulphide  of  carbon  and  one  part  of  ether  boils  at 
38°.  In  some  cases  the  boiling  point  of  a  mixture  is  lower  than  that  of 
either  of  its  constituents.  A  mixture  of  water  and  bisulphide  boils  at  43°, 
the  boiling  point  of  the  latter  being  46°.  On  this  depends  the  following 
curious  experiment.  If  water  and  bisulphide  of  carboy  both  at  the  tempe- 
rature 45°,  are  mixed  together,  the  mixture  at  once  begms  to  boil  briskly. 

366.  Influence  of  the  nature  of  the  vessel  on  the  boiling-  point. — 
Gay-Lussac  observed  that  water  in  a  glass  vessel  required  a  higher  tempera- 
ture for  ebullition  than  in  a  metal  one.  Taking  the  temperature  of  boiling- 
water  in  a  copper  vessel  at  100°,  its  boiling  point  in  a  glass  vessel  was 


320  On  Heat.  [366- 

found  to  be  101°  ;  and  if  the  glass  vessel  had  been  previously  cleaned  by 
means  of  sulphuric  acid  and  of  potass,  the  temperature  would  rise  to  105°,  or 

even  to  106°,  before  ebullition  com- 
menced. A  piece  of  metal  placed  in 
the  bottom  of  the  vessel  was  always 
sufficient  to  lower  the  temperature  to 
1 00°,  and  at  the  same  time  to  prevent 
the  violent  concussions  which  accom- 
pany the  ebullition  of  saline  or  acid 
solutions  in  glass  vessels.  Whatever 
be  the  boiling  point  of  water,  the  tem- 
perature of  its  vapour  is  uninfluenced 
by  the  substance  of  the  vessels. 

367.  Influence  of  pressure  on 
the  boiling:  point.— We  see  from  the 
table  of  tensions  (358)  that  at  100°, 
the  temperature  at  which  water  boils 
under  a  pressure  of  760  millimetres, 
which  is  that  of  the  atmosphere,  aque- 
ous vapour  has  a  tension  exactly  equal 
to  this  pressure.  This  principle  is 
general,  and  may  be  thus  enunciated  : 
A  liquid  boils  when  the  tension  of  its 
vapour  is  equal  to  the  pressure  it  sup- 
ports. Consequently,  as  the  pressure 


Fig.  310. 


increases  or  diminishes,  the  tension  of  the  vapour,  and  therefore  the  tempe- 
rature necessary  for  ebullition,  must  increase  or  diminish.  Hence  a  liquid 
has  strictly  speaking  an  indefinite  number  of  boiling  points. 

In  order  to  show  that  the  boiling  point  is  lower  under  diminished  pres- 
sure, a  small  dish  containing  water  at  30°  is  placed  under  the  receiver  of 
an  air-pump,  which  is  then  exhausted.  The  liquid  soon  begins  to  boil,  the 
vapour  formed  being  pumped  out  as  rapidly  as  it  is  generated. 

A  paradoxical  but  very  simple  experiment  also  well  illustrates  the  de- 
pendence of  the  boiling  point  on  the  pressure.  In  a  glass  flask,  water  is 
boiled  for  some  time,  and  when  all  air  has  been  expelled  by  the  steam,  the 
flask  is  closed  by  a  cork  and  inverted,  as  shown  in  fig.  310.  If  the  bottom 
is  then  cooled  by  a  stream  of  cold  water  from  a  sponge,  the  water  begins  to 
boil  again.  This  arises  from  the  condensation  of  the  steam  above  the 
surface  of  the  water,  by  which  a  partial  vacuum  is  produced. 

It  is  in  consequence  of  this  diminution  of  pressure  that  liquids  boil  on 
high  mountains  at  lower  temperatures.  On  Mont  Blanc,  for  example,  water 
boils  at  84°,  and  at  Quito  at  90°. 

On  the  more  rapid  evaporation  of  water  under  feeble  pressures  is  based 
the  use  of  the  air-pump  in  concentrating  those  solutions  which  either  cannot 
bear  a  high  degree  of  heat,  or  which  can  be  more  cheaply  evaporated  in  an 
exhausted  space.  Howard  made  a  most  important  and  useful  application  of 
this  principle  in  the  manufacture  of  sugar.  The  syrup,  in  his  method,  is 
enclosed  in  an  air-tight  vessel,  which  is  exhausted  by  a  steam-engine.  The 
evaporation  consequently  goes  on  at  a  lower  temperature,  which  secures  the 


Fig.  311. 


—369]        Measurement  of  Heights  by  the  Boiling  Point.  321 

syrup  from  injury.     The  same  plan  is  adopted  in  evaporating  the  juice  of 
certain  plants  used  in  preparing  medicinal  extracts. 

On   the    other  hand,  boiling   is    retarded  by  increasing   the   pressure  : 
under  the  pressure  of  two  atmospheres,  for  example,  water  only  boils  at  120° '6. 

368.  Franklin's  experiment. — The  influence  of  pressure  on  boiling  may 
further  be  illustrated  by  means  of  an  experiment  originally  made  by  Frank- 
lin.    The  apparatus  consists  of  a  bulb,  a,  and  a  tube,  b,  joined  by  a  tube  of 
smaller  dimensions  (fig.  311).     The 

tube  b  is  drawn  out,  and  the  appa- 
ratus filled  with  water,  which  is 
then  in  great  part  boiled  away  by 
means  of  a  spirit  lamp.  When  it 
has  been  boiled  sufficiently  long  to 
expel  all  the  air,  the  tube  b  is  sealed. 
There  is  then  a  vacuum  in  the 
apparatus,  or  rather  there  is  a 'pres- 
sure due  to  the  tension  of  aqueous 
vapour,  which  at  ordinary  tempe- 
ratures is  very  small.  Consequently  if  the  bulb,  a,  be  placed  in  the  hand,  the 
heat  is  sufficient  to  produce  a  pressure  which  drives  the  water  into  the  tube 
£,  and  causes  a  brisk  ebullition. 

369.  measurement  of  heights  by  the  boil- 
ing point. — From  the  connection  between  the 
boiling  point   of  water   and   the   pressure,  the 
heights  of  mountains  may  be  measured  by  the 
thermometer  instead  of  by  the  barometer.     Sup- 
pose, for  example,  it  is  found   that  water  boils 
on  the  summit  of  a  mountain  at  90°,  and  at  its 
base  at  98°;  at  these  temperatures  the  elastic 
force  or  tension  of  the  vapour  is  equal  to  that  of 
the  pressure  on  the  liquid  ;  that  is,  to  the  pres- 
sure of  the   atmosphere  at  the  two  places  re- 
spectively.    Now  the  tensions  of  aqueous  vapour 
for  various  temperatures  have  been  determined, 
and  accordingly  the  tensions  corresponding  to 
the  above  temperatures  are  sought  in  the  tables. 
These  numbers  represent  the  atmospheric  pres- 
sures at  the  two  places  :  in  other  words,  they 
give  the  barometric  heights,  and  from  these  the 
height  of  the  mountain  may  be  calculated  by 
the  method  already  given  (178).     An  ascent  of 
about  i, 080  feet  produces  a  diminution  of  i°  C. 
in  the  boiling  point. 

The  instruments  used  for  this  purpose  are 
called  thermo-ba^ometers  or  hypsometers,  and 
were  first  applied  by  Wollaston.  They  consist  es- 
sentially of  a  small  rnetallic  vessel  for  boiling  water 
(fig.  312),  fitted  with  very  delicate  thermometers, 
which  are  only  graduated  from  80°  to  100° ;  so  that,  as  each  degree  occupies 

Y 


322 


On  Heat, 


[369- 


a  considerable  space  on  the  scale,  the  loths,  and  even  the  looths,  of  a 
degree  may  be  estimated,  and  thus  it  is  possible  to  determine  the  height  of 
a  place  by  means  of  the  boiling  point  to  within  about  10  feet. 

370.  Formation  of  vapour  in  closed  tubes. — We  have  hitherto  con- 
sidered vapours  as  being  produced  in  an  indefinite  space,  or  where  they 
could  expand  freely,  and  it  is  only  under  this  condition  that  boiling  can 
take  place.  In  a  closed  vessel  the  vapours  produced  finding  no  issue,  their 
tension  and  their  density  increase  with  the  temperature,  but  the  rapid  disen- 
gagement of  vapour  which  constitutes  boiling  is  impossible.  Hence,  while 
the  temperature  of  a  liquid  in  an  open  vessel  can  never  exceed  that  of  boil- 
ing, in  a  closed  vessel  it  may  be  much  higher.  The  liquid  state  has, 
nevertheless,  a  limit ;  for,  according  to  experiments  by  Cagniard- 
Latour,  if  either  water,  alcohol,  or  ether  be  placed  in  strong  glass 
tubes,  which  are  hermetically  sealed  after  the  air  has  been  ex- 
pelled by  boiling,  and  if  then  these  tubes  are  exposed  to  a 
sufficient  degree  of  heat,  a  moment  is  reached  at  which  the 
jr||  liquid  suddenly  disappears,  and  is  converted  into  vapour  at 

200°,  occupying  a  space  less  than  double  its  volume  in  the  liquid 
state,  its  tension  being  then  38  atmospheres. 

Alcohol  which  half-fills  a  tube  is  converted  into  vapour  at 
207°  C.  If  a  glass  tube  about  half-filled  with  water,  in  which 
some  carbonate  of  soda  has  been  dissolved,  to  diminish  the 
action  of  the  water  in  the  glass,  be  heated,  it  is  completely 
vaporised  at  about  the  temperature  of  melting  zinc. 

When  chloride  of  ethyle  is  heated  in  a  very  thick  sealed 
tube,  the  upper  surface  ceases  to  be  distinct  at  170°,  and  is 
replaced  by  an  ill-defined  nebulous  zone.  As  the  temperature 
rises  this  zone  increases  in  width  in  both  directions,  becoming 
at  the  same  time  more  transparent ;  after  a  time  the  liquid  is 
completely  vaporised,  and  the  tube  becomes  transparent  and 
seemingly  empty.  On  cooling,  the  phenomena  are  reproduced  in 
opposite  order.  Similar  appearances  are  observed  on  heating 
ether  in  a  sealed  tube  at  190.° 

Andrews  made  a  series  of  observations  on  the  behaviour 
of  condensed  gases  at  different  temperatures,  by  means  of  an 
apparatus,  the  principal  features  of  which  are  represented  in 

fig-  3I3- 

The  pure  and  dry  gas  is  contained  in  a  tube  g,  which  is 
sealed  at  one  end,  and  the  gas  is  shut  in  by  a  thread  of  mer- 
cury.     The  tube  is  inserted  in  a  brass  end-piece,  E,  which  is 
firmly  screwed  on  a  strong  copper  tube,  R.     At  the  other  end  is 
a  similar  piece,  in  which  a  steel  screw  works,  perfect  tightness 
Fig.  313.         being  ensured  by  good  packing.     The  tube  is  full  of  water,  so 
that  by  turning  this  screw  the  pressure  on  the   enclosed  gas 
can  be  increased  up  to   500  atmospheres.     In  some  cases  the  projecting 
capillary  tube  is  bent  downwards,  so  that  it  can  be  placed  in  a  freezing 
mixture. 

Andrews  found  on  raising  liquid  carbonic  acid  in  such  a  tube  to  a  tempe- 
rature of  31°  C.  that  the  surface  of  demarcation  between  the  liquid  and  the 


-370] 


Formation  of  Vapour  in  Closed  Tubes. 


323 


gas   became    fainter,  lost  its  curvature,  and  gradually    disappeared.     The 
space  was  then  occupied  by  a  homogeneous  fluid,  which,  when  the  pressure 
was  suddenly  diminished,  or  the  temperature  slightly  lowered, 
exhibited  a  peculiar  appearance  of  moving  or  flickering  striae 
throughout  its  whole  mass.     Above  30°  no  apparent  liquefac- 
tion   of  carbonic   anhydride,  or    separation    into  two   distinct 
forms  of  matter,  could  be  effected,  not  even  when  the  pressure 
of  400  atmospheres  was  applied. 

The  phenomenon  of  the  critical  temperature  may  also  be 
conveniently  illustrated  by  the  following  arrangement  (fig.  314), 
which  is  also  well  adapted  for  projection  on  a  screen  by 
.means  of  a  magic-lantern  for  lecture  purposes.  A  stout  glass 
tube  about  2-5™™  wide  and  4Omm  long  contains  liquid  sulphurous 
acid,  and  is  supported  with  the  drawn-out  end  downwards,  in 
a  test-tube  by  means  of  a  wire  frame.  Pure  melted  paraffine 
is  added  to  about  iocm  above  the  inner  tube.  The  whole 
arrangement  is  suspended  in  a  retort-holder,  and  heat  applied 
with  a  spirit  lamp.  With  careful  manipulation  there  is  no  dan- 
ger, and  the  course  of  the  phenomenon  is  readily  seen  through 
the  clear  paraffine. 

From  similar  observations  made  with  other  substances  it 
seems  that  there  exists  for  every  liquid  a  temperature,  the 
critical  point  or  critical  temperature.  While  below  this  critical 
point  a  sudden  transition  from  gas  to  liquid  is  accompanied 
by  a  sudden  diminution  of  volume,  and  liquid  and  gas  are 
separated  by  a  sharp  line  of  demarcation  ;  above  this  critical 
point  the  change  is  connected  with  a  gradual  diminution  of 
volume,  and  is  quite  imperceptible.  The  condensation  can,  indeed,  only 
be  recognised  by  a  sudden  ebullition  when  the  pressure  is  lessened.  Hence 
ordinary  condensation  is  only  possible  at  a  temperature  below  the  critical 
point,  and  it  is  not  surprising,  therefore,  that  mere  pressure,  however  great, 
should  have  failed  to  liquefy  many  of  the  gases. 

The  boiling  point  of  a  body  may  be  defined  as  the  temperature  above 
which  a  body  passes  into  the  state  of  gas,  not  only  on  the  surface  but  in  the 
body  of  the  liquid  ;  this  temperature  is  therefore  different  for  different 
pressures,  and  is  accordingly  a  relative  magnitude.  The  absolute  boili?ig 
point  is  the  temperature  at  which  a  body  is  converted  into  gas,  whatever 
be  the  pressure  ;  it  is  identical  with  the  critical  temperature.  Mendelejeff 
found  that  a  relation  existed  between  the  absolute  temperature  and  the 
capillarity  of  liquids.  Increase  of  temperature  diminishes  the  cohesion,  and 
therefore  the  capillarity  of  liquids.  The  capillarity  ultimately  vanishes, 
and  the  temperature  at  which  this  takes  place  is  the  absolute  boiling 
point. 

A  vapour  may  be  defined  as  being  a  gas  at  any  temperature  below  its 
critical  point.  Hence  a  vapour  can  be  converted  into  a  liquid  by  pressure 
alone,  and  can  therefore  exist  in  the  pressure  of  its  own  liquid,  while  a  gas 
requires  cooling  as  well  as  pressure  to  convert  it  into  a  liquid  ;  that  is,  to  alter 
its  arrangement  in  such  a  manner  that  a  liquid  can  be  seen  to  be  separated 
from  a  gas  by  a  distinctly  bounded  surface. 

Y  2 


Fig.  314- 


324 


On  Heat. 


[371- 


Fig.  315- 


^  371.  Papin's  dig-ester. — Papin  appears  to  have  been  the  first  to  investi- 
gate the  effects  of  the  production  of  vapour  in  closed  vessels.  The  apparatus 

which  bears  his  name  consists  of  a  cylin- 
drical iron  vessel  (fig.  315),  provided  with 
a  cover,  which  is  firmly  fastened  down 
by  the  screw  B.  In  order  to  close  the 
vessel  hermetically,  sheet  lead  is  placed 
between  the  edges  of  the  cover  and  the 
vessel.  At  the  bottom  of  a  cylindrical 
cavity,  which  traverses  the  cylinder  S, 
and  the  tubulure  0,  the  cover  is  perforated 
by  a  small  orifice  in  which  there  is  a  rod 
n.  This  rod  presses  against  a  lever,  A, 
movable  at  a,  and  the  pressure  may  be 
regulated  by  means  of  a  weight  movable 
on  this  lever.  The  lever  is  so  weighted 
that  when  the  pressure  in  the  interior  is 
equal  to  6  atmospheres,  for  example,  the 
valve  rises  and  the  vapour  escapes.  The 
destruction  of  the  apparatus  is  thus 
avoided,  and  this  mechanism  has  hence 
received  the  name  of  safety-valve.  The 
digester  is  filled  about  two-thirds  with 
water,  and  is  heated  on  a  furnace.  The 
water  may  thus  be  raised  to  a  temperature 
far  above  100°,  and  the  pressure  of  the  vapour  increased  to  several  atmo- 
spheres, according  to  the  weight  on  the  lever. 

We  have  seen  that  water  boils  at  much  lower  temperatures  on  high 
mountains  (367) ;  the  temperature  of  water  boiling  in  open  vessels  in  such 
localities  is  not  sufficient  to  soften  animal  fibre  completely  and  extract 
the  nutriment,  and  hence  Papin's  digester  is  used  in  the  preparation  of 
food. 

Papin's  digester  is  used  in  extracting  gelatine.  When  bones  are  digested 
in  this  apparatus  they  are  softened,  so  that  the  gelatine  which  they  contain 
is  dissolved :  the  part  through  which  the  screw  B  passes  is  made  of  such 
elasticity  that  it  yields  and  the  lid  opens  when  the  pressure  of  the  vapour 
becomes  dangerous. 

^  372.  Latent  beat  of  vapour. — As  the  temperature  of  a  liquid  remains 
constant  during  boiling,  whatever  be  the  source  of  heat  (363),  it  follows 
that  a  considerable  quantity  of  heat  becomes  absorbed  in  boiling,  the 
only  effect  of  which  is  to  transform  the  body  from  the  liquid  to  the  gaseous 
condition.  And  conversely,  when  a  saturated  vapour  passes  into  the  state 
of  liquid  it  gives  out  a  definite  amount  of  heat. 

These  phenomena  were  first  observed  by  Black,  and  he  described  them 
by  saying  that  during  vaporisation  a  quantity  of  sensible  heat  became  latent, 
and  that  the  latent  heat  again  became  free  during  condensation.  The 
quantity  of  heat  which  a  liquid  must  absorb  in  passing  from  the  liquid  to 
the  gaseous  state,  and  which  it  gives  out  in  passing  from  the  state  of  vapour 
to  that  of  liquid,  is  spoken  of  as  the  latent  heat  of  evaporation. 


-372]  Latent  Heat  of  Evaporation.  325 

The  analogy  of  these  phenomena  to  those  of  fusion  will  be  at  once  seen  ; 
the  modes  of  determining  them  will  be  described  in  the  chapter  on  Calori- 
metry  ;  but  the  following  results,  which  have  been  obtained  for  the  latent 
heats  of  evaporation  of  a  few  liquids,  may  be  here  given  :  — 

Water     ....       536  Bisulphide  of  carbon         .  87 

Alcohol  ....       208  Turpentine        ...  74 

Acetic  acid      .         .         .102  Bromine  ....  49 

Ether       ....         90  Iodine       ....  24 

The  meaning  of  these  numbers  is,  in  the  case  of  water,  for  instance,  that 
it  requires  as  much  heat  to  convert  a  pound  of  water  from  the  state  of  liquid 
at  the  boiling  point,  to  that  of  vapour  at  the  same  temperature,  as  would  raise 
a  pound  of  water  through  536  degrees,  or  536  pounds  of  water  through  one 
degree  ;  or  that  the  conversion  of  one  pound  of  vapour  of  alcohol  at  78° 
into  liquid  alcohol  of  the  same  temperature  would  heat  208  pounds  of  water 
through  one  degree. 

Watt,  who  investigated  the  subject,  found  that  the  whole  quantity  of  heat 
necessary  to  raise  a  given  weight  of  water  from  zero  at  any  temperature, 
and  then  to  evaporate  it  entirely,  or  what  is  called  the  heat  of  evaporation, 
is  a  constant  quantity.  His  experiments  showed  that  this  quantity  is  640. 
Hence  the  lower  the  temperature  the  greater  the  latent  heat,  and,  on  the  other 
hand,  the  higher  the  temperature,  the  less  the  latent  heat.  The  latent  heat  of 
the  vapour  of  water  evaporated  at  100°  would  be  540,  while  at  50  degrees  it 
would  be  590.  At  higher  temperatures  the  latent  heat  of  aqueous  vapour 
would  go  on  diminishing.  Water  evaporated  under  a  pressure  of  15  atmo- 
spheres at  a  temperature  of  200°  would  have  a  latent  heat  of  440,  and  if  it 
could  be  evaporated  at  640°  it  would  have  no  latent  heat  at  all. 

Regnault,  who  examined  this  question  with  great  care,  found  that  the 
total  quantity  of  heat  necessary  for  the  evaporation  of  water  increases  with 
the  temperature,  and  is  not  constant,  as  Watt  had  supposed.  It  is  repre- 
sented by  the  formula 

O  =  606-5  +0-3054 

in  which  Q  is  the  total  quantity  of  heat,  and  t  the  temperature  of  the  water 
during  evaporation,  while  the  numbers  are  constant  quantities.  The  total 
quantity  of  heat  necessary  to  evaporate  water  at  100°  is  606-5  -i-  (0-305  x  100) 
=  637;  at  120°  it  is  643;  at  150°  it  is  651  ;  and  at  180°  it  is  661. 

Thus  the  heat  required  to  raise  a  pound  of  water  from  zero  and  convert 
'  it  into  steam  at  100°  represents  a  mechanical  work  of  885430  units,  which 
would  be  sufficient  to  raise  a  ton  weight  through  a  height  of  nearly  400 
feet. 

The  total  heat  of  the  evaporation  of  ether  is  expressed  by  a  formula 
similar  to  that  of  water,  namely,  Q  =  64  +  0-045^  ;  and  that  for  chloroform 


The  heat  which  is  expended  simply  in  evaporating  a  liquid  produces  no 
rise  of  temperature,  and  only  appears  as  doing  the  work  of  a  change  of 
state.  One  portion  of  this  work  is  expended  in  overcoming  the  cohesion  of 
the  particles  in  the  liquid  state,  and  enabling  them  to  assume  the  gaseous 


326 


On  Heat. 


[372- 


form — this  is  the  internal  work  ;  the  other,  the  external  work,  is  expended 
in  overcoming  the  external  pressure  on  the  vapour  formed,  and  which  is 
much  greater  than  in  the  original  liquid  state,  for  the  volume  is  greatly 
increased. 

Knowing  the  increase  of  volume,  and  the  pressure,  the  external  work  may 
be  calculated  ;  for  if  the  volumes  of  unit  weight  of  the  substance  in  the  state 
of  liquid  and  of  vapour  are  respectively  o-  and  j,  the  pressure  for  unit 
surface  is  p.  Thus  the  external  work  is  Ap  (a-  -  s),  A  being  the  mechanical 
equivalent  of  heat.  So  that,  if  r  is  the  total  heat  of  evaporation, 

r  —  p  +  Ap  (or  —  s~) 

in  which  p  is  the  internal  work.  From  the  values  of  r  and  of  Ap  (or  -  j),  it  is 
easy  to  deduce  that  of  p,  and  it  is  found  that  this  value  decreases  as  the  tem- 
perature increases. 

373.  Cold  due  to  evaporation.  Mercury  frozen. — Whatever  be  the 
temperature  at  which  a  vapour  is  produced,  an  absorption  of  heat  always 
takes  place.  If,  therefore,  a  liquid  evaporates,  and  does  not  receive  from 
without  a  quantity  of  heat  equal  to  that  which  is  expended  in  producing  the 
vapour,  its  temperature  sinks,  and  the  cooling  is  greater  in  proportion  as  the 
evaporation  is  more  rapid. 

Leslie  succeeded  in  freezing  water  by  means  of  rapid  evaporation. 
Under  the  receiver  of  the  air-pump  is  placed  a  vessel  containing  strong  sul- 
phuric acid,  and  above  it  a  thin  metal  capsule,  A  (fig.  316),  containing  a  small 

quantity  of  water.  By 
exhausting  the  receiver 
the  water  begins  to 
boil  (360),  and  since 
the  vapour  is  absorbed 
by  the  sulphuric  acid 
as  fast  as  it  is  formed, 
a  rapid  evaporation 
is  produced,  which 
quickly  effects  the 
freezing  of  the  water. 

This  experiment  is 
best  performed  by 
using,  instead  of  a  thin 

Fig.  316.  Fig.  317.  metal    dish,  a   watch- 

glass  coated  with  lamp- 
black and  resting  on  a  cork.  The  advantage  of  this  is  twofold  :  firstly,  the 
lampblack  is  a  very  bad  conductor;  and,  secondly,  it  is  not  moistened  by 
the  liquid,  which  remains  in  the  form  of  a  globule  not  in  contact  with  the 
glass.  A  small  porous  dish  may  also  advantageously  be  used. 

The  same  result  is  obtained  by  means  of  Wollaston's  cryophorus  (fig. 
317),  which  consists  of  a  bent  glass  tube  provided  with  a  bulb  at  each  end. 
The  apparatus  is  prepared  by  introducing  a  small  quantity  of  water,  which 
is  then  boiled  so  as  to  expel  all  air.  It  is  then  hermetically  sealed,  so  that 
on  cooling  it  contains  only  water  and  the  vapour  of  water.  The  water  being 
introduced  into  the  bulb  A,  the  other  bulb  is  immersed  in  a  freezing 


-373]  Cold  dne  to  Evaporation.  327 

mixture.  The  vapour  in  the  tube  is  thus  condensed  ;  the  water  in  A  rapidly 
yields  more.  But  this  rapid  production  of  vapour  requires  a  large  amount  of 
heat,  which  is  abstracted  from  the  water  in  A,  and  its  temperature  is  so  much 
reduced  that  it  freezes. 

By  using  liquids  more  volatile  than  water,  more  particularly  liquid  sul- 
phurous acid,  which  boils  at  —  10°,  or,  still  better,  chloride  of  methyle,  which 
is  now  prepared  industrially  in  large  quantities,  a  degree  of  cold  is  obtained 
sufficiently  low  to  freeze  mercury.  This  experiment  may  be  made  on  a 
small  scale  by  covering  the  bulb  of  a  thermometer  with  cotton  wool,  and 
after  having  moistened  it  with  the  liquid  in  question,  placing  it  under  the 
receiver  of  the  air-pump.  When  a  vacuum  is  produced  the  mercury  is 
quickly  frozen. 

By  passing  a  current  of  air  previously  cooled  through  liquid  chloride  of 
methyle,  temperatures  of  from  —  23°  to  —  70°  C.  may  be  maintained  with 
great  constancy  for  several  hours. 

Thilorier,  by  directing  a  jet  of  liquid  carbonic  acid  on  the  bulb  of  an  alcohol 
thermometer,  obtained  a  temperature  of  —  100°  without  freezing  the  alcohol. 
We  have  already  seen,  however  (343),  that  with  a  mixture  of  solid  carbonic 
.acid,  liquid  protoxide  of  nitrogen  and  ether,  Despretz  obtained  a  sufficient 
•degree  of  cold  to  reduce  alcohol  to  the  viscous  state. 

By  means  of  the  evaporation  of  bisulphide  of  carbon  the  formation  of  ice 
may  be  illustrated  without  the  aid  of  an  air-pump.  A  little  water  is  dropped 
on  a  board,  and  a  capsule  of  thin  copper  foil,  containing  bisulphide  of 
carbon,  is  placed  on  the  water.  The  evaporation  of  the  bisulphide  is  accele- 
rated by  means  of  a  pair  of  bellows,  and  after  a  few  minutes  the  water 
freezes  round  the  capsule  so  that  the  latter  adheres  to  the  wood. 

In  like  manner,  if  some  water  be  placed  in  a  test-tube,  which  is  then 
dipped  in  a  glass  containing  some  ether,  and  a  current  of  air  be  blown 
through  the  ether  by  means  of  a  glass  tube  fitted  to  the  nozzle  of  a  pair  of 
bellows,  the  rapid  evaporation  of  the  ether  very  soon  freezes  the  water  in 
the  tube.  Richardson's  apparatus  for  producing  local  anaesthesia  also 
•depends  on  the  cold  produced  by  the  evaporation  of  ether. 

The  cold  produced  by  evaporation  is  used  in  hot  climates  to  cool  water 
by  means  of  alcarrazas.  These  are  porous  earthen  vessels,  through  which 
water  percolates  so  that  on  the  outside  there  is  a  continual  evaporation,  which 
is  accelerated  when  the  vessels  are  placed  in  a  current  of  air.  For  the  same 
reason  wine  is  cooled  by  wrapping  the  bottles  in  wet  cloths  and  placing  them 
in  a  draught. 

In  Harrison's  method  of  making  ice  artificially,  a  steam-engine  is  used  to 
work  an  air-pump  which  produces  a  rapid  evaporation  of  some  ether,  in 
which  is  immersed  the  vessel  containing  the  water  to  be  frozen.  The  ap- 
paratus is  so  constructed  that  the  vaporised  ether  can  be  condensed  and 
used  again. 

The  cooling  effect  produced  by  a  wind  or  draught  does  not  necessarily 
.arise  from  the  wind  being  cooler,  for  it  may,  as  shown  by  the  thermometer, 
be  actually  warmer,  but  arises  from  the  rapid  evaporation  it  causes  from  the 
surface  of  the  skin.  We  have  the  feeling  of  oppression  even  at  moderate 
temperatures,  when  we  are  in  an -atmosphere  saturated  by  moisture,  in  which 
no  evaporation  takes  place. 


328 


On  Heat. 


[374. 


374.  Carre's  apparatus  for  freezing  water. — We  have  already  seen  that 
when  any  liquid  is  converted  into  vapour  it  absorbs  a  considerable  quantity 
of  sensible  heat ;  this  furnishes  a  source  of  cold  which  is  more  abundant  the 
more  volatile  the  liquid,  and  the  greater  its  heat  of  vaporisation. 

This  property  of  liquids  has  been  utilised  by  M.  Carre,  in  freezing  water 
by  the  distillation  of  ammonia.  The  apparatus  consists  of  a  cylindrical 
boiler  C  (figs.  318,  319),  and  of  a  slightly  conical  vessel  A,  which  is  \htfreezer- 
These  two  vessels  are  connected  by  a  tube,  m,  and  a  brace,  n,  binds  them 
firmly.  They  are  made  of  strong  galvanised  iron  plate,  and  can  resist  a 
pressure  of  seven  atmospheres. 

The  boiler  C,  which  holds  about  two  gallons,  is  three  parts  filled  with  a 
strong  solution  of  ammonia.  In  a  tubulure  in  the  upper  part  of  the  boiler 
some  oil  is  placed,  and  in  this  a  thermometer  /.  The  freezer  A  consists  of 
two  concentric  envelopes,  in  such  a  manner  that,  its  centre  being  hollow,  a 
metal  vessel,  G,  containing  the  water  to  be  frozen,  can  be  placed  in  this  space. 
Hence  only  the  annular  space  between  the  sides  of  the  freezer  is  in  commu- 
nication with  the  boiler  by  means  of  the  tube  m.  In  the  upper  part  of  the 
freezer  there  is  a  small  tubulure,  which  can  be  closed  by  a  metal  stopper, 
and  by  which  the  solution  of  ammonia  is  introduced. 

The  formation  of  ice  comprehends  two  distinct  operations.  In  the  first, 
the  boiler  is  placed  in  a  furnace  F,  and  the  freezer  in  a  bath  of  cold  water  of 
about  12°.  The  boiler  being  heated  to  130°,  the  ammoniacal  gas  dissolved 


Fig.  318. 


Fig-  3i9- 


in  the  water  of  the  boiler  is  disengaged,  and,  in  virtue  of  its  own  pressure,  is 
liquefied  in  the  freezer,  along  with  about  a  tenth  of  its  weight  of  water.  This 
distillation  of  C  towards  A  lasts  about  an  hour  and  a  quarter,  and  when  it  is- 
finished  the  second  operation  commences ;  this  consists  in  placing  the  boiler 
in  the  cold-water  bath  (fig.  319),  and  the  freezer  outside,  care  being  taken 
to  surround  it  with  dry  flannel.  The  vessel  G,  about  three-quarters  full  of 


374] 


Carre's  Apparatus  for  Freezing  Water. 


329 


water,  is  placed  in  the  freezer.  As  the  boiler  cools,  the  ammoniacal  gas 
with  which  it  is  filled  is  again  dissolved ;  the  pressure  thus  being  diminished, 
the  ammonia  which  has  been  liquefied  in  it  is  converted  into  the  gaseous 
form,  and  now  distils  from  A  towards  C,  to  redissolve  in  the  water  which 
has  remained  in  the  boiler.  During  this  distillation  the  ammonia  which  is 
gasified  absorbs  a  great  quantity  of  heat,  which  is  withdrawn  from  the  vessel 
G  and  the  water  it  contains.  Hence  it  is  that  this  water  freezes.  In  order 
to  have  better  contact  between  the  sides  of  the  vessel  G  and  the  freezer, 
alcohol  is  poured  between  them.  In  about  an  hour  and  a  quarter  a  perfectly 
compact  cylindrical  block  of  ice  can  be  taken  from  the  vessel  G. 

This  apparatus  gives  about  four  pounds  of  ice  in  an  hour,  at  a  price  of 
about  a  farthing  per  pound  ;  large  continuously  working  apparatus  have,  how- 
ever, been  constructed,  which  produce  as  much  as  800  pounds  of  ice  in  an  hour. 

Carre*  has  constructed  an  ice-making  machine  which  is  an  industrial 
application  of  Leslie's  experiment  (373),  and  by  which  considerable  quantities 
of  water  may  be  frozen  in  a  short  time.  It  consists  of  a  cylinder  R,  about  15 
inches  long  by  4  in  diameter,  made  of  an  alloy  of  lead  and  antimony 
(fig.  320).  At  one  end  is  a  funnel  E,  by  which  strong  sulphuric  acid  can  be 
introduced  :  at  the  other  is  a  tubulure  m,  to  which  is  screwed  a  dome  d  that 
supports  a  series  of  obstacles  intended  to  prevent  any  sulphuric  acid  from 
spirting  into  m  and  b.  There  are,  moreover,  on  the  receiver  a  wide  tube  ^, 
closed  by  a  thick  glass  disc  O,  and  a  long  tube  //,  to  the  top  of  which  is  fitted 
the  bottle  C  con- 
taining water  to  be 
frozen.  The  dome 
d,  the  disc  O,  and 
the  stopper  i  of  the 
funnel  E  are  all 
sealed  with  wax. 

On  the  side  of 
the  receiver  is  an 
air-pump  P,  con- 
nected with  it  by  a 
tube  b,  and  worked 
by  a  handle  M.  To 
this  handle  is  at- 
tached a  rod  /, 
which  by  the 
mechanism  repre- 
sented on  the  left 
of  the  figure  works 
a  stirrer  A  in  the 
sulphuric  acid.  A 
lever  x  connected 
with  a  horizontal 
axis  which  tra- 
verses a  small  stuff- 
ing-box n,  trans- 
mits its  backward  and  forward  motion  to  the  rod  e  and  to  the  stirrer.  This 


Fig.  320. 


330  On  Heat.  [374- 

and  the  stuffing-box  n  are  fitted   in  a  tubulure  on  the  side  of  the  tubu- 
lure  m. 

The  smallest  size  which  Carre  makes  contains  2*5  kilogrammes  of  sul- 
phuric acid,  and  the  water-bottle  about  400  grammes,  when  it  is  one-third  full. 
After  about  70  strokes  of  the  piston  the  water  begins  to  boil ;  the  acid  being 
in  continued  agitation,  the  vapour  is  rapidly  absorbed  by  it,  and  the  pump  is 
worked  until  freezing  begins.  For  this  purpose  it  is  merely  necessary  to 
give  a  few  strokes  every  five  minutes.  The  rate  of  freezing  depends  on  the 
strength  of  the  acid  ;  when  this  gets  very  dilute  it  requires  renewal  :  but  12 
water-bottles  can  be  frozen  with  the  same  quantity  of  acid. 

LIQUEFACTION   OF  VAPOURS   AND   GASES. 

375.  liquefaction   of  vapours. — The  liquefaction   or   condensation   of 
vapours  is  their  passage  from  the  aeriform  to  the  liquid  state.     Condensa- 
tion may  be  due  to  three  causes — cooling,  compression,  or  chemical  action. 
For  the  first,  two  causes  the  vapours  must  be  saturated  (353),  while  the 
latter  produces  the  liquefaction  of  the  most  rarefied  vapours.     Thus,  a  large 
number  of  salts  absorb  and  condense  the  aqueous  vapour  in  the  atmosphere, 
however  small  its  quantity. 

When  vapours  are  condensed,  their  latent  heat  becomes  free  ;  that  is,  it 
affects  the  thermometer.  This  is  readily  seen  when  a  current  of  steam  at 
ioo°is  passed  into  a  vessel  of  water  at  the  ordinary  temperature.  The  liquid 
becomes  rapidly  heated,  and  soon  reaches  100°.  The  quantity  of  heat  given 
up  in  liquefaction  is  equal  to  the  quantity  absorbed  in  producing  the  vapour. 

376.  Distillation.     Stills.—  Distillation    is    an    operation   by   which    a 


Fig.  321. 


volatile  liquid  may  be  separated  from  substances  which  it  holds  in  solution 
or  by  which  two   liquids   of  different  volatilities  may  be  separated.     The 


-377] 


Liebig's  Condenser. 


331 

•operation  depends  on  the  transformation  of  liquids  into  vapour  by  the  action 
•of  heat,  and  on  the  condensation  of  this  vapour  by  cooling. 

The  apparatus  used  in  distillation  is  called  a  still.  Its  form  may  vary 
greatly,  but  it  consists  essentially  of  three  parts  :  ist,  the  body  A  (fig.  321), 
a  copper  vessel  containing  the  liquid,  the  lower  part  of  which  fits  in  the 
furnace ;  2nd,  the  head,  B,  which  fits  on  the  body,  and  from  which  a 
lateral  tube,  C,  leads  to  :  3rd,  the  worm,  S,  a  long  spiral  tin  or  copper  tube 
placed  in  a  cistern  kept  constantly  full  of  cold  water.  The  object  of  the 
worm  is  to  condense  the  vapour  by  exposing  a  greater  extent  of  cold  surface. 

To  free  ordinary  water  from  the  many  impurities  which  it  contains,  it  is 
placed  in  a  still  and  heated.  The  vapours  disengaged  are  condensed  in  the 
worm,  and  the  distilled  water  arising  from  the  condensation  is  collected  in 
the  receiver  D.  The  vapours  in  condensing  rapidly  heat  the  water  in  the 
cistern,  which  must,  therefore,  be  constantly  renewed.  For  this  purpose  a 
continual  supply  of  cold  water  passes  into  the  bottom  of  the  cistern,  while 
the  lighter  heated  water  rises  to  the  surface  and  escapes  by  a  tube  in  the  top 
of  the  cistern. 

377.  liebig-'s  Condenser. — In  distilling  small  quantities  of  liquids 
or  in  taking  the  boiling  point  of  a  liquid,  so  as  not  to  lose  any  of  it,  the 
-apparatus  known  as  Liebig's  Condenser  is  extremely  useful.  It  consists  of  a 
glass  tube,  tt  (fig.  322),  about  thirty  inches  long,  fitted  in  a  copper  or  tin  tube 
by  means  of  perforated  corks.  A  constant  supply  of  cold  water  from  the 
vessel  a  passes  into  the  space  between  the  two  tubes,  being  conveyed  to  the 


rig.  322. 

lower  part  of  the  condenser  by  a  funnel  and  tube  f,  and  flowing  out  from  the 
upper  part  of  the  tube  g.  The  liquid  to  be  distilled  is  contained  in  a  retort, 
the  neck  of  which  is  placed  in  the  tube  ;  the  condensed  liquid  drops  quite 
•cold  into  a  vessel  placed  to  receive  it  at  the  other  extremity  of  the  con- 
densing tube. 


332 


On  Heat. 


L378- 


378.  Apparatus  for  determining-  the  alcoholic  value  of  wines. — One 

of  the  forms  of  this  apparatus  consists  of  a  glass  flask  resting  on  a  tripod^ 
and  heated  by  a  spirit  lamp  (fig.  323).  By  means  of  a  caoutchouc  tube  this 

is  connected 
with  a  worm, 
placed  in  a  cop- 
per vessel  filled 
with  cold  water, 
and  below  which 
is  a  test  glass 
for  collecting  the 
distillate.  On 
this  are  three 
divisions,  one  ay 
which  measures 
the  quantity  of 
wine  taken  ;  the 
two  others  indi- 
cating one-half 
and  one-third  of 
this  volume. 

F[s-  323-  The        test- 

glass  is  filled  with  the  wine  up  to  a\  this  is  then  poured  into  the  flask,, 
which  having  been  connected  with  the  worm,  the  distillation  is  commenced. 
The  liquid  which  distils  over  is  a  mixture  of  alcohol  and  water  ;  for  or- 
dinary wines,  such  as  clarets  and  hocks,  about  one-third  is  distilled  over, 
and  for  wines  richer  in  spirit,  such  as  sherries  and  ports,  one-half  must 
be  distilled  ;  experiment  has  shown  that  under  these  circumstances  all 
the  alcohol  passes  over  in  the  distillate.  The  measure  is  then  filled  up  with 
distilled  water  to  a  ;  this  gives  the  mixture  of  alcohol  and  water  of  the  same 
volume  as  the  wine  taken,  free  from  all  solid  matters,  such  as  sugar,  colour- 
ing matter,  and  acid,  but  containing  all  the  alcohol.  The  specific  gravity 
of  this  distillate  is  then  taken  by  means  of  an  alcoholometer  (128),  and  the 
number  thus  obtained  corresponds  to  a  certain  strength  of  alcohol  as  indicated 
by  the  tables. 

379.  Safety-tube, — In  preparing  gases  and  collecting  them  over  mercury 
or  water,    it  occasionally  happens   that    these  liquids  rush   back  into  the 

generating  vessel,  and  destroy  the  operation. 
This  arises  from  an  excess  of  atmospheric  pressure 
over  the  elastic  force  in  the  vessel.  If  a  gas — 
sulphurous  acid  for  example — be  generated  in  the 
flask  m  (fig.  324),  and  be  passed  into  water  in  the 
vessel  A,  as  long  as  the  gas  is  given  off  freely, 
its  elastic  force  exceeds  the  atmospheric  pressure 
and  the  weight  of  the  column  of  water,  on,  so  that 
the  water  in  the  vessel  cannot  rise  in  the  tube, 
and  absorption  is  impossible.  But  if  the  tension 
decreases,  either  through  the  flask  becoming 
cooled  or  the  gas  being  disengaged  too  slowly,  the  external  pressure  pre- 


-380] 


Liquefaction  of  Gases. 


333 


vails,  and  when  it  exceeds  the  internal  tension  by  more  than  the  weight  of 
the  column  of  water  co,  the  water  rises  into  the  flask,  and  the  operation  is 
spoiled.  This  accident  is  prevented  by  means  of  safety-tubes. 

These  are  tubes  which  prevent  absorption  by  allowing  the  air  to  enter  in 
proportion  as  the  internal  tension  decreases.  The  simplest  is  a  tube  C 
(fig.  325),  passing  through  the  cork  which 
closes  the  flask  M,  in  which  the  gas  is 
generated,  and  dipping  in  the  liquid. 
When  the  tension  of  the  gas  diminishes  in 
M,  the  atmospheric  pressure  on  the  water 
in  the  bath  E  causes  it  to  rise  to  a  certain 
height  in  the  tube  DA ;  but  this  pressure, 
acting  also  on  the  liquid  in  the  tube  C, 
depresses  it  to  the  same  depth,  assuming 
that  the  liquid  has  the  same  density  as 
the  water  in  E.  Now  as  this  depth  is 
less  than  the  height  DH,  air  enters  by  the 
aperture,  before  the  water  in  the  bath  can 
rise  to  A,  and  no  absorption  takes  place.  Fig.  325. 

4  380.  liquefaction  of  gases. — We  have  already  seen  that  a  saturated 
vapour,  the  temperature  of  which  is  constant,  is  liquefied  by  increasing  the 
pressure,  and  that,  the  pressure  remaining  constant,  it  is  brought  into  the 
liquid  state  by  diminishing  the  temperature. 

Unsaturated  vapours  behave  in  all  respects  like  gases.  And  it  is  natural 
to  suppose  that  what  are  ordinarily  called  permanent  gases  are  really  un- 
saturated  vapours.  For  the  gaseous  form  is  accidental,  and  is  not  inherent 
in  the  nature  of  the  substance.  At  ordinary  temperatures  sulphurous  anhy- 
dride is  a  gas,  while  in  countries  near  the  poles  it  is  a  liquid  ;  in  temperate 
climates  ether  is  a  liquid,  at  a  tropical  heat  it  is  a  gas.  And  just  as  unsatu- 
rated  vapours  may  be  brought  to  the  state  of  saturation,  and  then  liquefied, 
by  suitably  diminishing  the  temperature  or  increasing  the  pressure,  so  by  the 
same  means  gases  may  be  liquefied.  But  as  they  are  mostly  very  far  re- 
moved from  this  state  of  saturation,  great  cold  and  pressure  are  required. 
Some  of  them  may  indeed  be  liquefied  either  by  cold  or  by  pressure ;  for 
the  majority,  however,  both  agencies  must  be 
simultaneously  employed.  The  recent  researches 
of  Cailletet  and  of  Pictet  have  shown  that  the 
distinction  permanent  gas  no  longer  exists,  now 
that  all  are  liquefied. 

Faraday  was  the  first  to  liquefy  some  of  the 
gases.  His  method  consists  in  enclosing  in  a 
bent  glass  tube  (fig.  326)  substances  by  whose 
chemical  action  the  gas  to  be  liquefied  is  pro- 
duced, and  then  sealing  the  shorter  leg.  In 
proportion  as  the  gas  is  disengaged  its  pressure 
increases,  and  it  ultimately  liquefies  and  collects 
in  the  shorter  leg,  more  especially  if  its  condensation  is  assisted  by  placing 
the  shorter  leg  in  a  freezing  mixture.  A  small  manometer  may  be  placed 
in  the  apparatus  to  indicate  the  pressure. 


Fig.  326. 


334  On  Heat.  [380- 

Cyanogen  gas  is  readily  liquefied  by  heating  cyanide  of  mercury  in 
a  bent  tube  of  this  description  ;  and  carbonic  acid  by  heating  bicar- 
bonate of  sodium  ;  other  gases  have  been  condensed  by  taking  advan- 
tage of  special  reactions,  the  consideration  of  which  belongs  rather  to 
chemistry  than  to  physics.  For  example,  chloride  of  silver  absorbs  about 
200  times  its  volume  of  ammoniacal  gas  ;  when  the  compound  thus  formed 
is  placed  in  the  long  leg  of  a  bent  tube  and  gently  heated,  while  the  shorter 
leg  is  immersed  in  a  freezing  mixture,  a  quantity  of  liquid  ammoniacal 
gas  speedily  collects  in  the  shorter  leg. 

X  381.  Apparatus  to  liquefy  and  solidify  gases. — Thilorier  first  con- 
structed an  apparatus  by  which  considerable  quantities  of  carbonic  acid 
could  be  liquefied.  Its  principle  is  the  same  as  that  used  by  Faraday  in 
working  with  glass  tubes  ;  the  gas  is  generated  in  an  iron  cylinder,  and 
passes  through  a  metal  tube  into  another  similar  cylinder, -where  it  con- 
denses. The  use  of  this  apparatus  is  not  free  from  danger  ;  many  accidents 
have  already  happened  with  it,  and  it  has  been  superseded  by  an  apparatus 
constructed  by  Natterer,  of  Vienna,  which  is  both  convenient  and  safe. 

A  perspective  view  of  the  apparatus,  as  modified  by  Bianchi,  is  repre- 
sented in  fig.  328,  and  a  section  on  a  larger  scale  in  fig.  327.  It  consists  of 
a  wrought-iron  reservoir  A,  of  something  less  than  a  quart  capacity,  which 
can  resist  a  pressure  of  more  than  600  atmospheres.  A  small  force-pump  is 
screwed  on  the  lower  part  of  this  reservoir.  The  piston  rod  t  is  moved  by 
the  crank-rod  E,  which  is  worked  by  the  handle  M.  As  the  compression  of 
the  gas  and  the  friction  of  the  piston  produce  a  considerable  disengagement 
of  heat,  the  reservoir  A  is  surrounded  by  a  copper  vessel,  in  which  ice  or  a 
freezing  mixture  is  placed.  The  water  arising  from  the  melting  of  the  ice 
passes  by  a  tube  m  into  a  cylindrical  copper  case  C,  which  surrounds  the 
force-pump,  from  whence  it  escapes  through  the  tube  n,  and  the  stopcock  o. 
The  whole  arrangement  rests  on  an  iron  frame,  PQ. 

The  gas  to  be  liquefied  is  previously  collected  in  airtight  bags  R,  from 
whence  it  passes  into  a  bottle  V,  containing  some  suitable  drying  substance  ; 
it  then  passes  into  the  condensing  pump  through  the  vulcanised  india-rubber 
tube  H.  After  the  apparatus  has  been  worked  for  some  time  the  reservoir 
A  can  be  unscrewed  from  the  pump  without  any  escape  of  the  liquid,  for  it  is 
closed  below  by  a  valve  S  (fig.  327).  In  order  to  collect  sorhe  of  the  liquid 
gas,  the  reservoir  is  inverted  and  on  turning  the  stopcock  r  the  liquid  escapes 
by  a  small  tubulure  x. 

When  carbonic  acid  has  been  liquefied  and  is  allowed  to  escape  into  the 
air,  a  portion  only  of  the  liquid  volatilises;  in  consequence  of  the  heat  ab- 
sorbed by  this  evaporation,  the  rest  is  so  much  cooled  as  to  solidify  in  white 
flakes  like  snow  or  anhydrous  phosphoric  acid.  This  may  be  collected  by 
placing  a  stout  woollen  bag  like  a  tobacco  pouch  over  a  pipe  attached  to  the 
tube  x ;  if  the  porous  mass  is  compressed  or  hammered  in  stout  wooden 
cylinders  sticks  of  solid  carbonic  acid  are  obtained,  very  like  chalk  in  appear- 
ance. 

Solid  carbonic  acid  evaporates  very  slowly.  By  means  of  an  alcohol 
thermometer  its  temperature  has  been  found  to  be  about  —90.  A  small 
quantity  placed  on  the  hand  does  not  produce  the  sensation  of  such  great 
cold  as  might  be  expected.  This  arises  from  the  imperfect  contact.  But  if 


-381]  Apparatus  to  Liquefy  and  Solidify  Gases.  335 

the  solid  be  mixed  with  ether  the  cold  produced  is  so  intense  that  when  a 
little  is  placed  on  the  skin  all  the  effects  of  a  severe  burn  are  produced.  A 
mixture  of  these  two  substances  solidifies  four  times  its  weight  of  mercury 
in  a  few  minutes.  When  a  tube  containing  liquid  carbonic  acid  is  placed  in 
this  mixture,  the  liquid  becomes  solid  and  looks  like  a  transparent  piece 
of  ice. 


Fig.  328. 

The  most  remarkable  liquefaction  obtained  by  this  apparatus  is  that  of" 
nitrous  oxide.     The  gas  once  liquefied  only  evaporates  slowly,  and  produces 
a  temperature  of  88°  below  zero.     Mercury  placed  in  it  in  small  quantities 
instantly  solidifies.     The  same  is  the  case  with  water  ;  it  must  be  added 
drop  by  drop,  otherwise,   its  latent  heat  being  much  greater  than  that  of 
mercury,  the  heat  given  up  by  the  water  in  solidifying  would  be  sufficient  to 
cause  an  explosion  of  the  nitrous  oxide. 

Nitrous  oxide   is   readily  decomposed  by  heat,  and   has  the   property 
of  supporting  the  combustion  of  bodies  with  almost  as  much  brilliancy  as> 


336 


On  Heat. 


[381- 


oxygen  ;  and  even  at  low  temperatures  it  preserves  this  property.  When  a 
piece  of  incandescent  charcoal  is  thrown  on  liquid  nitrous  oxide  it  continues 
to  burn  with  a  brilliant  light. 

The  cold  produced  by  the  evaporation  of  ether  (373)  has  been  used  by 
Loir  and  Drion  in  the  liquefaction  of  gases.  By  passing  a  current  of  air 
from  a  blowpipe  bellows  through  several  tubes  into  a  few  ounces  of  ether,  a 
temperature  of  -  34°  C.  can  be  reached  in  five  or  six  minutes,  and  may  be 
kept  up  for  fifteen  or  twenty  minutes.  By  evaporating  liquid  sulphurous 
acid  in  the  same  manner  a  great  degree  of  cold,  -  50°  C.,  is  obtained.  At 
this  temperature  ammoniacal  gas  may  be  liquefied.  By  rapidly  evaporating 
liquid  ammonia  under  the  air-pump,  in  the  presence  of  sulphuric  acid,  a 
temperature  of  —  87°  is  attained,  which  is  found  sufficient  to  liquefy  carbonic 
acid  under  the  ordinary  pressure  of  the  atmosphere. 

382.  Cailletet's  and  Pictet's  researches. — Cailletet  and  Pictet,  work- 
ing independently,  but  simultaneously,  have  effaced  the  old  distinction 
between  permanent  and  non-permanent  gases,  by 
effecting  the  liquefaction  of  the  gases  oxygen  and 
hydrogen,  and  other  gases  hitherto  supposed  to  be 
incoercible.  This  has  been  accomplished  by  means 
of  powerful  material  appliances  directed  with  great 
skill  and  ingenuity. 

The  essential  parts  of  Cailletet's  apparatus  are 
represented  in  fig.  329.  The  gas  to  be  condensed 
is  contained  in  the  tube  TP,  which  is  fitted,  by 
means  of  a  bronze  screw  A  into  a  strong  wrought- 
iron  mercury  bath  B.  By  means  of  a  screw  RE, 
and  a  tube  U,  this  is  connected  with  a  hydraulic 
or  a  screw  press  not  represented  in  the  figure.  The 
capillary  part  P  of  the  tube  T  is  placed  in  a 
vessel  M,  in  which  it  can  be  surrounded  by  a  freez- 
ing mixture,  and  this  again  is  surrounded  by  a 
stout  safety  bell -jar  C. 

When  a  pressure  of  250  to  300  atmospheres  is 
applied  by  means  of  the  hydraulic  press,  after 
waiting  until  the  heat  due  to  the  compression  has 
disappeared,  if  a  screw  arranged  in  the  press  is 
suddenly  opened,  the  pressure  being  diminished, 
the  cold  produced  by  the  sudden  expansion  of  the 
gas  in  the  tube  TP  is  so  great  as  to  liquefy  a  por- 
tion of  the  rest,  as  is  shown  by  the  production  of  a 
mist. 

This  observation  was  first  made  with  binoxide  of  nitrogen,  but  similar 
results  have  been  obtained  with  marsh  gas,  carbonic  acid,  and  oxygen. 

The  principle  of  Pictet's  method  is  that  of  liberating  the  gas  under  great 
pressure  combined  with  the  application  of  great  degrees  of  cold.  The 
essential  parts  of  the  apparatus  are  the  following  : — Two  double-acting 
pumps,  A  and  B  (fig.  330),  are  so  coupled  together  that  they  cause  the 
evaporation  of  liquid  sulphurous  acid  contained  in  the  annular  receiver  C. 
By  the  play  of  the  pumps  the  gas  thus  evaporated  is  forced  into  the  re- 


Fig.  329- 


Cailletefs  and  Pictefs  Researches. 


337 


-382] 

ceiver  D,  where  it  is  cooled  by  a  current  of  water,  and  again  liquefied  under 
a  pressure  of  three  atmospheres.  Thence  it  passes  again  by  the  narrow  tube 
d  to  the  receiver  C,  to  replace  that  which  is  evaporated. 

In  this  way  the  temperature  of  the  liquid  sulphurous  acid  is  reduced  to 
—  65°.  Its  function  is  to  produce  a  sufficient  quantity  of  liquid  carbonic  acid, 
which  is  then  submitted  to  a  perfectly  analogous  process  of  rarefaction  and 
condensation.  This  is  effected  by  means  of  two  similar  pumps  E  and  F. 
The  carbonic  acid  gas,  perfectly  pure  and  dry,  is  drawn  from  a  reservoir 
through  a  tube  not  represented  in  the  figure,  and  is  forced  into  the  condenser 
K,  which  is  cooled  by  the  liquid  sulphurous  acid  to  a  temperature  of  -65°, 
and  is  there  liquefied. 

H  is  a  tube  of  stout  copper  in  connection  with  the  condenser  K  by  a 
narrow  tube  k.  When  a  sufficient  quantity  of  carbonic  acid  has  been  liquefied., 
the  connection  with  the  gasholder  is  cut  off,  and  by  working  the  pumps  E 
and  F  a  vacuum  is  created  over  the  liquid  carbonic  acid  in  H,  which  pro- 
duces so  great  a  cold  as  to  solidify  it. 

L  is  a  stout  wrought-iron  retort  capable  of  standing  a  pressure  of  1,500 
atmospheres.  In  it  are  placed  the  substances  by  whose  chemical  actions 
the  gas  is  produced; 
potassium  chlorate 
in  the  case  of 
oxygen.  This  re- 
tort is  closed  by  a 
strong  copper  tube 
in  which  the  actual 
condensation  is  ef- 
fected, near  the  end 
of  which  is  a  spe- 
cially constructed 
manometer  R,,and 
which  is  closed  by 
a  stopcock  N. 

When  the  four 
pumps  are  set  in 
action,  for  which  a 
steam-engine  of  15 
horse-power  is  re- 
quired, heat  is  ap- 
plied to  the  retort. 
Oxygen  is  liberated 
in  a  calculated 
quantity,  the  tem- 


Fig.  33°. 


perature  of  the  retort  being  about  48 5°-  Towards  the  close  of  the  de- 
composition the  manometer  indicates  a  pressure  of  500  atmospheres,  and 
then  sinks  to  320.  This  diminution  is  due  to  the  condensation  of  gas, 
and  at  this  stage  the  tube  contains  liquefied  oxygen.  If  the  cock  N  is 
opened,  the  gas  issues  with  violence,  having  the  appearance  of  a  dazzling 
white  pencil.  This  lasts  three  or  four  seconds.  On  closing  the  stopcock 
the  pressure,  which  had  diminished  to  400  atmospheres  now  rises  again,  and 


338  On  Heat.  [382- 

again  becomes  stationary,  proving  that  the  gas  is  once  more  being  con- 
densed. The  density  of  liquid  oxygen  has  been  found  to  be  0-9. 

The  phenomena  presented  by  the  jet  of  oxygen  when  viewed  by  the 
electric  light  showed  that  the  light  it  emits  was  partially  polarised,  indicating 
a  probable  transient  crystallisation  of  the  gas. 

For  hydrogen  the  gas  was  disengaged  by  heating  a  mixture  of  potassic 
formate  and  hydrate,  and  protoxide  of  nitrogen  was  used  instead  of  carbonic 
acid,  by  which  the  temperature  could  be  reduced  to  —  140°  C.  When  the 
pressure  had  reached  650  atmospheres,  and  the  cock  was  opened,  a  steel- 
blue  jet  issued  from  the  aperture  with  a  brisk  noise.  This  suddenly  became 
intermittent,  and  resembled  a  shower  of  hailstones.  As  the  separate  granules 
struck  the  ground,  they  produced  a  loud  noise,  and  Pictet  considers  that  in 
all  probability  the  hydrogen  in  the  interior  was  frozen. 

In  some  later  experiments,  the  details  of  which  are  too  complicated  to 
reproduce  here,  Cailletet  has  produced  very  low  temperatures  by  the  use  of 
liquid  ethylene  gas.  This  gas  can  be  liquefied  by  a  pressure  of  45  atmo- 
spheres at  a  temperature  of  i°.  By  promoting  the  evaporation  of  this  liquid, 
by  passing  through  it  a  current  of  air  or  hydrogen  which  has  been  previously 
cooled  by  the  rapid  evaporation  of  chloride  of  methyle,  the  temperature  is 
easily  reduced  to  —120°.  When  oxygen  gas  is  cooled  to  this  temperature 
the  application  of  pressure  is  sufficient  to  resolve  it  into  a  colourless,  trans- 
parent liquid  sharply  separated  from  the  gas  by  a  meniscus. 

By  surrounding  the  gas  under  experiment  by  concentric  tubes  containing 
liquid  oxygen,  which  in  turn  is  surrounded  by  liquid  ethylene,  Olszewski 
obtained  temperatures  low  enough  to  solidify  nitrogen,  carbonic  oxide,  marsh 
gas,  and  nitric  oxide.  The  evaporation  of  solid  nitrogen  under  a  pressure 
of  4tnm  produces  a  temperature  of  —225°. 


MIXTURE  OF  GASES  AND  VAPOURS. 

383.  X»aws  of  the  mixture  of  gases  and  vapours. — Every  mixture  of  a 
gas  and  a  vapour  obeys  the  two  following  laws  : — 

I.  The  pressure,  and,  consequently,  the  quantity,  of  vapour  which  saturates 
a  given  space  are  the  same  for  the  same  temperature,  whether  this  space  con- 
tains a  gas  or  is  a  vactium. 

II.  The  pressure  of  the  mixture  of  a  gas  and  a  vapour  is  equal  to  the  sum 
of  the  pressures  which  each  would  possess  if  it  occupied  the  same  space  alone. 

These  are  known  as  Daltoris  laws,  from  their  discoverer,  and  are  de- 
monstrated by  the  following  apparatus,  which  was  invented  by  Gay-Lussac  : — 
It  consists  of  a  glass  tube  A  (fig.  331),  to  which  two  stopcocks,  b  and  d,  are 
cemented.  The  lower  stopcock  is  provided  with  a  tubulure  which  connects 
the  tube  A  with  a  tube  B  of  smaller  diameter.  A  scale  between  the  two 
tubes  serves  to  measure  the  heights  of  the  mercurial  columns  in  these  tubes. 

The  tube  A  is  filled  with  mercury,  and  the  stopcocks  b  and  d  are  closed. 
A  glass  globe  M,  filled  with  dry  air  or  any  other  gas,  is  screwed  on  by  means 
of  a  stopcock  in  the  place  of  the  funnel  C.  All  three  stopcocks  are  then 
opened,  and  a  little  mercury  is  allowed  to  escape,  which  is  replaced  by  the 
dry  air  of  the  globe.  The  stopcocks  are  then  closed,  and  as  the  air  in  the 


-384] 


Mixture  of  Qases  and  Vapours. 


339 


tube  expands  on  leaving  the  globe,  the  pressure  on  it  is  less  than  that  of 

the  atmosphere.     Mercury  is  accordingly  poured  into  the  tube  B  until  it  is 

at  the  same  level  in  both  tubes.     The  globe  is  then  removed,  and  replaced 

by  the  funnel  C,  provided  with  a  stopcock  a  of  a  peculiar  construction.    It  is 

not  perforated,  but  has  a  small  cavity,  as  represented  in  n,  on  the  left  of  the 

figure.     Some  of  the  liquid  to  be  vaporised  is 

poured  into  C,  and  the  height  of  the  mercury, 

k,  having  been  noted,  the  stopcock  b  is  opened, 

and  a  turned  so  that  its  cavity  becomes  filled 

with  liquid ;    being  again    turned,   the    liquid 

enters  the  space  A  and  vaporises.     The  liquid 

is  allowed  to  fall  drop  by  drop  until  the  air  in 

the  tube  is  saturated,  which  is  the  case  when 

the  level  k  of  the  mercury  ceases  to  sink  (353). 

As  the  tension  of  the  vapour  produced  in 
the  space  A  is  added  to  that  of  the  air  already 
present,  the  total  volume  of  gas  is  increased. 
It  may  easily  be  restored  to  its  original  volume 
by  pouring  mercury  into  B.  When  the  mercury 
in  the  large  tube  has  been  raised  to  the  level  k, 
there  is  a  difference  B<?  in  the  level  of  the 
mercury  in  the  two  tubes,  which  obviously  re- 
presents the  pressure  of  the  vapour  ;  for  as  the 
air  has  resumed  its  original  volume,  its  pressure 
has  not  changed.  Now,  if  a  few  drops  of  the 
same  liquid  be  passed  into  the  vacuum  of  a 
barometric  tube,  a  depression  exactly  equal  to 
B<?  is  produced,  which  proves  that,  for  the 
same  temperature,  the  pressure  of  a  saturated 
vapour  is  the  same  in  a  gas  as  in  a  vacuum  : 
from  which  it  is  concluded  that  at  the  same 
temperature  the  quantity  of  vapour  is  also  the 
same. 

The  second  law  is  likewise  proved  by  this 
experiment,  for,  when  the  mercury  has  regained  its  level,  the  mixture 
supports  the  atmospheric  pressure  on  the  top  of  the  column  B,  in  addition 
to  the  weight  of  the  column  of  mercury  Bo.  But  of  these  two  pressures, 
one  represents  that  of  the  dry  air,  and  the  other  that  of  the  vapour.  The 
second  law  is,  moreover,  a  necessary  consequence  of  the  first. 

Experiments  can  only  be  made  with  this  apparatus  at  ordinary  tempera- 
tures ;  but  Regnault,  by  means  of  an  apparatus  which  can  be  used  at 
different  temperatures,  investigated  the  tensions  of  the  vapours  of  water, 
ether,  bisulphide  of  carbon,  and  benzole,  both  in  a  vacuum  and  in  air.  He 
found  that  the  tension  in  air  is  less  than  it  is  in  a  vacuum,  but  the  differences 
are  so  small  as  not  to  invalidate  Dalton's  law.  Regnault  was  even  inclined  to 
consider  this  law  as  theoretically  true,  attributing  the  differences  which  he 
observed  to  the  hygroscopic  properties  of  the  sides  of  the  tubes. 

384.  Problems  on  mixtures  of  gases  and  vapours. — i.  A  volume  of 
dry  air  V,  at  the  pressure  H,  being  given,  what  will  be  its  volume  V,  when 

z  2 


Fig.  331. 


340  On  Heat.  [384- 

it  is  saturated  with  vapour,  the  temperature  and  the  pressure  remaining  the 
same  ? 

If  F  be  the  elastic  force  of  the  vapour  which  saturates  the^air,  the  latter, 
in  the  mixture,  only  supports  a  pressure  equal  to  H  —  F  (381).  But  by  Boyle's 
law  the  volumes  V  and  V'  are  inversely  as  their  pressures,  consequently 

V'._5_,   whence   V'-™-. 

ii.  Let  V  be  a  given  volume  of  saturated  air  at  the  pressure  H,  and  the 
temperature  /;  what  will  be  its  volume  V,  also  saturated,  at  the  pressure  H' 
and  the  temperature  t'  ? 

Ify  be  the  maximum  tension  of  aqueous  vapour  at  /c,  and  ff  its  maxi- 
mum tension  at  //0,  the  air  alone  in  each  of  the  mixtures  V  and  V  will  be 
respectively  under  the  pressures  H  —J  and  W  —f ;  consequently,  assuming 
first  that  the  temperature  is  constant,  we  obtain 

V^W^f' 

But  as  the  volumes  V/  and  V  of  air,  at  the  temperatures  tf  and  /,  are  in  the 
ratio  of  i  +  at'  to  i  +  af,  a  being  the  coefficient  of  the  expansion  of  air,  the 
equation  becomes 


V     H'-/'     i+at 

iii.  What  is  the  weight  P  of  a  volume  of  air  V,  saturated  with  aqueous 
vapour  at  the  temperature  t  and  pressure  H  ? 

If  F  be  the  maximum  pressure  of  the  vapour  at  /°,  the  pressure  of 
the  air  alone  will  be  H  — F,  and  the  problem  reduces  itself  to  finding  :  ist, 
the  weight  of  V  cubic  inches  of  dry  air  at  /,  and  under  the  pressure  H  —  F  ; 
and  2nd,  the  weight  of  V  cubic  inches  of  saturated  vapour  at  t°  under  the 
pressure  F. 

To  solve  the  first  part  of  the  problem,  we  know  that  a  cubic  inch  of  dry 
air  at  o°  and  the  pressure  760  millimetres  weighs  0-31  grain,  and  that  at  /°, 

and  the  pressure  H  -  F,  it  weighs  °'31  ^     ~    '  (332),  consequently  V  cubic 

inches  of  dry  air  weigh 

o-3i(H-F)V  , 

(i+at)  760 

To  obtain  the  weight  of  the  vapour,  the  weight  of  the  same  volume  of 
dry  air  at  the  same  temperature  and  pressure  must  be  sought,  and  this  is  to 
be  multiplied  by  the  relative  density  of  the  vapour.  Now  as  V  cubic  inches 

of  dry  air  at  /°,  and  the  pressure  F,  weigh  — - — *  V  cubic  inches  of 

'    (i+at)  760 

aqueous  vapour,  whose  density  is  f  that  of  air  (385),  weigh 

o-3ixVFxs  (2] 


(i+af)?6o     « 
and  as  the  weight  P  is  equal  to  the  sum  of  the  weights  (i)  and  (2)  we  have 

p_o-3ixV(H-F)+  0-31  xVF  x5^    0-31  xV    /H_sF) 
(i  +  at}  760         (i+af)  760     8     (i  +  at}  760 - 


-385]  Spheroidal  Condition.  341 

SPHEROIDAL   CONDITION. 

N  385.  Xieidenfrost's  phenomena. — Boutigny's  experiments. — When 
liquids  are  thrown  upon  incandescent  metal  surfaces  they  present  remark- 
able phenomena,  which  were  first  observed  by  Leidenfrost  a  century  ago, 
and  have  been  named  after  their  discoverer.  They  have  since  then  been 
studied  by  other  physicists,  and  more  especially  by  Boutigny. 

Figure  332  represents  an  interesting  method  of  illustrating  this.  F  is  a 
small  copper  flask  which  is  heated  to  dull  redness  over  a  spirit  lamp,  and 
a  small  quantity  of  boil- 
ing hot  water  is  carefully 

introduced;     a     cork    C  IflliilT        1W>W  db c 

having  been  loosely  fitted, 
the  lamp  is  removed,  and 
in  a  short  time  steam  is 
formed  rapidly  with  such 
explosive  violence  as  to 
drive  out  the  cork. 

When  a  tolerably 
thick  silver  or  platinum 
dish  is  heated  to  redness, 
and  a  little  water,  pre- 
viously warmed,  is 

dropped  into  the  dish  by  means  of  a  pipette,  the  liquid  does  not  spread  itself 
out  on  the  dish,  and  does  not  moisten  it,  as  it  would  at  the  ordinary  tempera- 
ture, but  assumes  the  form  of  a  flattened  globule,  which  fact  Boutigny  ex- 
presses by  saying  that  it  has  passed  into  the  spheroidal  state.  It  rotates 
rapidly  round  on  the  bottom  of  the  dish,  taking  sometimes  the  form  of  a  star, 
and  not  only  does  it  not  boil,  but  its  evaporation  is  only  about  one-fiftieth 
as  rapid  as  if  it  boiled.  As  the  dish  cools,  a  point  is  reached  at  which  it  is 
not  hot  enough  to  keep  the  water  in  the  spheroidal  state  ;  it  is  accordingly 
moistened  by  the  liquid,  and  a  violent  ebullition  suddenly  ensues. 

All  volatile  liquids  can  assume  the  spheroidal  condition  ;  the  lowest 
temperature  at  which  it  can  be  produced  varies  with  each  liquid,  and  is 
more  elevated  the  higher  the  boiling  point  of  the  liquid.  For  water,  the 
dish  must  have  at  least  a  temperature  of  200°  ;  for  alcohol,  134°  ;  and  for 
ether,  61°. 

The  temperature  of  a  liquid  in  the  spheroidal  state  is  always  below  its 
boiling  point.  This  temperature  has  been  measured  by  Boutigny  by  means 
of  a  very  delicate  thermometer  ;  but  his  method  is  not  free  from  objections, 
and  it  is  probable  that  the  temperatures  he  obtained  were  too  high.  He 
found  that  of  water  to  be  95°  ;  alcohol,  75°  ;  ether,  34°  ;  and  liquid  sulphur- 
ous acid,  —  11°.  But  the  temperature  of  the  vapour  which  is  disengaged 
appears  to  be  as  high  as  that  of  the  vessel  itself. 

This  property  of  liquids  in  the  spheroidal  state  remaining  below  their 
boiling  point  was  applied  by  Boutigny  in  a  remarkable  experiment,  that 
of  freezing  water  in  a  red-hot  crucible.  He  heated  a  platinum  dish  to 
bright  redness,  and  placed  a  small  quantity  of  liquid  sulphurous  acid  in  it. 
It  immediately  assumed  the  spheroidal  condition,  and  its  evaooration  was 


342 


On  Heat. 


[385- 


remarkably  slow.  Its  temperature,  as  has  been  stated,  was  about  -  1 1°,  and 
when  a  small  quantity  of  water  was  added,  it  immediately  solidified,  and  a 
small  piece  of  ice  could  be  thrown  out  of  the  red-hot  crucible.  In  a  similar 
manner  Faraday,  by  means  of  a  mixture  of  solid  carbonic  acid  and  ether, 
succeeded  in  freezing  mercury  in  a  red-hot  crucible. 

In  the  spheroidal  state  the  liquid  is  not  in  contact  with  the  vessel. 
Boutigny  proved  this  by  heating  a  silver  plate  placed  in  a  horizontal  position 
and  dropping  on  it  a  little  dark-coloured  water.  The  liquid  assumed  the 
spheroidal  condition,  and  the  flame  of  a  candle  placed  at  some  distance 
could  be  distinctly  seen  between  the  drop  and  the  plate  (fig.  333).  If  a  plate 
perforated  by  several  fine  holes  be  heated,  a  liquid  will  assume  the  spheroidal 

state  when  pro- 
jected upon  it. 
This  is  also  the 
case  with  a  flat 
.helix  of  plati- 
num wire 
pressed  into  a 
slightly  concave 
shape.  An  ex- 
periment of  an- 
other class,  due 
to  Prof.  Church, 
Fig- 333'  also  illustrates 

the  same  fact.  A  polished  silver  dish  is  made  red-hot,  and  a  few  drops 
of  a  solution  of  sulphide  of  sodium  are  projected  on  it.  The  liquid  passes 
into  the  spheroidal  condition,  and  the  silver  undergoes  no  alteration.  But 
if  the  dish  is  allowed  to  cool,  the  liquid  instantly  moistens  it,  producing  a 
dark  spot,  due  to  the  formation  of  sulphide  of  silver.  In  like  manner 
nitric  acid  assumes  the  spheroidal  state  when  projected  on  a  heated  silver 
plate,  and  does  not  attack  the  metal  so  long  as  the  plate  remains  hot. 

An  analogous  phenomenon  is  observed  when  potassium  is  placed  on 
water.  Hydrogen  is  liberated,  and  burns  with  a  yellow  flame ;  hydrate  of 
potassium,  which  is  formed  at  the  same  time,  floats  on  the  surface  without 
touching  it,  owing  to  its  high  temperature.  In  a  short  time  it  cools  down, 
and  the  globule  coming  in  contact  with  water,  bursts  with  an  explosion. 

Similarly,  liquids  may  be  made  to  roll  upon  liquids,  and  solid  bodies 
which  vaporise  without  becoming  liquid  also  assume  a  condition  analogous 
to  the  spheroidal  state  of  liquids  when  they  are  placed  on  a  surface  whose 
temperature  is  sufficiently  high  to  vaporise  them  rapidly.  This  is  seen  when 
a  piece  of  carbonate  of  ammonium  is  placed  in  a  red-hot  platinum  crucible. 

The  phenomena  of  the  spheroidal  state  seem  to  prove  that  the  liquid 
globule  rests  upon  a  sort  of  cushion  of  its  own  vapour,  produced  by  the  heat 
radiated  from  the  hot  surface  against  its  under  side.  As  fast  as  this  vapour 
escapes  from  under  the  globule,  its  place  is  supplied  by  a  fresh  quantity 
formed  in  the  same  way,  so  that  the  globule  is  constantly  buoyed  up  by  it, 
and  does  not  come  in  actual  contact  with  the  heated  surface.  When,  how- 
ever, the  temperature  of  the  latter  falls,  the  formation  of  vapour  at  the  under 
surface  becomes  less  and  less  rapid,  until  at  length  it  is  not  sufficient  to  pre- 


-386] 


Gay-Lussads  MetJwd. 


343 


vent  the  globule  touching  the  hot  metal  or  liquid  on  which  it  rests.  As  soon 
as  contact  occurs,  heat  is  rapidly  imparted  to  the  globule,  it  enters  into  ebul- 
lition and  quickly  boils  away. 

This  explanation  is  confirmed  by  the  experiments  of  Budde,  who  found 
that  in  an  exhausted  receiver  water  passes  into  the  spheroidal  state,  even 
when  the  temperature  of  the  support  is  not  more  than  80°  or  90°  ;  for  then 
the  vapour  has  only  to  support  the  drop,  and  not  the  atmospheric  pressure  also. 

These  experiments  on  the  spheroidal  state  explain  the  fact  that  the  hand 
may  be  dipped  into  melted  lead,  or  even  melted  iron,  without  injury.  It  is 
necessary  that  the  liquid  metal  be  heated  greatly  above  its  solidifying  point. 
Usually  the  natural  moisture  of  the  hand  is  sufficient,  but  it  is  better  to  wipe 
it  with  a  damp  cloth.  In  consequence  of  the  great  heat  the  hand  becomes 
covered  with  a  layer  of  spheroidal  fluid,  which  prevents  the  contact  of  the 
metal  with  the  hand.  Radiant  heat  alone  operates,  and  this  is  principally 
expended  in  forming  aqueous  vapour  on  the  surface  of  the  hand.  If  the 
hand  is  immersed  in  boiling  water,  the  water  adheres  to  the  flesh,  and  con- 
sequently a  scald  is  produced. 

The  tales  of  ordeals  by  fire  during  the  middle  ages,  of  men  who  could 
run  bare-footed  over  red-hot  iron  without  being  injured,  are  possibly  true  in 
some  cases,  and  would  find  an  explanation  in  the  preceding  phenomena. 


DENSITY   OF   VAPOURS. 

V  386.  Gay-Iiussac's  method. — -The  density  of  a  vapour  is  the  relation 
between  the  weight  of  a  given  volume  of  this  vapour  and  that  of  the  same 
volume  of  air  at  the  same  temperature  and 
pressure. 

Two  methods  principally  are  used  in  deter- 
mining the  density  of  vapours  :  Gay-Lussac's, 
which  serves  for  liquids  that  boil  at  about  100°, 
and  Dumas',  which  can  be  used  up  to  350°. 

Fig.  334  represents  the  apparatus  used  by 
Gay-Lussac.  It  consists  of  an  iron  vessel  con- 
taining mercury,  in  which  there  is  a  glass 
cylinder  M.  This,  is  filled  with  water  or  oil, 
and  the  temperature  is  indicated  by  the  ther- 
mometer T.  In  the  interior  of  the  cylinder  is 
a  graduated  gas  jar  C,  which  at  first  is  filled 
with  mercury. 

The  liquid  whose  vapour  density  is  to  be 
determined  is  placed  in  a  small  glass  bulb  A, 
represented  on  the  left  of  the  figure.  The  bulb 
is  then  sealed  and  weighed ;  the  weight  ot  the 
liquid  taken  is  obviously  the  weight  of  the  bulb 
when  filled,  minus  its  weight  while  empty.  The 
bulb  is  then  introduced  into  the  jar  C,  and  the 
liquid  in  M  gradually  heated  somewhat  higher 
than  the  boiling  point  of  the  liquid  in  the  bulb. 
In  consequence  of  the  expansion  of  this  liquid  the  bulb  breaks,  and  the 


344 


On  Heat. 


[386- 


liquid  becoming  converted  into  vapour,  the  mercury  is  depressed,  as  repre- 
sented in  the  figure.  The  bulb  must  be  so  small  that  all  the  liquid  in  it  is 
vaporised.  The  volume  of  the  vapour  is  given  by  the  graduation  on  the  jar. 
Its  temperature  is  indicated  by  the  thermometer  T,  and  the  pressure  is 
shown  by  the  difference  between  the  height  of  the  barometer  at  the  time 
of  the  observation  and  the  height  of  the  column  of  mercury  in  the  gas  jar. 
It  is  only  necessary  then  to  calculate  the/jweight  of  a  volume  of  air  equal 
to  that  of  the  vapour  under  the  samejconditions  of  temperature  and  pressure. 
The  quotient,  obtained  by  dividing  the  weight  of  the  vapour  by  that  of  the 
air,  gives  the  required  density  of  the  vapour. 

Let  p  be  the  weight  of  the  vapour  in  grains,  v  its  volume  in  cubic  inches, 
and  t  Its  temperature  ;  if  H  be  the  height  of  the  barometer,  and  h  that  of 
the  mercury  in  the  gas  jar,  the  pressure  on  the  vapour  will  be  H  —  h. 

It  is  required  to  find  the  weight/7  of  a  volume  of  air  -z/,  at  the  tempera- 
ture /,  and  under  a  pressure  H  —  h.  At  zero,  under  a  pressure  of  760  milli- 
metres, a  cubic  inch  of  air  weighs  0-31  grain  ;  consequently,  under  the 
same  conditions,  v  cubic  inches  will  weigh  0-3 IT/  grains.  And  therefore 
the  weight  of  v  cubic  inches  of  air,  at  /°  and  the  pressure  760  millimetres,  is 

grain  [332,  prob.  ii.]. 


As  the  weight  of  a  volume  of  air  is 
proportional  to  the  pressure,  the  above 
weight  may  be  reduced  to  the  pressure 


H  —  h    by    multiplying    by 


gives 


H->fr 
760  ' 


which 


760 


for  the  weight/'  of  the  volume  of  air  v, 
under  the  pressure  H  —  h  and  at  t°.  Con- 
sequently, for  the  desired  density  we  have 


p'     o'3i2/(H—  h] 

387.  Hofmann's  method. — Hofmann 
has  materially  improved  the  method 
of  Gay-Lussac  by  having  the  mercury 
tube  fb,  in  which  the  vapour  is  pro- 
duced, about  a  metre  in  length  (fig.  335)  ; 
it  is,  in  fact,  a  barometer,  and  the  vapour 
is  formed  in  the  Torricellian  vacuum. 
This  tube  is  surrounded  by  another  glass 
tube  a,  which  is  connected,  by  a  bent  tube 
r,  with  a  canister  <?,  so  that  water,  amylic 
alcohol,  or  aniline,  or  indeed  any  sub- 
stance with  a  constant  boiling  point,  may 
be  distilled  through  the  tube  a,  and  the 
vapour  issues  by  the  tube  d,  which  is 
connected  with  a  condensing  arrangement  not  represented  in  the  figure.  In 


Fig.  335- 


-388] 


Dumas'  Method. 


345 


this  way  more  constancy  in  the  temperatures  is  ensured  than  with  the  use 
of  a  mercury  bath.  The  liquid  is  contained  in  very  minute  stoppered  tubes, 
h,  holding  from  20  to  100  milligrammes  of  water  ;  the  stoppers  come  out  in 
the  vacuum,  and  the  tubes  can  be  used  over  and  over  again. 

As,  under  the  above  conditions,  the  liquid  vaporises  into  a  vacuum,  the 
vapour  is  formed  under  a  very  much  lower  pressure  than  that  of  the  atmo- 
sphere, and  therefore  at  a  temperature  much  below  its  ordinary  boiling  point. 
Thus,  the  vapour-density  of  a  body  which  only  boils  at  a  temperature  of 
150°  can  be  determined  at  the  temperature  of  boiling  water.  This  is  of  great 
use  in  the  case  of  those  bodies  which  decompose  at  their  boiling  point 
under  the  ordinary  atmospheric  pressure. 

Y  388.  Dumas'  method. — The  original  method  of  Gay-Lussac  cannot  be 
applied  to  liquids  whose  boiling  point  exceeds  150°  or  160°.  In  order  to  raise 
the  oil  in  the  cylinder  to  this  temperature  it  would  be  necessary  to  heat  the 
mercury  to  such  a  degree  that  its  vapour  would  be  dangerous  to  the  operator. 
And,  moreover,  the  pressure  of  the  mercurial  vapour  in  the  graduated  jar 
would  add  itself  to  that  of  the  vapour  of  the  liquid,  and  so  far  vitiate  the 
result. 

The  following  method,  devised  by  Dumas,  can  be  used  up  to  the  tem- 
perature at  which  glass  begins  to  soften  ;  that  is,  about  400°.  A  glass 
globe  is  used  with  the  neck  drawn  out  to  a  fine  point  (fig.  336).  The  globe, 
having  been  dried  externally  and  internally,  is  weighed,  the  temperature  t 
and  barometric  height  h  being  noted.  This  weight,  W,  is  the  weight  of  the 
glass  G  in  addition  to  /,  the  weight  of  the  air  it  contains.  The  globe  is 
then  gently  warmed  and  its  point  immersed  in  the  liquid  whose  vapour- 
density  is  to  be  determined  :  on  cooling,  the  air  contracts,  and  a  quantity 
of  liquid  enters  the  globe.  The  globe  is  then  immersed  in  a  bath,  either 
of  oil  or  fusible  metal,  according  to  the  tempera- 
ture to  which  it  is  to  be  raised.  In  order  to  keep 
the  globe  in  a  vertical  position  a  metal  support, 
on  which  a  movable  rod  slides,  is  fixed  on  the 
side  of  the  vessel.  This  rod  has  two  rings,  be- 
tween which  the  globe  is  placed,  as  shown  in  the 
figure.  There  is  another  rod,  to  which  a  weight 
thermometer,  D  (324),  is  attached. 

The  globe  and  thermometer  having  been  im- 
mersed in  the  bath,  the  latter  is  heated  until 
slightly  above  the  boiling  point  of  the  liquid  in 
the  globe.  The  vapour  which  passes  out  by  the 
point  expels  all  the  air  in  the  interior.  When 
the  jet  of  vapour  ceases,  which  is  the  case  when 
all  the  liquid  has  been  converted  into  vapour,  the 
point  of  the  globe  is  hermetically  sealed,  the 
temperature  of  the  bath  t',  and  the  barometric 
height  h\  being  noted.  When  the  globe  is  cooled 
it  is  carefully  cleaned  and  again  weighed.  This 

weight,  W',  is  that  of  the  glass  G,  plus  p',  the  weight  of  the  vapour  which  fills 
the  globe  at  the  temperature  /',  and  pressure  h',  or  W'  =  G  +p'.  To  obtain 
the  weight  of  the  glass  alone,  the  weight/  of  air  must  be  known,  which  is 


346  On  Heat.  [388- 

determined  in  the  following  manner  : — The  point  of  the  globe  is  placed  under 
mercury  and  the  extremity  broken  off  with  a  small  pair  of  pincers  :  the 
vapour  being  condensed,  a  vacuum  is  produced,  and  mercury  rushes  up, 
completely  filling  the  globe,  if,  in  the  experiment,  all  the  air  has  been  com- 
pletely expelled.  The  mercury  is  then  poured  into  a  carefully  graduated 
measure,  which  gives  the  volume  of  the  globe.  From  this  result,  the  volume 
of  the  globe  at  the  temperature  tf  may  be  easily  calculated,  and  consequently 
the  volume  of  the  vapour.  From  this  determination  of  the  volume  of  the 
globe,  the  weight  p  of  the  air  at  the  temperature  /  and  pressure  h  is  readily 
calculated,  and  this  result  subtracted  from  W  gives  G,  the  weight  of  the 
glass.  Now  the  weight  of  the  vapour  p'  is  W  —  G.  We  now  know  the 
weight  p'  of  a  given  volume  of  vapour  at  the  temperature  t'  and  pressure  h\ 
and  it  is  only  necessary  to  calculate  the  weight  p"  of  the  same  volume  of 
air  under  the  same  conditions,  which  is  easily  accomplished.  The  quotient 

£•-  is  the  required  density  of  the  vapour. 

Deville  and  Troost  modified  Dumas'  method  so  that  it  can  be  used  for 
determining  the  vapour-density  of  liquids  with  very  high  boiling  points. 
The  globe  is  heated  in  an  iron  cylinder  in  the  vapour  of  mercury  or  of 
sulphur,  the  temperatures  of  which  are  constant  respectively  at  350°  and  440°. 
In  other  respects  the  determination  is  the  same  as  in  Dumas'  method. 

For  determinations  at  higher  temperatures,  Deville  and  Troost  em- 
ployed the  vapour  of  zinc,  the  temperature  of  which  is  1040°.  As  glass 
vessels  are  softened  by  this  heat,  they  used  porcelain  globes  with  finely 
drawn-out  necks,  which  are  sealed  by  means  of  the  oxyhydrogen  flame. 

In  the  case  of  substances  having  a  high  boiling  point,  Victor  Meyer  has 
advantageously  used  a  non-volatile  substance,  Wood's  fusible  alloy,  which 
melts  at  70°,  instead  of  mercury.  Habermann  has  introduced  into  Dumas' 
method,  Hofmann's  modification  of  Gay-Lussac's,  by  connecting  the  open 
end  of  the  vessel  B  (fig.  336)  with  a  space  in  which  a  partial  vacuum  is  made. 
Thus  the  vapour-density  can  be  determined  for  temperatures  far  below  the 
boiling  point.  Victor  Meyer  has  also  devised  a  method  which  depends  on 
the  displacement  of  air. 

389.  Relation  of  vapour  density  to  molecular  weight.  Dissocia- 
tion.— The  densities  of  vapours,  determined  at  temperatures  a  few  degrees 
above  their  boiling  points,  and  when  they  may  be  considered  as  perfect 
gases,  are  governed  by  a  simple  but  very  important  law,  that  the  densities 
of  vapours  are  proportional  to  their  molecular  weights.  If  both  densities 
and  molecular  weights  are  referred  to  the  same  standard,  that  of  hydrogen 
being  taken  as  2  for  instance,  the  vapour  densities  are  equal  to  the  mole- 
cular weights.  If  the  density  of  air  is  taken  at  I,  that  of  hydrogen  is 
0-0693  =  28-Vw)  and  hence  for  all  other  gases  and  superheated  vapours  the 
density  is  ^-Ve  °f  the  molecular  weight. 

This  law  is  of  great  importance  in  chemistry  and  in  fixing  the  molecular 
weights  of  bodies,  more  especially  in  organic  chemistry.  In  some  cases 
exceptions  are  met  with  ;  these,  when  small,  may  be  ascribed  to  imperfection 
of  the  gaseous  state.  A  more  important  cause  is  the  following  : — When  sal- 
ammoniac,  NH4C1,  for  instance,  is  strongly  heated,  it  is  resolved  into 
ammonia,  NHa,  and  hydrochloric  acid,  HC1,  and  in  that  case  it  occupies  a 


-390]  Dissociation.  347 

volume  double  that  required  by  the  law.  But  there  is  a  partial  decomposi- 
tion even  at  temperatures  below  this,  so  that  the  vapour  consists  of  molecules 
of  sal-ammoniac,  mixed  with  molecules  of  free  hydrochloric  acid  and  of  free 
ammonia.  The  amount  of  decomposition  depends  on  the  temperature,  but 
for  the  same  temperature,  the  quantity  decomposed  is  in  a  constant  ratio  to 
that  temperature.  In  such  cases  the  vapour  density  is  said  to  be  abnormal ; 
and  this  partial  decomposition,  in  which  there  is  a  mixture  of  undecomposed 
and  of  decomposed  molecules,  is  spoken  of  as  dissociation.  Thus,  sulphuric 
acid,  SO4H2,  at  325°,  consists  of  one  half  undecomposed  molecules,  while  the 
other  half  decomposes  into  sulphuric  anhydride,  SO3,  and  water,  H2O. 

Densities  of  Vapours. 

Air      .         .          .          r         •  J  'oooo  Vapour  of  carbon  bisulphide  2*6447 

Vapour  of  water    .         ...  0*6225  ,,          phosphorus.         .  4*3256 

„         alcohol      ;.-. .  ,.     .  1*6138  „          turpentine    .         .  5*0130 

„         acetic  acid    .         .  2*0800  „          sulphur         .         .  6*6542 

„         ether    .     .    .         .  2*5860  „          mercury       .         .  6-9760 

„         benzole      ,...     .  2*7290  „          iodine.         .         .  8*7160 

The  density  of  aqueous  vapour,  when  a  space  is  saturated  with  it,  is  at 
all  temperatures  f,  or,  more  accurately,  0*6225,  of  the  density  of  air  at  the 
same  temperature  and  pressure. 

390.  Relation  between  the  volume  of  a  liquid  and  that  of  its 
vapour. — The  density  of  vapour  being  known,  we  can  readily  calculate  the 
ratio  between  the  volume  of  a  vapour  in  the  saturated  state  at  a  given  tem- 
perature, and  that  of  its  liquid  at  zero.  We  may  take,  as  an  example,  the 
relation  between  water  at  zero  and  steam  at  100°. 

The  ratio  between  the  weights  of  equal  volumes  of  air  at  zero,  and  the 
normal  barometric  pressure,  and  of  water  under  the  same  circumstances,  is 
as  i  :  773.  But  from  what  has  been  already  said  (332),  the  density  of 
air  at  zero  is  to  its  density  at  100°  as  i+at  :  i.  Hence  the  ratio  between 
the  weights  of  equal  volumes  of  air  at  100°  and  water  at  o°  is 

—  :  773,  or  073178  :  773. 
i  +0*003665  x  100 

Now  from  the  above  table  the  density  of  steam  at  100°  C.,  and  the 
normal  pressure,  compared  with  that  of  air  under  the  same  circumstances, 
is  as  0*62225  :  I-  Hence  the  ratio  between  the  weights  of  equal  volumes  of 
steam  at  100°  and  water  at  o°  is 

0*73178  x  0*6225  :  773,  or  0*4555  '  773,  or  i  :  1698. 

Therefore,  as  the  volumes  of  bodies  are  inversely  as  their  densities,  one 
volume  of  water  at  zero  expands  into  1*698  volumes  of  steam  at  100°  C. 
The  practical  rule,  that  a  cubic  inch  of  water  yields  a  cubic  foot  of  steam, 
though  not  quite  accurate,  expresses  the  relation  in  a  convenient  form. 


348  On  Heat.  [391- 


CHAPTER  VI. 

HYGROMETRY. 

391.  Province  of  hygrometry. — The  province  of  hygrometry  is  to  deter- 
mine the   quantity  of  aqueous  vapour  contained  in  a  given  volume  of  air. 
This  quantity  is  very  variable  ;  but   the   atmosphere  is   seldom  or  never 
completely  saturated  with  vapour,  even  in  our  climate.     Nor  is  it  ever  com- 
pletely dry  ;  for  if  hygrometric  substances — that  is  to  say,  substances  with  a 
great  affinity  for  water,  such  as  chloride  of  calcium,  sulphuric  acid,  £c. — be 
at  any  time  exposed  to  the  air,  they  absorb  aqueous  vapour. 

392.  Hygrometric  state. — As,  in  general,  the  air  is  never  saturated,  the 
ratio  of  the  quantity  of  aqueous  vapour  actually  present  in  the  atmosphere 
to  that  which  it  would  contain  if  it  were  saturated,  the  temperature  remain- 
ing the  same,  is  called  the  hygrometric  state,  or  degree  of  saturation. 

The  absolute  moisture  is  measured  by  the  weight  of  water  actually  present 
in  the  form  of  vapour  in  the  unit  of  volume. 

We  say  the  'air  is  dry'  when  water  evaporates  and  moist  objects  dry 
rapidly  ;  and  the  '  air  is  moist '  when  they  do  not  dry  rapidly,  and  when 
the  least  lowering  in  temperature  brings  about  deposits  of  moisture.  The 
air  is  dry  or  moist  according  as  it  is  more  or  less  distant  from  its  point 
of  saturation.  Our  judgment  is,  in  this  respect,  independent  of  the  absolute 
quantity  of  moisture  in  the  air.  Thus,  if  in  summer,  at  a  temperature  of 
25°  C,  we  find  that  each  cubic  metre  of  air  contains  13  grammes  of  vapour, 
we  say  it  is  very  dry,  for  at  this  temperature  it  could  contain  22^5  grammes. 
If,  on  the  other  hand,  in  winter  we  find  that  the  same  volume  contains  6 
grammes,  we  call  it  moist,  for  it  is  nearly  saturated  with  vapour,  and  the 
slightest  diminution  of  temperature  produces  a  deposit.  When  a  room  is 
warmed,  the  quantity  of  moisture  is  not  diminished,  but  the  humidity  of 
the  air  is  lessened,  because  its  point  of  saturation  is  raised.  The  air 
may  thus  become  so  dry  as  to  be  injurious  to  the  health,  and  hence  it  is 
usual  to  place  vessels  of  water  on  the  stoves  used  for  heating  in  France  and 
Germany. 

As  Boyle's  law  applies  to  non-saturated  vapours  as  well  as  to  gases  (354), 
it  follows  that,  with  the  same  temperature  and  volume,  the  weight  of  vapour 
in  an  unsaturated  space  increases  with  the  pressure,  and  therefore  with 
the  pressure  of  the  vapour  itself.  Instead,  therefore,  of  the  ratio  of  the 
quantities  of  vapour,  that  of  the  corresponding  pressures  may  be  substituted, 
and  it  may  be  said  that  the  hygrometric  state  is  the  ratio  of  the  elastic 
force  of  the  aqueous  vapour  which  the  air  actually  contains,  to  the  elastic 
force  of  the  vapour  which  it  would  contain  at  the  same  temperature  if  it 
were  saturated. 

If/ is  the  actual  pressure  of  aqueous  vapour  in  the  air,  and  F  that  of  satu- 


-394]  Chemical  Hygrometer.  349 

rated  vapour  at  the  same  temperature,  and  E  the  hygrometric  state,  we  have 

E  =  -L  ;  whence  /=  F  x  E. 
F 

As  a  consequence  of  this  second  definition,  it  is  important  to  notice  that, 
the  temperature  having  varied,  the  air  may  contain  the  same  quantity  of 
vapour  and  yet  not  have  the  same  hygrometric  state.  For,  when  the  tem- 
perature rises,  the  tension  of  the  vapour  which  the  air  would  contain,  if  satu- 
rated, increases  more  rapidly  than  the  tension  of  the  vapour  actually  present 
in  the  atmosphere,  and  hence  the  ratio  between  the  two  forces — that  is  to  say, 
the  hygrometric  state — becomes  smaller. 

Jamin   proposes   to   replace  this  ratio  •£,  which   expresses  the  relative 

moisture,  by  the  ratio  *f—~  in  which  H  is  the  barometric  height  :  he  calls 
H-/ 

this  the  hygrometric  richness,  and  contends  that  it  brings  out  changes  in  the 
quantity  of  moisture  present  in  the  air  with  greater  distinctness. 

It  will  presently  be  explained  (401)  how  the  weight  of  the  vapour,  con- 
tained in  a  given  volume  of  air,  may  be  deduced  from  the  hygrometric  state. 

393.  Different   kinds  of  hygrometers. — Hygrometers  are   instruments 
for  measuring  the  hygrometric  state  of  the  air.     There  are  numerous  varieties 
of  them — chemical  hygrometers,  condensing  hygrometers,  and  psychrometers. 

394.  Chemical  hygrometer. — The  method  of  the  chemical  hygrometer 
consists  in  passing  a  known  volume  of  air  over  a  substance  which  readily 
absorbs  moisture — chloride  of  calcium,  for  instance.     The  substance  having 
been  weighed  before  the  passage  of  air,  and  then  afterwards,  the  increase 


Fig.  337- 


in  weight  represents  the  amount  of  aqueous  vapour  present  in  the  air.     By 
means  of  the  apparatus  represented  in  fig.  337,  it  is  possible  to  examine  any 


350  On  Heat.  [394- 

given  volume  of  air.  Two  brass  reservoirs,  A  and  B,  of  the  same  size  and 
construction,  act  alternately  as  aspirators,  by  being  fixed  to  the  same  axis, 
about  which  they  can  turn.  They  are  connected  by  a  central  tubulure,  and 
•  by  means  of  two  tubulures  in  the  axis  the  lower  reservoir  is  always  in  con- 
nection with  the  atmosphere,  while  the  upper  one,  by  means  of  a  caoutchouc 
tube,  is  connected  with  two  tubes  M  and  N,  filled  either  with  chloride  of 
calcium,  or  with  pumice-stone  impregnated  with  sulphuric  acid.  The  first 
absorbs  the  vapours  in  the  air  drawn  through,  while  the  other,  M,  stops  any 
vapour  which  might  diffuse  from  the  reservoirs  into  the  tube  N. 

The  lower  reservoir  being  full  of  water,  and  the  upper  one  of  air,  the 
apparatus  is  inverted  so  that  the  liquid  flows  slowly  from  A  to  B.  A  vacuum 
being  formed  in  A,  air  enters  by  the  tubes  NM,  in  the  first  of  which  all  the 
vapour  is  absorbed.  When  all  the  water  is  run  into  B  it  is  inverted  ;  the 
same  flow  recommences,  and  the  same  volume  of  air  is  drawn  through 
the  tube  N.  Thus,  if  each  reservoir  holds  a  gallon,  .for  example,  and  the 
apparatus  has  been  turned  five  times,  6  gallons  of  air  have  traversed  the 
tube  N,  and  have  been  dried.  If  then,  before  the  experiment,  the  tube  with 
its  contents  has  been  weighed,  the  increase  of  weight  gives  the  weight  of 
aqueous  vapour  present  in  6  gallons  of  air  at  the  time  of  the  experiment. 

Edelmann  has  devised  a  new  form  of  hygrometer,  the  principle  of  which 
is  to  enclose  a  given  volume  of  air,  and  then  to  absorb  the  aqueous  vapour 
present  by  means  of  strong  sulphuric  acid  ;  in  this  way  a  diminution  in  the 
pressure  is  produced  which  is  determined,  and  which  is  a  direct  measure  of 
the  tension /of  the  aqueous  vapour  previously  present. 

Similar  apparatus  have  been  devised  by  Rudorff  and  Neesen. 

395.  Condensing-  hygrometers. — When    a   body  gradually  cools    in  a 
moist  atmosphere — as,  for  instance,  when  a  lump  of  ice  is  placed  in  water 
contained  in  a  polished  metal  vessel — the  layer  of  air  in  immediate  contact 
with  it  cools  also,  and  a  point  is  ultimately  reached  at  which  the  vapour 
present  is  just  sufficient  to  saturate  the  air  ;  the  least  diminution  of  tempera- 
ture then  causes  a  precipitation  of  moisture  on  the  vessel  in  form  of  dew. 
When  the  temperature  rises  again,  the  dew  disappears.     The  mean  of  these 
two  temperatures  is  taken  as  the  dew-point,  and  the  object  of  condensing 
hygrometers  is  to  observe  this  point.     Daniell's  and  Regnault's  hygrometers 
belong  to  this  class. 

396.  Daniell's  hygrometer. — This    consists  of  two    glass  bulbs  at  the 
extremities  of  a  glass  tube  bent  twice  (fig.  338).    The  bulb  A  is  two-thirds  full 
of  ether,  and  a  very  delicate  thermometer  plunged  in  it  ;  the  rest  of  the 
space  contains  nothing  but  the  vapour  of  ether,   the  ether  having  been 
boiled  before  the  bulb  B  was  sealed.     The  bulb  B  is  covered  with  muslin 
and  ether  is  dropped  upon  it.     The  ether  in  evaporating<ools  the  bulb,  and 
the  vapour  contained  in  it  is  condensed.     The  internal  pressure  being  thus 
diminished,  the  ether  in  A  forms  vapour  which  condenses  in  the  other  bulb  B. 
In  proportion  as  the  liquid  distils  from  the  lower  to  the  upper  bulb,  the  ether 
in  A  becomes  cooler,  and  ultimately  the  temperature  of  the  air  in  immediate 
contact  with  A  sinks  to  that  point  at  which  its  vapour  is  more  than  sufficient 
to  saturate  it,  and  it  is,  accordingly,  deposited  on  the  outside  as  a  ring  of  dew 
corresponding  to  the  surface  of  the  ether.     The  temperature  of  this  point  is 
noted'by  means  of  the  thermometer  in  the  inside.     The  addition  of  ether  to 


-397] 


Regnaults  Hygrometer. 


351 


the  bulb  B  is  then  discontinued,  the  temperature  of  A  rises  and  the  tempera- 
ture at  which  the  dew  disappears  is  noted.     In  order  to  render  the  deposition 
of  dew  more  perceptible,  the  bulb  A  is 
made  of  black  glass. 

These  two  points  having  been  deter- 
mined, their  mean  is  taken  as  that  of 
the  dew-point.  The  temperature  of  the 
air  at  the  time  of  the  experiment  is 
indicated  by  the  thermometer  on  the 
stem.  The  pressure/  corresponding  to 
the  temperature  of  the  dew-point,  is  then 
found  in  the  table  of  pressures  (358). 
This  pressure  is  exactly  that  of  the  va- 
pour present  in  the  air  at  the  time  of 
the  experiment.  The  pressure  F  of  va- 
pour saturated  at  the  temperature  of 
the  atmosphere  is  found  by  means  of 
the  same  table  ;  the  quotient  obtained 
by  dividing  f  by  F  represents  the  hy- 
grometric  state  of  the  air  (392).  For 
instance,  the  temperature  of  the  air 
being  15°,  suppose  the  dew-point  is  5°.  is 
From  the  table  the  corresponding  pres- 
sures are  /=  6-534  millimetres,  and 
F—  12-699  rnillimetres,  which  gives  0*514 
for  the  ratio  of /to  F,  or  the  hygrometric  state. 

There  are  many  sources  of  error  in  DanielPs  hygrometer.  The  principal 
are  :  ist,  that  as  the  evaporation  in  the  bulb  A  only  cools  the  liquid  on  the 
surface,  the  thermometer  dipping  on  it  does  not  exactly  give  the  dew-point  ; 
2nd,  that  the  observer  standing  near  the  instrument  modifies  the  hygrome- 
tric state  of  the  surrounding  air,  as  well  as  its  temperature  ;  the  cold  ether 
vapour  also  flowing  from  the  upper  bulb  may  cause  inaccuracy. 

397.  Reg-nault's  hygrometer. — Regnault's  hygrometer  is  free  from  the 
sources  of  error  incidental  to  the  use  of  Daniell's.  It  consists  of  two  very 
thin  polished  silver  thimbles  175  inch  in  height,  and  075  inch  in  diameter 
(fig.  339).  In  these  are  fixed  two  glass  tubes,  D  and  E,  in  each  of  which  is 
a  thermometer.  A  bent  tube,  A,  open  at  both  ends,  passes  through  the  cork 
of  the  tube  D,  and  reaches  nearly  to  the  bottom  of  the  thimble.  There  is  a 
tubulure  on  the  side  of  D,  fitting  in  a  brass  tube  which  forms  a  support  for 
the  apparatus.  The  end  of  this  tube  is  connected  with  an  aspirator  G.  The 
tube  E  is  not  connected  with  the  aspirator  ;  its  thermometer  simply  indicates 
the  temperature  of  the  atmosphere. 

The  tube  D  is  then  half-filled  with  ether,  and  the  stopcock  of  the  aspirator 
opened.  The  water  contained  in  it  runs  out,  and  just  as  much  air  enters 
through  the  tube  A,  bubbling  through  the  ether,  and  causing  it  to  evaporate. 
This  evaporation  produces  a  diminution  of  temperature,  so  that  dew  is  de- 
posited on  the  silver  just  as  on  the  bulb  in  Daniell's  hygrometer  ;  the  ther- 
mometer T  is  then  instantly  to  be  read,  and  the  stream  from  the  aspirator 
stopped.  The  dew  will  soon  disappear  again,  and  the  thermometer  T  is 


Fig.  338. 


352  On  Heat.  [397- 

again  to  be  read  ;  the  mean  of  the  two  readings  is  taken  ;  the  thermometer 
/  gives  the  corresponding  temperature  of  the  air,  and  hence  there  are  all  the 

elements  necessary  for 
calculating  the  hygro- 
metric  state. 

As  in  this  instru- 
ment all  the  ether  is 
at  the  same  tempera- 
ture in  consequence  of 
the  agitation,  and  the 
temperatures  may  be 
read  off  at  a  distance  by 
means  of  a  telescope, 
the  sources  of  error  in 
DanielPs  hygrometer 
are  avoided. 

A  much  simpler 
form  of  the  apparatus 
may  be  constructed 
out  of  a  common  test- 
tube  containing  a 
depth  of  i£  inch  of 
ether.  The  tube  is 
provided  with  a  loosely 
fitting  cork  in  which  is 
a  delicate  thermometer 
and  a  narrow  bent  tube  dipping  in  the  ether.  On  blowing  into  the  ether, 
through  a  caoutchouc  tube  of  considerable  length,  a  diminution  of  temperature 
is  caused,  and  dew  is  ultimately  deposited  on  the  glass  ;  after  a  little  practice 
the  whole  process  can  be  conducted  almost  as  well  as  with  Regnault's  more 
complete  instrument.  The  temperature  of  the  air  is  indicated  by  a  detached 
thermometer. 

397#.  Dynes'  hygrometer.  —  Dynes  has  constructed  a  hygrometer  which 
is  also  one  of  condensation,  but  which  dispenses  with  the  use  of  such  volatile 
liquids  as  ether.  The  principle  of  this  instrument  is  to  have  a  thin  flat 
metal  box,  through  which  a  small  stream  of  cooled  water  is  allowed  to  flow 
for  a  few  seconds.  The  dew  is  deposited  on  the  top  of  the  box,  which  is  of 
thin  dark  polished  metal.  By  alternately  stopping  the  flow  and  allowing  it 
to  continue,  the  disappearance  and  formation  of  the  dew  may  be  very  accu- 
rately observed,  and  the  corresponding  temperatures  read  off  by  a  delicate 
thermometer  placed  inside. 

398.  PsycHrometer.  Wet-bulb  hygrometer.  —  A  moist  body  evaporates 
in  the  air  more  rapidly  in  proportion  as  the  air  is  drier,  and  the  temperature 
of  the  body  sinks  in  consequence  of  this  evaporation.  The  psychrometer, 
or  wet-bulb  hygrometer^  is  based  on  this  principle,  the  application  of  which 
to  this  purpose  was  first  suggested  by  Leslie.  The  form  usually  adopted  in 
this  country  is  due  to  Mason.  It  consists  of  two  delicate  thermometers 
placed  on  a  wooden  stand  (fig.  340).  One  of  the  bulbs  is  covered  with  muslin, 
and  is  kept  continually  moist  by  being  connected  with  a  reservoir  of  water 


339< 


-398] 


Psychrometer.      Wet-Bulb  Hygrometer. 


353 


by  means  of  a  string.  Unless  the  air  is  saturated  with  moisture  the  wet-bulb 
thermometer  always  indicates  a  lower  temperature  than  the  other,  and  the 
difference  between  the  indications  of  the  two  thermometers  is  greater  in  pro- 
portion as  the  air  can  take  up  more  moisture.  The  tension  e  of  the  aqueous 
vapour  in  the  atmosphere  may  be  calculated  from  the  indications  of  the  two 
thermometers  by  means  of  the  following  empirical  formula  :  — 

£  =  £'-  0-00077  (t-t^h, 

in  which  e'  is  the  maximum  tension  corresponding  to  the  temperature  of  the 
wet-bulb  thermometer,  h  is  the  barometric  height,  and  /  and  /'  the  respective 
temperatures  of  the  dry  and  wet  bulb  thermometers.    If,  for  example,  h  =  750 
millimetres,  /=  15°  C,  f  =  10°  C.  ;  according  to  the  table  of 
pressures  (358),  e'  =  9*165,  and  we  have 

£  =  9-  1  65  -0-00077  x  5  x  750  =  6-278. 

This  pressure  corresponds  to  a  dew-point  of  about  4-5°  C. 
If  the  air  had  been  saturated,  the  pressure  would  have  been 
12-699,  anc*  the  air  is  therefore  about  half  saturated  with 
moisture. 

This  formula  expresses  the  result  with  tolerable  accuracy, 
but  the  above  constant  0-00077  requires  to  be  controlled  for 
different  positions  of  the  instrument  ;  in  small  closed  rooms 
it  is  0-00128,  in  large  rooms  it  is  o-ooioo,  and  in  the  open 
air  without  wind  it  is  0*00090  :  the  number  0*00077  is  its 
value  in  a  large  room  with  open  windows.  Regnault  found 
that  the  difference  in  temperature  of  the  two  bulbs  depends 
on  the  rapidity  of  the  current  of  air  ;  he  also  found  that  at 
a  low  temperature,  and  in  very  moist  air,  the  results  ob- 
tained with  the  psychrometer  differed  from  those  yielded  by 
his  hygrometer.  It  is  probable  that  the  indications  of  the 
psychrometer  are  only  true  for  mean  and  high  temperatures, 
and  when  the  atmosphere  is  not  too  moist. 

According  to  Glaisher  the  temperature  of  the  dew-point 
may  be  obtained  by  multiplying  the  difference  between  the  F'ls-  340. 

temperatures  of  the  wet  and  dry  bulb  by  a  constant  depend- 
ing on  the  temperature  of  the  air  at  the  time  of  observation,  and  subtracting 
the  product  thus  obtained  from  this  last-named  temperature. 

The  table  at  the  end  of  this  article  gives  the  numbers,  which  are  known 
as  Glaisher  s  factors. 

A  formula  frequently  used  in  this  country  is  that  given  by  Dr.  Apjohn. 
It  is. 

d      h  d      h 


in  which  d  is  the  difference  of  the  wet  and  dry  bulb  thermometers  in 
Fahrenheit  degrees  ;  h  the  barometric  height  in  inches  ;  f  the  pressure  of 
vapour  for  the  temperature  of  the  wet  bulb,  and  F  the  pressure  of  vapour 
at  the  dew-point,  from  which  the  dew-point  may,  if  necessary,  be  found  from 
the  tables.  The  constant  coefficient  88,  for  the  specific  heats  of  air  and 

A  A 


354 


On  Heat. 


[398- 


aqueous  vapour,  is  to  be  used  when  the  reading 
F.,  and  96  when  it  is  below. 


of  the  wet  bulb  is  above  32° 


Dry  bulb 
Temperature  F.° 

Factor 

Dry  bulb 
Temperature  F.° 

Factor 

Below  24° 

8'5 

34  to  35 

2-8 

24  to  25 

6-9 

35—40 

2'5 

25—26 

6-5 

40—45 

2*2 

20  —  27 

6-1 

45—50 

2'I 

27—28 

5-6 

50—55 

2'0 

28—29 

5'i 

55—60 

I'9 

29—30 

4-6 

60  —  65 

I  '8 

30—31 

4'i 

65—70 

r8 

31—32 

37 

70—75 

17 

32—33 

3  '3 

75—80 

17 

33—34 

3-0 

80—85 

r6 

| 

1 

399.  Absorption  hygrometers. — These  hygrometers  are  based  on  the 
property  which  organic  substances  have  of  elongating  when  moist,  and  of 
again  contracting  as  they  become  dry.  The  most  common  form  is  the  hair 
or  Saussure's  hygrometer. 

It  consists  of  a  brass  frame  (fig.  341),  on  which  is  fixed  a  hair,  <:,  fastened 
at  the  top  in  a  clamp,  «,  provided  with  a  screw,  d.  This  clamp  is  moved  by 
a  screw,  b.  The  lower  part  of  the  hair  passes  round  a 
pulley,  <?,  and  supports  a  small  weight,  p.  On  the 
pulley  there  is  a  needle,  which  moves  along  a  graduated 
scale.  When  the  hair  becomes  shorter  the  needle  rises, 
when  it  becomes  longer  the  weight^  makes  it  sink. 

The  scale  is  graduated  by  calling  that  point  zero  at 
which  the  needle  would  stand  if  the  air  were  completely 
dry,  and  100  the  point  at  which  it  stands  in  air  completely 
saturated  with  moisture.  The  distance  between  these 
points  is  divided  into  loo  equal  degrees. 

Regnault  devoted  much  study  in  order  to  render  the 
hair  hygrometer  scientifically  useful,  but  without  much 
success.  The  utmost  that  can  be  claimed  for  it  is  that  it 
can  be  used  as  a  hygroscope  ;  that  is,  an  instrument  which 
shows  approximately  whether  the  air  is  more  or  less 
moist,  without  giving  any  indication  as  to  the  quantity  of 
moisture  present.  To  this  class  of  hygroscopes  belong 
the  chimney  ornaments,  one  of  the  most  common  forms 
of  which  is  that  of  a  small  male  and  female  figure,  so 
arranged  in  reference  to  a  little  house,  with  two  doors,  that 
when  it  is  moist  the  man  goes  out  and  the  woman  goes 
in,  and  vice  versa  when  it  is  fine.  They  are  founded  on  the  property  which 
twisted  strings  or  pieces  of  catgut  possess  of  untwisting  when  moist,  and  of 
twisting  when  dry.  As  these  hygroscopes  only  change  slowly,  their  indi- 
cations are  always  behindhand  with  the  state  of  the  weather ;  nor  are  they, 
moreover,  very  exact. 


—401]  Problem  on  Hygrometry.  355 

400.  Moisture  of  the  atmosphere.  —  The  absolute  moisture  varies  with 
the  temperature  both  in  the  course  of  the  year  and  of  the  day.  In  summer 
there  is  a  maximum  at  eight  in  the  morning  and  evening,  and  a  minimum  at 
3  P.M  and  3  A.M,  because  the  ascending  current  of  air  carries  the  moisture 
upwards.  The  absolute  moisture  is  greatest  in  the  tropics,  where  it  repre- 
sents a  pressure  of  25  mm.,  while  in  our  latitudes  it  does  not  exceed  10  mm. 
The  relative  moisture,  on  the  other  hand,  is  at  the  minimum  in  the  hottest  and 
at  its  maximum  in  the  coolest  part  of  the  day.  It  varies  also  in  different 
regions.  It  is  greater  in  the  centre  of  continents  than  it  is  on  the  sea  or  the 
sea-coast.  That  the  dryness  increases  with  the  distance  from  the  sea  is 
shown  by  the  clearer  skies  of  continental  regions.  In  Platowskya  in  Siberia 
the  air,  at  a  temperature  of  24°,  was  found  to  contain  a  quantity  of  moisture 
only  sufficient  to  saturate  it  at  —  3°  ;  the  air  might  therefore  have  been 
cooled  through  27°  without  any  deposit  of  moisture.  In  some  parts  of  East 
Africa  the  springs  of  powder-flasks  exposed  to  the  damp  snap  like  twisted 
quills  ;  on  the  contrary  paper  becomes  soft  and  sloppy  by  the  loss  of  its 
glaze  ;  and  gunpowder,  if  not  kept  hermetically  sealed,  refuses  to  ignite. 
On  the  other  hand  in  North  America,  where  the  south-west  winds  blow  over 
large  tracts  of  land,  the  relative  moisture  is  less  and  the  evaporation  is  far 
more  rapid  than  in  Europe  ;  clothes  dry  quickly,  bread  soon  becomes  hard, 
newly  built  houses  can  be  at  once  inhabited,  European  pianos  soon  give  way 
there,  while  American  ones  are  very  durable  on  this  side  of  the  ocean.  As 
regards  the  animal  economy,  liquids  evaporate  more  rapidly,  by  which  the 
circulation  and  the  assimilation  is  accelerated,  and  the  whole  character  is 
more  nervous.  For  evaporation  is  quicker  the  drier  the  air,  and  the  more 
frequently  it  is  renewed  ;  it  is,  moreover,  more  rapid  the  higher  the  temper- 
ature, and  the  less  the  pressure.  This  is  not  in  disaccord  with  the  statement 
that  the  quantity  of  vapour  which  saturates  a  given  space  is  the  same 
however  this  be  filled  with  air  ;  a  certain  space  takes  up  the  same  weight  of 
vapour  whether  it  is  vacuous,  or  filled  with  rarefied  or  dense  air  ;  the  saturation 
with  vapour  takes  place  the  more  rapidly  the  smaller  the  pressure  of  the  air. 

401.  Problem  on  hygrometry.  —  To  calculate  the  weight  P  of  a  volume 
of  moist  air  V,  the  hygrometric  state  of  which  is  E,  the  temperature  /,  and 
the  pressure  H,  the  density  of  the  vapour  being  f  that  of  air. 

From  the  second  law  of  the  mixture  of  gases  and  vapours,  it  will  be  seen 
that  the  moist  air  is  nothing  more  than  a  mixture  of  V  cubic  inches  of  dry 
air  at  /°,  under  the  pressure  H  minus-  that  of  the  vapour,  and  of  V  cubic 
inches  of  vapour  at  t°  and  the  pressure  given  by  the  hygrometric  state  ; 
these  two  values  must,  therefore,  be  found  separately. 

The  formula/=  F  x  E  (392)  gives  the  pressure  /  of  the  vapour  in  the  air, 
for  E  has  been  determined,  and  F  is  found  from  the  tables.  The  pressure  f 
being  known,  if/'  is  the  pressure  of  the  air,  f+f  =  H,  from  which 


The  question  consequently  resolves  itself  into  calculating  the  weight  of 
V  cubic  inches  of  dry  air  at  /°,  and  the  pressure  H  -FE,  and  then  that  of  V 
cubic  inches  of  aqueous  vapour  also  at  /°,  but  under  the  pressure  FE. 

Now   V   cubic   inches    of  dry   air   under   the   given   conditions   weigh 


356  On  Heat.  [401- 

0  31 (     ~ — *.  and  we  readily  see  from  problem  III.  art.  384,  that  V  cubic 

(i  +  at)  760 

inches  of  vapour  at  /°,  and  the  pressure  FE,  weigh  ^  x  °$l  .    Adding 

8     (i  +  at)  760 

these  two  weights,  and  reducing,  we  get 

p_o-3iV(H-|FE)> 

(i  +  a/)  760 

If  the  air  were  saturated  we  should  have  E  =»  i,  and  the  formula  would  thus 
be  changed  into  that  already  found  for  the  mixture  of  gases  and  saturated 
vapours  (384). 

This  formula  contains,  besides  the  weight  P,  many  variable  quantities  V, 
E,  H,  and  /,  and  consequently,  by  taking  successively  each  of  these  quanti- 
ties as  unknown,  as  many  different  problems  might  be  proposed. 

402.  Correction  for  the  loss  of  weight  experienced  by  bodies 
weighed  in  the  air. — It  has  been  seen  in  speaking  of  the  balance  that  the 
weight  which  it  indicates  is  only  an  apparent  weight,  and  is  less  than  the 
real  weight.  The  latter  may  be  deduced  from  the  former  when  it  is  remem- 
bered that  every  body  weighed  in  the  air  loses  a  weight  equal  to  that  of  the 
displaced  air  (195).  This  problem  is,  however,  very  complicated,  for  not 
only  does  the  weight  of  the  displaced  air  vary  with  the  temperature,  the 
pressure,  and  the  hygrometric  state,  but  the  volume  of  the  body  to  be 
weighed,  and  that  of  the  weights,  vary  also  with  the  temperature  ;  so  that  a 
double  correction  has  to  be  made  •  one  relative  to  the  weights,  the  other  to 
the  body  weighed. 

Correction  relative  to  the  weights. — In  order  to  make  this  correction  let 
P  be  their  weight  in  air,  and  n  their  weight  in  vacua ;  further,  let  V  be  the 
volume  of  these  weights  at  o°,  D  the  density  of  the  substance  of  which  they 
are  made,  and  K  its  coefficient  of  linear  expansion. 

The  volume  V  becomes  V  (i  +  3K/)  at  t°,  hence  this  is  the  volume  of  air 
displaced  by  the  weights.  If  p.  be  the  weight  of  a  cubic  inch  of  air  at  t,  and 
the  pressure  H  at  the  time  of  weighing,  we  have  ,  , 


From  the  formula  P  =  VD  (125)  V  may  be  replaced  by  5,  and  the 
formula  becomes 

X=n[i    -^(I 

which  gives  the  value,  in  air,  of  a  weight  n,  when  p,  is  replaced  by  its  value. 
But  since  /i  is  the  weight  of  a  cubic  inch  of  air  more  or  less  moist,  at  the 
temperature  t  and  the  pressure  H,  its  value  may  be  calculated  by  means  of 
the  formula  in  the  foregoing  paragraph. 

Correction  relative  to  the  body  weighed. — Let  p  be  the  apparent  weight 
of  the  body  to  be  weighed,  TT  its  real  weight  in  vacua,  d  its  density,  k  its 
coefficient  of  expansion,  and  /  its  temperature ;  by  the  same  reasoning  as 
above  we  have 


-402]  Correction  for  Loss  of  Weight  in  Air.  357 

By  using  the  method  of  double  weighing,  and  of  a  counterpoise  whose 
apparent  weight  is  p\  the  real  weight  TT',  the  density  d',  and  the  coefficient 
k\  and  assuming  that  the  pressure  does  not  change,  which  is  usually  the 
case,  we  have  again 


If  a  and  b  are  the  two  arms  of  the  beam,  we  have  in  the  first  weighing  ap  =pb ; 
and  in  the  second  dP  =  bp,  whence/  =  P.  Replacing  P  and^  by  their  values 
deduced  from  the  above  equations,  we  have 


whence 

which  solves  the  problem. 


358  On  Heat.  [403- 

tT"  & 


CHAPTER  VII. 

CONDUCTIVITY   OF   SOLIDS,   LIQUIDS,   AND   GASES. 

403.  Transmission  of  neat. — When  we  stand  at  a  little  distance  from  a 
fire  or  other  source  of  heat  we  experience  the  sensation  of  warmth.     The 
heat  is  not  transmitted  by  the  intervening  air ;  it  passes  through  it  without 
raising  its  temperature,  for  if  we  place  a  screen  before  the  fire  the  sensation 
ceases  to  be  felt.     The  heat  from  the  sun  reaches  us  in  the  same  manner. 
The  heat,  which,  as  in  this  case,  is  transmitted  to  a  body  from  the  source  of 
heat  without  affecting  the  temperature  of  the  intervening  medium,  is  said  to 
be  radiated. 

That  heat  can  be  transmitted  through  a  medium  without  raising  its  tem- 
perature is  proved  by  a  remarkable  experiment  of  Prevost  in  1811.  Water 
from  a  spring  was  allowed  to  fall  in  a  thin  sheet ;  on  one  side  of  this  was  held 
a  red-hot  iron  ball,  and  on  the  other  a  delicate  thermometer.  The  tempera- 
ture of  the  latter  was  observed  to  rise  steadily,  a  result  which  could  not  have 
been  due  to  any  heating  effect  of  the  water  itself,  as  this  was  cold,  and  was 
continually  renewed.  It  could  only  have  been  due  to  heat  which  traversed 
the  water  without  raising  its  temperature.  A  similar  experiment  has  been 
made  by  a  hollow  glass  lens  through  which  cold  water  flowed  in  a  constant 
stream.  The  sun's  rays  concentrated  by  this  arrangement  ignited  a  piece  of 
wood  placed  in  the  focus. 

Heat  is  transmitted  in  another  way.  When  the  end  of  a  metal  bar  is 
heated,  a  certain  increase  of  temperature  is  presently  observed  along  the 
bar.  Where  the  heat  is  transmitted  in  the  mass  of  the  body  itself,  as  in  this 
case,  it  is  said  to  be  conducted.  We  shall  first  consider  the  transmission  of 
heat  by  conduction. 

404.  Conductivity  of  solids. — Bodies  conduct  heat  with  different  de- 

grees of  facility.  Good  conductors  are  those 
which  readily  transmit  heat,  such  as  are  the 
metals  ;  while  bad  conductors,  to  which  class 
belong  the  resins,  glass,  wood,  and  more  espe- 
cially liquids  and  gases,  offer  a  greater  or  less 
resistance  to  the  transmission  of  heat. 

In  order  to  compare  roughly  the  conducting 
power  or  conductivity  of  different  solids  Ingen- 
haus  constructed  the  apparatus  which  bears  his 
name  and  which  is  represented  in  fig.  342.  It 
is  a  metal  trough,  in  which,  by  means  of  tubu- 

lures  and  corks,  are  fixed  rods  of  the  same  dimensions,  but  of  different 
materials  ;  for  instance,  iron,  copper,  wood,  glass.  These  rods  extend  to 
a  slight  distance  in  the  trough,  and  the  parts  outside  are  coated  with  wax 


404] 


Conductivity  of  Solids. 


359 


which  melts  at  61°.  The  box  being  filled  with  boiling  water,  it  is  observed 
that  the  wax  melts  to  a  certain  distance  on  the  metal  rods,  while  on  the 
others  there  is  no  trace  of  fusion.  The  conducting  power  is  evidently  greater 
in  proportion  as  the  wax  has  fused  to  a  greater  distance.  The  experiment  is 
sometimes  modified  by  attaching  glass  balls  or  marbles  to  the  ends  of  the 
rods  by  means  of  wax.  As  the  wax  melts,  the  balls  drop  off,  and  this  in  the 
order  of  their  respective  conductivities.  The  quickness  with  which  melting 
takes  place  is,  however,  only  a  measure  of  the  conducting  power,  in  case  the 
metals  have  the  same  or  nearly  the  same  specific  heat. 

Despretz  compared  the  conducting  powers  of  solids  by  forming  them  into 
bars  (fig.  343),  in  which  small  cavities  are  made  at  short  intervals  :  these 


Fig.  343- 

cavities  contain  mercury,  and  a  delicate  thermometer  is  placed  in  each  of 
them.  Such  a  bar,  AB,  is  exposed  at  one  end  to  a  constant  source  of  heat, 
such  as  that  of  a  bath  of  paraffin  or  of  fusible  metal  heated  by  a  Bunsen's 
burner ;  the  thermometers  gradually  rise  until  they  indicate  fixed  tempera- 
tures, which  are  less  according  as  the  thermometers  are  farther  from  the 
source  of  heat.  By  this  method  Despretz  verified  the  following  law  : — If  the 
distances  a,  a{  a{  ....  «vi  from  the  source  of  heat  increase  in  arithmetical 
progression,  the  excess  of  temperature  over  that  of  the  surrounding  air, 
/,  /,,  4  .  .  .  .  /vi,  decreases  in  geometrical  progression. 

This  law,  however,  only  prevails  in  the  case  of  very  good  conductors, 
such  as  gold,  platinum,  silver,  and  copper ;  it  is  only  approximately  true  for 
iron,  zinc,  lead,  and  tin,  and  does  not  apply  at  all  to  non-metallic  bodies, 
such  as  marble,  porcelain,  &c. 

Taking  the  conducting  power  of  gold  at  1000,  Despretz  constructed  the 
following  table  of  conductivities  : — 


Platinum  . 
Silver 
Copper 
Iron . 
Zinc  . 


981 

973 
897 

374 
363 


Tin  . 
Lead 

Marble     . 
Porcelain 
Brick  earth 


304 
179 

23 

12 
II 


360  On  Heat.  [404- 

By  making  cavities  in  the  bars,  as  in  Despretz's  method,  their  form  is 
altered,  and  the  continuity  partially  destroyed.  Wiedemann  and  Franz 
avoided  this  source  of  error  by  measuring  the  temperature  of  the  bars  in 
different  places  by  applying  to  them  the  junction  of  a  thermo-electric  couple 
(412).  The  metal  bars  were  made  as  regular  as  possible,  one  of  the  ends 
was  heated  to  100°,  the  rest  of  the  bar  being  surrounded  by  air  at  a  constant 
temperature.  The  thermo-electric  couple  was  of  small  dimensions,  in  order 
not  to  abstract  too  much  heat. 

By  this  method  Wiedemann  and  Franz  obtained  results  which  differ  con- 
siderably from  those  of  Despretz.  Representing  the  conductivity  of  silver 
by  100°,  they  found  the  following  numbers  for  the  other  metals  : — 

Silver     .         .         .         .  locro  Iron         .  .  .      11-9 

Copper  ....  73-6  Steel      \  .  .  .11-6 

Gold       ....  53-2  Lead        .  .  .  -8-5 

Brass      .         .         .  '-     .  23-1  Platinum  .  .  .8*4 

Zinc        .         .         .         .  19-0  Rose's  alloy  .  .  .2-8 

Tin         .         .         .         .  14-5  Bismuth  .  .  .  .1-8 

These  experimenters  found  that  the  conducting  power  of  the  pure  metals 
for  heat  and  electricity  is  the  same. 

Organic  substances  conduct  heat  badly.  De  la  Rive  and  De  Candolle 
showed  that  woods  conduct  better  in  the  direction  of  their  fibres  than  in  a 
transverse  direction,  and  this  difference  is  greater  with  the  soft  than  with  the 
hard  woods  ;  they  remarked  upon  the  influence  which  this  feeble  conduct- 
ing power,  in  a  transverse  direction,  exerts  in  preserving  a  tree  from  sudden 
changes  of  temperature,  enabling  it  to  resist  alike  a  sudden  abstraction  of 
heat  from  within,  and  the  sudden  accession  of  heat  from  without.  Tyndall  has 
also  shown  that  this  tendency  is  aided  by  the  low  conducting  power  of  the 
bark,  which  is  in  all  cases  less  than  that  of  the  wood.  Cotton,  wool,  straw, 
bran,  &c.,  are  all  bad  conductors. 

405.  Coefficient  of  conductivity. — The  numbers  given  in  the  foregoing 
article  only  express  the  relative  conducting  powers  of  the  respective  sub- 
stances. Numerous  experiments  have  been  made  to  determine  the  quantity 
of  heat,  W,  which  passes,  for  instance,  through  a  plate  the  two  sides  of  which. 
are  kept  at  a  constant  difference  of  temperature.  This  will  clearly  be  pro- 
portional to  the  area  of  the  plate  A  and  to  the  time  /.  It  is  further  propor- 
tional to  the  excess  of  the  temperature  of  the  one  face  6l  over  that  of  the 
other  6  —  that  is,  to  0^  —  6;  and  as  the  flow  of  heat  is  different  in  different 
substances,  it  will  be  proportional  to  a  constant  k. 

On  the  other  hand  it  will  be  inversely  proportional  to  the  thickness  of  the 
plate  d.  These  results  are  expressed  by  the  formula 

) LA' from  which*  =  -— W 
d  (#!-  6)  htd' 

On  the  CGS  system  of  units,  the  coefficient  of  thermal  m  calorimetrical 
conductivity^  *,  is  the  quantity  of  heat  which  passes  in  a  second  of  time, 
between  the  two  opposite  faces  of  a  cube  of  the  substance  one  centimetre  in 
thickness,  and  which  are  kept  at  a  constant  difference  of  one  degree.  The 


-407] 


Conductivity  of  Liquids. 


361 


mean  values,  as  found  by  Neumann,  are  as  follows  :— copper,  1*108;  zinc, 
0-307  ;  iron,  0*163  ;  argentan,  0*109  5  ice-  0*0057. 

Thus  if  the  two  opposite  faces  of  a  cube  of  iron  one  centimetre  in  thick- 
ness, that  is  to  say,  a  cubic  centimetre  of  iron,  are  kept  at  a  constant  differ- 
ence of  i°  C.,  the  quantity  of  heat  which  passes  in  each  second  of  time  will 
be  sufficient  to  raise  0*163  gramme  of  water  through  i°  C.  From  this,  which 
is  often  called  the  calorimetrical  measure  of  conductivity,  we  must  distin- 
guish the  thermometric  measure  of  conductivity ;  that  is  to  say,  the  number 
of  degrees  through  which  the  cube  in  question  would  be  heated  when  the 
above  quantity  of  heat  passes  through  it  under  the  given  conditions.  This 
is  obtained  from  the  constants  given,  by  dividing  them  by  the  reduced  value 
of  the  cube  c,  or  the  specific  heat  of  unit  volume ;  that  is,  by  the  product  of 
its  specific  heat  into  its  specific  gravity. 

406.  Senarmont's  experiment. — It  is  only  in  homogeneous  bodies  that 
heat  is  conducted  with  equal  facility  in  all  directions.     If  an  aperture  be 
made  in  a  piece  of  ordinary  glass  covered  with  a  thin  layer  of  wax,  and  a 
platinum  wire  ignited  by  a  voltaic  current  be  held  through  the  aperture,  the 
wax  will  be  melted  round  the  hole  in  a  circular  form.     Senarmont  made,  on 
this  principle,  a  series  of  experiments  on  the  conductivity  of  heat  in  crystals. 
A  plate  cut  from  a  crystal  of  the  regular  system  was  covered  with  wax,  and 
a  heated  metallic  point  was  held  against  it.     The  part  melted  had  a  circular 
form  ;  but  when  plates  of  crystals  belonging  to  other  systems  were  investi- 
gated in  a  similar  manner,  it  was  found  that  the  form  of  the  isothermal  line 
or  line  of  equal  temperature — that  is,  the  boundary  of  the  melted  part — 
varied  with  the  different  systems  and  with  the  position  of  the  axes.     In 
plates  of  uniaxial  crystals  cut  parallel  to  the  principal  axis  it  was  an  ellipse, 
the  major  axis  of  which  was  in  the  direction  of  the  principal  axis.     In  plates 
cut  perpendicular  to  the  principal  axis  it  was  a  circle.     In  biaxial  crystals, 
for  which  selenite  is  well  adapted,  the  line  was  always   an  ellipse.     The 
isothermal  surface  agrees  in  general  character  with  the  wave  surface  of  the 
extraordinary  ray. 

Instead  of  wax  the  plate  may  be  coated  with 
the  double  iodide  of  mercury  and  copper ;  this 
substance  is  of  a  brick-red  colour,  which  when 
heated  changes  into  a  purplish  black. 

Rontgen  makes  the  experiment  very  simply  by 
breathing  on  the  plate,  and  then  holding  a  hot  steel 
point  against  it.  When  a  space  free  from  moisture 
has  been  found  about  the  point,  the  whole  plate  is 
dusted  with  lycopodium,  which  shows  the  outline  of 
the  figure  with  great  sharpness. 

407.  Conductivity    of  liquids. — The    conduc- 
tivity of  liquids  is  very  small,  as  is  seen  from  the 
following    experiment : — A  delicate    thermoscope 
B,  consisting  of  two  glass  bulbs,  joined  by  a  tube 
m,  in   which   there   is  a  small  index  of  coloured 

liquid,  is  placed  in  a  large  cylindrical  glass  vessel,  D  (fig.  344).  This  vessel 
is  filled  with  water  at  the  ordinary  temperature,  and  a  tin  vessel,  A,  contain- 
ing oil  at  a  temperature  of  two  or  three  hundred  degrees,  is  dipped  in  it. 


Fig.  344- 


362  On  Heat.  [407- 

The  bulb  near  the  vessel  A  is  only  very  slightly  heated,  and  the  index  m 
moves  through  a  very  small  distance.  Other  liquids  give  the  same  result. 
That  liquids  conduct  very  badly  is  also  demonstrated  by  a  simpler  experi- 
ment. A  long  test-tube  is  half  filled  with  water,  and  some  ice  so  placed  in 
it  that  it  cannot  rise  to  the  surface.  By  inclining  the  tube  and  heating  the 
surface  of  the  liquid  by  means  of  a  spirit  lamp,  the  liquid  at  the  top  may 
be  made  to  boil,  while  the  ice  at  the  bottom  remains  unmelted. 

Despretz  made  a  series  of  experiments  with  an  apparatus  analogous  to 
that  here  described,  but  he  kept  the  liquid  in  the  vessel,  A,  at  a  constant 
temperature,  and  arranged  a  series  of  thermometers  one  below  the  other  in 
the  vessel  D.  In  this  manner  he  found  that  the  conductivity  of  heat  in 
liquid  obeys  the  same  laws  as  in  solids,  but  is  much  more  feeble.  For  ex- 
ample, the  conductivity  of  water  is  ±  that  of  copper. 

Guthrie  examined  the  conductivity  of  liquids  in  the  following  man- 
ner : — Two  hollow  brass  cones  are  placed  near  each  other  so  that  the  top 
of  one  points  upwards,  that  of  the  other  downwards  (fig.  345).  The  distance 


Fig-  345- 

of  the  bases,  which  are  of  platinum,  can  be  regulated  by  a  micrometer  screw. 
The  liquid  to  be  examined  is  introduced  between  the  bases  by  means  of  a 
pipette.  The  lower  cone  is  fitted  with  a  glass  tube  which  dips  in  a  coloured 
liquid,  and  thus  constitutes  an  air  thermometer.  The  base  of  the  upper  cone 
is  kept  at  a  constant  temperature  by  means  of  a  current  of  hot  water;  it  thus 
warms  the  liquid,  and  the  base  of  the  lower  cone,  in  consequence  of  which 
the  air  in  the  interior  is  expanded  and  the  column  of  liquid  in  the  stem 
depressed. 

The  bases  of  the  cones  were  first  brought  in  contact  and  the  depression 
of  the  column  of  liquid  was  observed.  A  column  of  liquid  of  a  given  thick- 
ness was  then  interposed  and  the  depression  observed  after  a  certain  time. 
The  same  thicknesses  of  other  liquids  were  then  successively  introduced, 


409] 


Conductivity  of  Gases. 


363 


Water 

.     0-00124 

Ether     . 

Solution  of  NaCl 

.     0-00115 

Olive  oil 

Glycerine   . 

.     0-00067 

Chloroform 

Alcohol 

.     0-00049 

Benzole 

Carbon 

,     0-00042 

and  the  corresponding  depressions  noted.  The  difference  of  the  depressions 
was  a  measure  for  the  resistance  which  the  liquid  offered  to  the  passage  of 
heat. 

The  most  complete  researches  on  the  conductivity  of  liquids  are  those  of 
Weber,  who  made  use  of  the  following  method.  A  copper  disc  about  8 
cm.  in  radius  was  separated  from  another  similar  one  by  three  pieces  of 
glass,  about  0-2  cm.  thick.  The  space  thus  formed  between  the  two  is 
filled  with  the  liquid  to  be  examined,  and  the  system  placed  horizontally  on 
a  smooth  block  of  ice.  The  lower  plate  rapidly  assumed  the  temperature  of 
the  ice,  and  heat  travelled  through  the  liquid  from  the  upper  plate,  the 
changes  in  temperature  of  which  were  noted  by  a  thermo-electrical  arrange- 
ment. He  thus  observed  the  following  values  for  k  (405)  :— 

.  0-00040 

.  0-00039 

.  0-00037 

.  0-00032 

Weber  deduced  from  his  researches  the  law  that  for  the  liquids  examined  by 
him,  the  conductivity  is  proportional  to  the  specific  heat  of  unit  volume — that 
is,  to  the  density  multiplied  by  the  specific  heat. 

408.  Manner  in  which  liquids  are  heated. — When  a  column  of  liquid 
is  heated  at  the  bottom,  ascending  and  descending  currents  are  produced. 
It  is  by  these  that  heat  is  mainly  distributed 

through  the  liquid,  and  not  by  its  conductivity. 
These  currents  arise  from  the  expansion  of 
the  inferior  layers,  which,  becoming  less 
dense,  rise  in  the  liquid,  and  are  replaced 
by  colder  and  denser  layers.  They  may  be 
made  visible  by  projecting  bran  or  wooden 
shavings  into  water,  which  rise  and  descend 
with  the  currents.  The  experiment  is 
arranged  as  shown  in  fig.  346.  The  mode 
in  which  heat  is  thus  propagated  in  liquids 
and  in  gases  is  said  to  be  by  convection. 

409.  Conductivity    of    gases.— It    has 
been  a  disputed  question  whether  gases  have 
a  true  conductivity,  that  is  to  say,  a  conduc- 
tion from  layer  to  layer  as  with  the  metals  ; 
but    certainly   when  they  are   restrained   in 
their  motion  their  conductivity  is  very  small. 

All  substances,  for  instance,  between  whose  particles  air  remains  stationary, 
offer  great  resistance  to  the  propagation  of  heat.  This  is  well  seen  in  straw, 
eider-down,  and  furs.  The  propagation  of  heat  in  a  gaseous  mass  is  effected 
by  means  of  the  ascending  and  descending  currents  formed  in  it,  as  is  the 
case  with  liquids. . 

The  following  experiment,  a  modification  of  one  originally  devised  by 
Sir  W.  Grove,  is  considered  to  prove  that  gases  have  a  certain  conductivity. 

A  glass  tube,  fig.  347,  with  two  lateral  tubes  d  and  e  opening  into  it  at 


Fig.  346. 


364  On  Heat.  [409- 

one  end,  is  closed  in  the  middle  by  a  cork,  ^,  through  which  a  stout  copper 
wire  passes.  This  is  connected  by  thin  platinum  wires  with  similar  stout 
copper  wires  also  passing  through  the  corks  a  and  c.  When  the  current  of 
a  Grove's  battery  is  passed  through  the  wires,  both  platinums  are  equally 
incandescent.  If,  now,  one  half  of  the  tube  is  filled  with  hydrogen  by  con- 
necting one  of  the  small  tubes  with  a  supply  of  that  gas,  and  the  current  is 
again  passed,  the  wire  in  the  hydrogen  is  scarcely  luminous,  while  that  in 
air  is  still  brightly  incandescent. 

This  greater  chilling  of  the  wire  in  hydrogen  than  in  air  is  considered 
by  Magnus  to  be  an  effect  of  conduction ;  while  Tyndall  ascribes  it  to  the 
greater  mobility  of  the  particles  of  hydrogen. 

Stefan  found  the  value  of  k  for  air  to  be  0-0000558  in  CGS  units,  so 
that  its  conductivity  is  only  ^55  that  of  copper,  and  ^i  ^at  °f  ^ron-  He 


also  found  that  hydrogen  conducts  seven  times  as  well  as  air,  and  that 
difference  of  density  seems  to  have  no  influence  on  the  conductivity. 

410.  Applications. — The  greater  or  less  conductivity  of  bodies  meets 
with  numerous  applications.  If  a  liquid  is  to  be  kept  warm  for  a  long  time, 
it  is  placed  in  a  vessel  and  packed  round  with  non-conducting  substances, 
such  as  shavings,  straw,  or  bruised  charcoal.  For  this  purpose  water-pipes 
and  pumps  are  wrapped  in  straw  at  the  approach  of  frost.  The  same  means 
are  used  to  hinder  a  body  from  becoming  heated.  Ice  is  transported  in 
summer  by  packing  it  in  bran  or  folding  it  in  flannel. 

Double  walls -constructed  of  thick  planks  having  between  them  any  finely 
divided  materials,  such  as  shavings,  sawdust,  dry  leaves,  £c.,  retain  heat 
extremely  well ;  and  are  likewise  advantageous  in  hot  countries,  for  they 
prevent  its  access.  Pure  silica  in  the  state  of  rock  crystal  is  a  better  con- 
ductor than  lead,  but  in  a  state  of  powder  it  conducts  very  badly.  If  a  layer 
of  asbestos  is  placed  on  the  hand  a  red-hot  iron  ball  can  be  held  without 
inconvenience.  Red-hot  cannon-balls  can  be  wheeled  to  the  gun's  mouth  in 
wooden  barrows  partially  filled  with  sand.  Lava  has  been  known  to  flow 
over  a  layer  of  ashes  underneath  which  was  a  bed  of  ice,  and  the  non- 
conducting power  of  the  ashes  has  prevented  the  ice  from  melting. 

The  clothes  which  we  wear  are  not  warm  in  themselves ;  they  only 
hinder  the  body  from  losing  heat,  in  consequence  of  their  spongy  texture 
and  the  air  they  enclose.  The  warmth  of  bed-covers  and  of  counterpanes 
is  explained  in  a  similar  manner.  Double  windows  are  frequently  used  in 
cold  climates  to  keep  a  room  warm — they  do  this  by  the  non-conducting 
layer  of  air  interposed  between  them.  During  the  night  the  windows  are 
opened,  while  during  the  day  they  are  kept  closed.  It  is  for  the  same  reason 
that  two  shirts  are  warmer  than  one  of  the  same  material  but  of  double  the 
thickness.  Hence,  too,  the  warmth  of  furs,  eider-down,  &c. 

The  small  conducting  power  of  felt  is  used  in  the  North  of  Europe  in  the 


-410]  Applications.  365 

construction  of  the  Norwegian  stove,  which  consists  merely  of  a  wooden 
box  with  a  thick  lining  of  felt  on  the  inside.  In  the  centre  is  a  cavity  in 
which  can  be  placed  a  stew-pan  provided  with  a  cover.  On  the  top  of  this 
is  a  lid,  also  made  of  felt,  so  that  the  pan  is  surrounded  by  a  very  badly 
conducting  envelope.  Meat,  with  water  and  suitable  additions,  is  placed  in 
the  pan,  and  the  contents  are  then  raised  to  boiling.  The  whole  is  then 
enclosed  in  the  box  and  left  to  itself ;  the  cooking  will  go  on  without  fire, 
and  after  the  lapse  of  several  hours  it  will  be  quite  finished.  The  cooling 
down  is  very  slow,  owing  to  the  bad  conducting  power  of  the  lining  ;  at  the 
end  of  three  hours  the  temperature  is  usually  not  found  to  have  sunk  more 
than  from  10°  to  15°. 

That  water  boils  more  rapidly  in  a  metallic  vessel  than  in  one  of  porcelain 
of  the  same  thickness  ;  that  a  burning  piece  of  wood  can  be  held  close  to 
the  burning  part  with  the  naked  hand,  while  a  piece  of  iron  heated  at  one 
end  can  only  be  held  at  a  great  distance,  are  easily  explained  by  reference 
to  their  various  conductivities. 

The  sensation  of  heat  or  cold  which  we  feel  when  in  contact  with  certain 
bodies  is  materially  influenced  by  their  conductivity.  If  their  temperature  is 
lower  than  ours,  they  appear  colder  than  they  really  are,  because  from  their 
conductivity  heat  passes  away  from  us.  If,  on  the  contrary,  their  temperature 
is  higher  than  that  of  our  body,  they  appear  warmer  from  the  heat  which 
they  give  up  at  different  parts  of  their  mass.  Hence  it  is  clear  why  carpets, 
for  example,  are  warmer  than  wooden  floors,  and  why  the  latter  again  are 
warmer  than  stone  floors. 

The  closer  the  contact  of  the  hand  with  a  substance,  the  greater  is  the 
difference  of  temperature  felt.  With  smooth  surfaces  there  are  more  points 
of  contact  than  with  rough  ones.  A  hot  glass  rod  feels  hotter  than  a  piece 
of  rusted  iron  of  the  same  temperature,  although  the  latter  is  a  better  con- 
ductor. The  closer  the  substance  is  pressed,  the  more  intimate  the  contact ; 
an  ignited  piece  of  charcoal  can  be  lifted  by  the  fingers,  if  it  is  not  closely 
pressed. 


366 


On  Heat. 


[411- 


CHAPTER   VIII. 

RADIATION   OF   HEAT. 

411.  Radiant  beat. — It  has  been  already  stated  (403)  that  heat  can  be 
transmitted  from  one  body  to  another  without  altering  the  temperature  of  the 
intervening  medium.    If  we  stand  in  front  of  a  fire  we  experience  a  sensation 
of  warmth  which  is  not  due  to  the  temperature  of  the  air,  for  if  a  screen  be 
interposed  the  sensation  immediately  disappears,  which  would  not  be  the 
case  if  the  surrounding  air  had  a  high  temperature.     Hence  bodies  can  send 
out  rays  which  excite  heat,  and  which  penetrate  through  the  air  without 
heating  it,  as  rays  of  light  through  transparent  bodies.    Heat  thus  propagated 
is  said  to  be  radiated;  and  we  shall  use  the  terms  ray  of  heat,  or  thermal,  or 
calorific  ray,  in  a  similar  sense  to  that  in  which  we  use  the  term  ray  of  light 
or  luminous  ray. 

We  shall  find  that  the  property  of  radiating  heat  is  not  confined  to 
luminous  bodies,  such  as  a  fire  or  a  red-hot  ball,  but  that  bodies  of  all  tem- 
peratures radiate  heat.  It  will  be  convenient  to  make  a  distinction  between 
luminous  and  obscure  rays  of  heat. 

412.  Detection  and  measurement  of  radiant  neat. — In  demonstrating 
the  phenomena  of  radiant  heat,  very  delicate  thermometers  are  required,  and 
the  thermo-electrical  multiplier  of  Melloni  is  used  for  this  purpose  with  great 
advantage  ;  for  it  not  only  indicates  minute  differences  of  temperature,  but 
it  also  measures  them  with  accuracy. 

This  instrument  cannot  be  properly  understood  without  a  knowledge  of 
the  principles  of  thermo-electricity,  for  which  Book  X.  must  be  consulted. 
It  may,  however,  be  stated  here  that  when  two  different  metals  A  and  B  are 
soldered  together  at  one  end  (figs.  348,  349),  the  free  ends  being  joined  by  a 

wire,  when  the  soldering 
C  is  heated,  a  current  of 
electricity  circulates 
through  the  system  ;  if, 
on  the  contrary,  the 
soldering  be  cooled,  a 
current  is  also  produced, 
but  it  circulates  in  exactly 
the  opposite  direction. 

This  is  called  a  thermo-electric  couple  or  pair.  If  a  number  of  such  pairs  be 
alternately  soldered  together,  as  represented  in  fig.  349,  the  strength  of  the 
current  produced  by  heating  the  ends  is  increased  ;  or,  what  amounts  to  the 
same  thing,  a  smaller  degree  of  heat  will  produce  the  same  effect.  Such  an 
arrangement  of  a  number  of  thermo-electric  pairs  is  called  a  thermo-electric 
battery  or  pile. 


Fig.  348. 


-413] 


Laws  of  Radiation. 


367 


Melloni's  thermomultiplier  consists  of  a  thermo-electric  pile  connected 
with  a  delicate  galvanometer.  The  thermo-electric  pile  is  constructed  of  a 
number  of  minute  bars  of  bismuth  and  antimony  soldered  together  alternately, 
though  kept  insulated  from  each  other,  and  contained  in  a  rectangular  box 
P  (fig.  350).  The  terminal  bars  are  connected  with  two  binding  screws  ;;/ 
and  T/,  which  in  turn  are  connected  with  the  galvanometer  G  by  means  of  the 
wires  a  and  b. 

The  galvanometer  consists  of  a  quantity  of  fine  insulated  copper  wire 
coiled  round  a  frame,  in  the  centre  of  which  a  delicate  magnetic  needle  is 
suspended  by  means  of  a  silk  thread.  When  an  electric  current  is  passed 
through  this  coil,  the  needle  is  deflected  through  an  angle  which  depends  on 
the  strength  of  the  current.  The  angle  is  measured  on  a  dial  by  an  index 
connected  with  the  needle. 

It  may  then  be  sufficient  to  state  that  the  thermo-electric  pile  being  con- 
nected with  the  galvanometer  by  means  of  the  wires  a  and  £,  an  excess  of 


Fig.  350. 

temperature  at  one  end  of  the  pile  causes  the  needle  to  be  deflected  through 
an  angle  which  depends  on  the  extent  of  this  excess  ;  and  similarly  if  the 
temperature  is  depressed  below  that  of  the  other  end,  a  corresponding 
deflection  is  produced  in  the  opposite  direction.  By  arrangements  of  this 
kind  Melloni  was  able  to  measure  differences  of  temperature  of  g^th  of  a 
degree.  The  object  of  the  cone  C  is  to  concentrate  the  thermal  rays  on  the 
face  of  the  pile. 

413.  Xiaws  of  radiation, — The  radiation  of  heat  is  governed  by  three 
laws  : — 

I.  Radiation  takes  place  in  all  directions  round  a  body.    If  a  thermometer 
be  placed  in  different  positions  round  a  heated  body,  it  indicates  everywhere 
a  rise  in  temperature. 

II.  In  a  homogeneous  medium,  radiation  takes  place  in  aright  line.    For, 
if  a  screen  be  placed  in  a  right  line  which  joins  the  source  of  heat  and  the 
thermometer,  the  latter  is  not  affected. 


368 


On  Heat. 


[413- 


But  in  passing  obliquely  from  one  medium  into  another,  as  from  air  into 
glass,   calorific-like  luminous   rays  become  deviated,   an  effect   known  as 
refraction.     The  laws  of  this  phenomenon  are  the  same  for 
heat  as  for  light,  and  they  will  be  more  fully  discussed  under 
the  latter  subject. 

III.  Radiant  heat  is  propagated  in  vacua  as  well  as  in 
air.     This  is  demonstrated  by  the  following  experiment  : — 

In  the  bottom  of  a  glass  flask  a  thermometer  is  fixed  in 
such  a  manner  that  its  bulb  occupies  the  centre  of  the  flask 
(fig.  351).  The  neck  of  the  flask  is  carefully  narrowed  by 
means  of  the  blowpipe,  and  then  the  apparatus  having  been 
suitably  attached  to  an  air-pump,  a  vacuum  is  produced  in 
the  interior.  This  having  been  done,  the  tube  is  sealed  at 
the  narrow  part.  On  immersing  this  apparatus  in  hot  water, 
or  on  bringing  near  it  some  hot  charcoal,  the  thermometer  is 
at  once  seen  to  rise.  This  could  only  rise  from  radiation 
through  the  vacuum  in  the  interior,  for  glass  is  so  bad  a 
conductor  that  the  heat  could  not  travel  with  this  rapidity  through  the  sides 
of  the  flask  and  the  stem  of  the  thermometer. 

414.  Causes  which  modify  the  intensity  of  radiant  heat. — By  the 
intensity  of  radiant  heat  is  understood  the  quantity  of  heat  received  on  the 
unit  of  surface.  Three  causes  are  found  to  modify  this  intensity  :  the  tem- 
perature of  the  source  of  heat,  its  distance,  and  the  obliquity  of  the  calorific 
rays  in  reference  to  the  surface  which  emits  them.  The  laws  which  regulate 
these  modifications  may  be  thus  stated  : — 

I.  The  intensity  of  radiant  heat  is  proportional  to  the  temperatttre  of  the 
source. 

I 1.  The  intensity  is  inversely  as  the  square  of  the  distance. 

III.  The  intensity  is  less,  the  greater  the  obliquity  of  the  rays  with  respect 
to  the  radiating  surface. 

The  first  law  is  demonstrated  by  placing  a  metal  box  containing  water 
at  10°,  20°,  or  30°  successively  at  equal  distances  from  the  bulb  of  a  differen- 
tial thermometer.  The  temperatures  indicated 
by  the  latter  are  then  found  to  be  in  the  same 
ratio  as  those  of  the  box  :  for  instance,  if  the 
temperature  of  that  corresponding  to  the  box  at 
10°  be  2°,  those  of  others  will  be  4°  and  6°  re- 
spectively. 

The  truth  of  the  second  law  follows  from  the 
geometrical  principle  that  the  surface  of  a  sphere 
increases  as  the  square  of  its  radius.  Suppose 
a  hollow  sphere  ab  (fig.  352)  of  any  given  radius, 
and  a  source  of  heat,  C,  in  its  centre  ;  each  unit 
of  surface  in  the  interior  receives  a  certain  quan- 
tity of  heat.  Now  a  sphere,  ef,  of  double  the  radius  will  present  a  surface 
four  times  as  great ;  its  internal  surface  contains,  therefore,  four  times  as 
many  units  of  surface,  and  as  the  quantity  of  heat  emitted  is  the  same,  each 
unit  must  receive  one-fourth  the  quantity. 

To  demonstrate  the  same  law  experimentally,  a  narrow  tin  plate  box  is 


Fig. 352. 


-414]  Causes  which  Modify  the  Intensity  of  Radiant  Heat.      369 

taken  (fig.  353),  filled  with  hot  water,  and  coated  on  one  side  with  lampblack. 
The  thermopile  with  its  conical  reflector  is  placed  so  that  its  face  is  at 
a  certain  definite  distance,  co,  say  9  inches,  from  this  box,  and  the  cover 


Fig.  353- 

having  been  lowered,  the  needle  of  the  galvanometer  is  observed  to  be  de- 
flected through  80°,  for  example. 

If  now  the  pile  is  removed  to  a  distance,  CO  (fig.  354),  double  that  of  co, 
the  deflection  of  the  galvanometer  remains  the  same,  which  shows  that  the 
battery  receives  the  same  amount  of  heat ;  the  same  is  the  case  if  the 


M 


Fig.  354- 

battery  is  removed  to  three  or  four  times  the  distance.  This  result,  though 
apparently  in  opposition  to  the  second  law,  really  confirms  it.  For  at  first 
the  battery  only  receives  heat  from  the  circular  portion  ab  of  the  side  of  the 
box,  while,  in  the  second  case,  the  circular  portion  AB  radiates  towards  it. 
But,  as  the  two  cones  ACB  and  acb  are  similar,  and  the  height  of  ACB  is 
double  that  of  acb,  the  diameter  AB  is  double  that  of  ab,  and  therefore  the 

B  B 


370  On  Heat.  [414- 

area  AB  is  four  times  as  great  as  that  of  ab,  for  the  areas  of  circles  are 
proportional  to  the  squares  of  the  radii.  But  since  the  radiating  surface 
increases  as  the  square  of  the  distance,  while  the  galvanometer  is  stationary, 
the  heat  received  by  the  battery  must  be  inversely  as  this  same  square. 

The  third  law  is  demonstrated  by  means  of  the   following  experiment, 
which  is  a  modification  of  one  originally  devised  by  Leslie  (fig.  355)  : — P 


Fig-  355 

represents  the  thermomultiplier  which  is  connected  with  its  galvanometer, 
and  A  a  metal  cube  full  of  hot  water.  The  cube  being  first  placed  in  such 
a  position,  A,  that  its  front  face,  ac,  is  vertical,  the  deflection  of  the  galvano- 
meter is  noted.  Supposing  it  amounts  to  45°,  this  represents  the  radiation 
from  ac.  If  this  now  be  turned  in  the  direction  represented  by  A7,  the 
galvanometer  is  still  found  to  mark  45°. 

The  second  surface  is  larger  than  the  first,  and  it  therefore  sends  more 
rays  to  the  mirror.  But  as  the  action  on  the  thermometer  is  no  greater 
than  in  the  first  case,  it  follows  that  in  the  second  case,  where  the  rays 
are  oblique,  the  intensity  is  less  that  in  the  first  case,  where  they  are 
perpendicular. 

In  order  to  express  this  in  a  formula,  let  /  be  the  intensity  of  the  rays 
emitted  perpendicularly  to  the  surface,  and  **'  that  of  the  oblique  rays. 
These  intensities  are  necessarily  inversely  as  the  surfaces  ac  and  aS,  for  the 
effect  is  the  same  in  both  cases,  and  therefore  z'  x  surface  a'c'  =  i  x  surface  ac ; 

hence  if  =  i   Sur  '  ac  =  i'  —  =  /  cos,  aoa' ;  which  signifies  that  the  intensity 
surf,  a?         a? 

of  oblique  rays  is  proportional  to  the  cosine  of  the  angle  which  these  rays  form 
with  the  normal  to  the  surface ;  for  this  angle  is  equal  to  the  angle  aoa'. 
This  law  is  known  as  the  law  of  the  cosine  ;  it  is,  however,  not  general ; 
Desains  and  De  la  Provostaye  have  shown  that  it  is  only  true  within  very 
narrow  limits  ;  that  is,  only  with  bodies  which,  like  lampblack,  are  entirely 
destitute  of  reflecting  power  (423). 

415.  Mobile  equilibrium.  Tneory  of  exchanges. — Prevost  of  Geneva 
suggested  the  following  hypothesis  in  reference  to  radiant  heat,  known  as 
Pre  vest's  theory  of  exchanges,  which  is  now  universally  admitted.  All  bodies, 
whatever  their  temperatures,  constantly  radiate  heat  in  all  directions.  If 
we  imagine  two  bodies  at  different  temperatures  placed  near  one  another, 
the  one  at  a  higher  temperature  will  experience  a  loss  of  heat,  its  temperature 
will  sink,  because  the  rays  it  emits  are  of  greater  intensity  than  those  it 
receives  ;  the  colder  body,  on  the  contrary,  will  rise  in  temperature,  because 
it  receives  rays  of  greater  intensity  than  those  which  it  emits.  Ultimately 


-417]  Laws  of  Reflection.  371 

the  temperature  of  both  bodies  becomes  the  same,  but  heat  is  still  exchanged 
between  them,  only  each  receives  as  much  as  it  emits,  and  the  temperature 
remains  constant.  This  state  is  called  the  mobile  equilibrium  of  temperature. 

416.  Newton's  law  of  cooling:. — A  body  placed  in  a  vacuum  is  only 
cooled  or  heated  by  radiation  In  the  atmosphere  it  becomes  cooled  or 
heated  by  its  contact  with  the  air  according  as  the  latter  is  colder  or  hotter 
than  the  radiating  body.  In  both  cases  the  velocity  of  cooling  or  of  heating 
— that  is,  the  quantity  of  heat  lost  or  gained  in  a  second — is  greater  accord- 
ing as  the  difference  of  temperature  is  greater. 

Newton  enunciated  the  following  law  in  reference  to  the  cooling  or 
heating  of  a  body  : — The  quantity  of  heat  lost  or  gained  by  a  body  in  a  second 
is  proportional  to  the  difference  between  its  temperature  and.  that  of  the  sur- 
rounding medium.  Dulong  and  Petit  have  proved  that  this  law  is  not  so 
general  as  Newton  supposed,  and  only  applies  where  the  differences  of 
temperature  do  not  exceed  1 5°  to  20°.  Beyond  that,  the  quantity  of  heat  lost 
or  gained  is  greater  than  that  required  by  this  law. 

Two  consequences  follow  from  Newton's  law  : — 

I.'  When  a  body  is  exposed  to  a  constant  source  of  heat,  its  temperature 
does  not  increase  indefinitely,  for  the  quantity  which  it  receives  in  the  same 
time  is  always  the  same  ;  while  that  which  it  loses  increases  with  the  excess 
of  its  temperature  over  that  of  the  surrounding  medium.  Consequently 
a  point  is  reached  at  which  the  quantity  of  heat  emitted  is  equal  to  that 
absorbed,  and  the  temperature  then  remains  stationary. 

II.  Newton's  law,  as  applied  to  the  differential  thermometer,  shows  that 
its  indications  are  proportional  to  the  quantities  of  heat  which  it  receives. 
If  one  of  the  bulbs  of  a  differential  thermometer  receives  rays  of  heat  from 
a  constant  source,  the  instrument  exhibits,  first,  increasing  temperature,  but 
afterwards  becomes  stationary.  In  this  case,  the  quantity  of  heat  which  it 
receives  is  equal  to  that  which  it  emits.  But  the  latter  is  proportional  to  the 
excess  of  the  temperature  of  the  bulb  above  that  of  the  surrounding  atmo- 
sphere— that  is,  to  the  number  of  degrees  indicated  by  the  thermometer  ; 
consequently,  the  temperature  indicated  by  the  differential  thermometer  is 
proportional  to  the  quantity  of  heat  it  receives. 


REFLECTION   OF   HEAT. 

417.  Laws  of  reflection. — When  thermal  rays  fall  upon  a  body  they  are, 
speaking  generally,  divided  into  two  parts,  one  of  which  penetrates  the  body 
while  the  other  rebounds  as  if  repelled  from  the 
surface  like  an  elastic  ball.     This  is  said  to  be  p 

reflected. 

If  mn  be  a  plane  reflecting  surface  (fig.  356), 
CB  an  incident  ray,  DC  a  line  perpendicular  to 
the  surface  called  the  normal,  and  BA  the  re- 
flected ray  ;  the  angle  CBD  is  called  the  angle 
of  incidence,  and  DBA  the  angle  of  reflection. 
The  reflection  of  heat,  like  that  of  light,  is  Fig.  356. 

governed  by  the  two  following  laws  : — 

I.   The  angle  of  reflection  is  equal  to  the  angle  of  incidence. 

6  B  2 


372 


On  Heat. 


[417- 


II.  Both  the  incident  and  the  reflected  ray  are  in  the  same  plane  with  the 
normal  to  the  reflecting  surface. 

418.   Experimental  demonstration  of  the  laws  of  reflection  of  heat. — 

This  may  be  effected  by  means  of  Melloni's  thermopile  and  also  by  the  con- 
jugate mirrors  (420).  Fig.  357  represents  the  arrangement  adopted  in  the 
former  case.  MN  is  a  horizontal  bar,  about  a  metre  in  length,  graduated  in 
millimetres,  on  which  slide  various  parts,  which  can  be  clamped  by  means 
of  screws.  The  source  of  heat,  S,  is  a  platinum  spiral,  kept  at  a  white  heat 
in  a  spirit  lamp.  A  screen  K,  when  raised,  cuts  off  the  radiation  from  the 
source  ;  a  second  screen,  F,  with  an  aperture  in  fhe  centre,  gives  the  rays  a 
parallel  direction.  At  the  other  end  is  an  upright  rod,  I,  with  a  graduated 
dial,  the  zero  of  which  is  in  the  direction  of  MN,  and  therefore  parallel  to 
the  pencil  Sm.  In  the  centre  of  the  dial  is  an  aperture,  in  which  turns  an 
axis  that  supports  a  metallic  mirror  m.  About  this  axis  turns  an  index,  *R, 


Fig.  357- 

on  which  is  fixed  the  thermopile,  P,  in  connection  with  the  galvanometer  G ; 
H  is  a  screen,  the  object  of  which  is  to  cut  off  any  direct  radiation  from  the 
source  of  heat  towards  the  pile.  In  order  not  to  mask  the  pile,  it  is  not  re- 
presented in  the  position  it  occupies  in  the  experiment. 

By  lowering  the  screen  K,  a  pencil  of  parallel  rays,  passing  through  the 
aperture  F,  falls  from  the  mirror  ;/z,  and  is  there  reflected.  If  the  index  R 
is  not  in  the  direction  of  the  reflected  pencil,  this  latter  does  not  fall  on 
the  pile,  and  the  needle  of  the  galvanometer  remains  stationary  ;  but  by 
slowly  turning  the  index  R,  a  position  is  found  at  which  the  galvanometer 
attains  its  greatest  deviation,  which  is  the  case  when  the  pile  receives  the 
reflected  pencil  perpendicularly  to  its  surface.  Reading  off  then  on  the  dial 
the  position  of  a  small  needle  perpendicular  to  the  mirror,  it  is  observed  that 
this  bisects  the  angle  formed  by  the  incident  and  the  reflected  pencil,  which 
demonstrates  the  first  law. 

The  second  law  is  also  proved  by  the  same  experiment,  for  the  various 
pieces  of  the  apparatus  are  arranged  so  that  the  incident  and  reflected  rays 


-420]  Verification  of  the  Laws  of  Reflection.  373 

are  in  the  same  horizontal  plane,  and  therefore  at  right  angles  to  the  reflect- 
ing surface,  which  is  vertical. 

419.  Reflection  from  concave  mirrors. — Concave  mirrors  or  reflectors 
are  polished  spherical  or  parabolic  surfaces  of  metal  or  of  glass,  which  are 
used  to  concentrate  luminous  or  calorific  rays  in  the  same  point. 

We  shall  only  consider  the  case  of  spherical  mirrors.  Fig.  359  represents 
two  of  these  mirrors  ;  fig.  358  gives  a  medial  section,  which  is  called  the 


Fig.  358. 

principal  section.  The  centre  C  of  the  sphere  to  which  the  mirror  belongs 
is  called  the  centre  of  curvature  ;  the  point  A,  the  middle  of  the  reflector,  is 
the  centre  of  the  figure  ;  the  straight  line  AB  passing  through  these  points, 
is  the  principal  axis  of  the  mirror. 

In  order  to  apply  to  spherical  mirrors  the  laws  of  reflection  from  plane 
surfaces,  they  are  considered  to  be  composed  of  an  infinite  number  of  in- 
finitely small  plane  surfaces,  each  belonging  to  the  corresponding  tangent 
plane  ;  the  normals  to  these  small  surfaces  are  all  radii  of  the  same  sphere, 
and  therefore  meet  at  its  centre,  the  centre  of  curvature  of  the  mirror. 

Suppose  now,  on  the  axis  AB  of  the  mirror  MN,  a  source  of  heat  so 
distant  that  the  rays  EK,  PH  .  .  .  .  which  start  from  it  may  be  considered 
as  parallel.  From  the  hypothesis  that  the  mirror  is  composed  of  an  infini- 
tude of  small  planes,  the  ray  EK  is  reflected  from  the  plane  K  just  as  from 
a  plane  mirror ;  that  is  to  say,  CK  being  the  normal  to  this  plane,  the 
reflected  ray  takes  a  direction  such  that  the  angle  CKF  is  equal  to  the 
angle  CKE.  The  other  rays,  PH,  GI  .  .  .  .  are  reflected  in  the  same 
manner,  and  all  converge  approximately  towards  the  same  point  F,  on  the 
line  AC.  There  is  then  a  concentration  of  the  rays  in  this  point,  and  conse- 
quently a  higher  temperature  than  at  any  other  point.  This  point  is  called 
the  focus,  and  the  distance  from  the  focus  to  the  mirror  at  A  is  the  focal 
distance. 

In  the  above  figure  the  heat  is  propagated  along  the  lines  EKF,  LDF,  in 
the  direction  of  the  arrows  ;  butj  conversely,  if  the  heated  body  be  placed  at 
F,  the  heat  is  propagated  along  the  lines  FKE,  FDL,  so  that  the  rays  emitted 
from  the  focus  are  nearly  parallel  after  reflection. 

420.  Verification  of  the  laws  of  reflection. — The  following  experiment, 
which  was  made  for  the  first  time  by  Pictet  and  Saussure,  and  which  is 
known  as  the  experiment  of  the  conjugate  mirrors,  demonstrates  not  only 
the  existence  of  the  foci,  but  also  the  laws  of  reflection.  Two  reflectors, 
M  and  N  (fig.  359),  are  arranged  at  a  distance  of  4  to  5  yards,  and  so  that 


374 


On  Heat. 


[420- 


their  axes  coincide.  In  the  focus  of  one  of  them,  A,  is  placed  a  small  wire 
basket  containing  a  red-hot  iron  ball.  In  the  focus  of  the  other  is  placed 
B,  an  inflammable  body,  such  as  gun-cotton  or  phosphorus.  The  rays 
emitted  from  the  focus  A  are  first  reflected  from  the  mirror  M,  in  a  direction 
parallel  to  the  axis  (419),  and  impinging  on  the  other  mirror,  N,  are  reflected 
so  that  they  coincide  in  the  focus  B.  That  this  is  so,  is  proved  by  the  fact 
that  the  gun-cotton  at  this  point  takes  fire,  which  is  not  the  case  if  it  is  above 
or  below  it. 

The  experiment  also  serves  to  show  that  light  and  heat  are  reflected  in 
the  same  manner.  For  this  purpose  a  lighted  candle  is  placed  in  the  focus 
of  A,  and  a  ground  glass  screen  in  the  focus  of  B,  when  a  luminous  focus  is 
•seen  on  it  exactly  in  the  spot  where  the  gun-cotton  ignites.  Hence  the 
luminous  and  the  calorific  foci  are  produced  at  the  same  point,  and  the 
reflection  takes  place  in  both  cases  according  to  the  same  laws,  for  it  will  be 


Fig-  359- 

afterwards  shown  that  for  light,  the  angle  of  reflection  is  equal  to  the  angle 
of  incidence,  and  that  both  the  incident  and  the  reflected  rays  are  in  the  same 
plane  perpendicular  to  the  plane  reflecting  surface. 

In  consequence  of  the  high  temperature  produced  in  the  foci  of  concave 
mirrors  they  have  been  called  burning  mirrors.  It  is  stated  that  Archi- 
medes burnt  the  Roman  vessels  before  Syracuse  by  means  of  such  mirrors. 
Buffon  constructed  burning  mirrors  of  such  power  as  to  prove  that  the  feat 
attributed  to  Archimedes  was  not  impossible.  The  mirrors  were  made  of  a 
number  of  silvered  plane  mirrors  about  8  inches  long  by  5  broad.  They 
could  be  turned  independently  of  each  other  in  such  a  manner  that  the  rays 
reflected  from  each  coincided  in  the  same  point.  With  128  mirrors  and  a 
hot  summer's  sun  Buffon  ignited  a  plank  of  tarred  wood  at  a  distance  of  70 
yards. 


-423] 


Reflecting  Power. 


375 


421.  Reflection  in  a  vacuum. — Heat  is  reflected  in  a  vacuum  as  well  as 
in  air,  as  is  seen  from  the  following  experiment  (fig.  360),  due  to  Sir  Hum- 
phry Davy.     Two  small  concave  reflectors  were  placed  opposite  each  other 
under  the  receiver  of  an  air-pump.     In  the  focus  of  one  was  placed  a  delicate 
thermometer,  and  in  the  focus  of  the  other  a  platinum  wire  made  incandescent 
by  means  of  a  galvanic  current.     The  thermometer  was  immediately  seen  to 
rise  several  degrees,  which  could  only  be  due  to  reflected  heat,  for  the  ther- 
mometer did  not  show  any  increase  of 

temperature  if  it  were  not  exactly  in 
the  focus  of  the  second  reflector. 

422.  Apparent  reflection  of  cold. 
If  two  mirrors  are  arranged  as  repre- 
sented in  fig.  359,  and  a  piece  of  ice  is 
placed  in  one  of  the  foci  instead  of  the 
red-hot  ball,  the  surrounding  tempera- 
ture being  greater  than  zero,  a  diffe- 
rential   thermometer    placed    in    the 
focus  of  the  second  reflector  would  ex- 
hibit  a    decrease    in    temperature    of 
several     degrees.      This    appears    at 
first  to  be  caused  by  the  emission  of 
frigorific  rays  from   ice.     It  is,  how- 
ever, easily  explained  from  what  has 
been  said  about  the  mobile  equilibrium 
of  temperature  (415).    There  is  still  an 
interchange  of  temperature,  but  here 

the  thermometer  is  the  warmest  body.  As  the  rays  which  the  thermometer 
emits  are  hotter  than  those  emitted  by  the  ice,  the  former  gives  out  more 
heat  than  it  receives,  and  hence  its  temperature  sinks. 

The  sensation  of  cold  experienced  when  we  stand  near  a  plaster  or  stone 
wall  whose  temperature  is  lower  than  that  of  our  body,  or  when  we  stand  in 
front  of  a  wall  of  ice,  is  explained  in  the  same  way. 

423.  Reflecting'  power. — The  reflecting  power  of  a  substance  is  its  pro- 
perty of  throwing  off  a  greater  or  less  proportion  of  incident  heat. 

This  power  varies  in  different  substances.  In  order  to  study  this  power 
in  different  bodies  without  having  recourse  to  as  many  reflectors,  Leslie 
arranged  his  experiment  as  shown  in  fig.  361.  The  source  of  heat  is  a 
cubical  canister,  M,  now  known  as  Leslies  cube,  filled  with  hot  water.  A 
plate,  a,  of  the  substance  to  be  experimented  upon  is  placed  on  the  axis  of  a 
reflecting  mirror  between  the  focus  and  the  mirror.  In  this  manner  the  rays 
emitted  by  the  source  are  first  reflected  from  the  mirror  and  impinge  on  the 
plate  a,  where  they  are  again  reflected  and  converge  to  the  focus  between  the 
plate  and  the  mirror,  at  which  point  a  differential  thermometer  is  placed. 
The  reflector  and  the  thermometer  are  always  in  the  same  position,  and  the 
water  of  the  cube  is  always  kept  at  100°,  but  it  is  found  that  the  temperature 
indicated  by  the  thermometer  varies  with  the  nature  of  the  plate.  This 
method  gives  a  means  of  determining,  not  the  absolute  reflecting  power  of  a. 
body,  but  its  power  relatively  to  that  of  some  body  taken  as  a  standard  of 
comparison.  For  from  what  has  been  said  on  the  application  of  Newton's  law 


Fig.  360. 


376 


On  Heat. 


[423- 


to  the  differential  thermometer  (416),  the  temperatures  which  this  instrument 
indicates  are  proportional  to  the  quantities  of  heat  which  it  receives.  Hence, 
if  in  the  above  experiment  a  plate  of  glass  causes  the  temperature  to  rise  i° 
and  a  plate  of  lead  6°,  it  follows  that  the  quantity  of  heat  reflected  by  the 
latter  is  six  times  as  great  as  that  reflected  by  the  former.  For  the  heat 
emitted  by  the  source  remains  the  same,  the  concave  reflector  receives  the 
same  portion,  and  the  difference  can  only  arise  from  the  reflecting  power  of 
the  plate  a. 


Fig.  361. 

By  this  method  Leslie  determined  the  reflecting  powers  of  the  following 
substances,  relatively  to  that  of  brass,  taken  as  100  : — 


Polished  brass  . 

Silver 

Steel 

Lead 


100 

90 
70 
60 


Indian  ink 
Glass 

Oiled  glass 
Lampblack 


13 
10 

5 
o 


The  numbers  only  represent  the  relative  reflecting  power  as  compared 
with  that  of  brass.  Their  absolute  power  is  the  relation  of  the  quantity  of 
heat  reflected  to  the  quantity  of  heat  received,  Desains  and  De  la  Provostaye, 
who  examined  the  absolute  reflecting  power  of  certain  metals,  obtained  the 
following  results  by  means  of  Melloni's  thermomultiplier  (412),  the  heat 
being  reflected  at  an  angle  of  50°  : — 


Silver  plate 
Gold 
Brass 
Platinum  . 


•  0-97 

.  0-95 

.  0-93 

.  0-83 


Steel 
Zinc 
Iron 
Cast  iron 


0-82 
0-8 1 
077 
074 


-425]  Radiating  Power.  377 

424.  Absorbing  power. — The  absorbing  power  of  a  body  is  its  property 
of  allowing  a  greater  or  less  quantity  of  the  heat  which  falls  upon  it  to  pass 
into  its  mass.    Its  absolute  value  is  the  ratio  of  the  quantity  of  heat  absorbed 
to  the  quantity  of  heat  received. 

The  absorbing  power  of  a  body  is  always  inversely  as  its  reflecting 
power  :  a  body  which  is  a  good  absorbent  is  a  bad  reflector,  and  vice  versa* 
It  was  formerly  supposed  that  the  two  powers  were  exactly  complementary, 
that  the  sum  of  the  reflected  and  absorbed  heat  was  equal  to  the  total  quan- 
tity of  incident  heat.  This  is  not  the  case  ;  it  is  always  less  :  the  incident 
heat  is  divided  into  three  parts — ist,  one  which  is  absorbed  ;  2nd,  another 
which  is  reflected  regularly — that  is,  according  to  laws  previously  demon- 
strated (417) ;  and  a  third,  which  is  irregularly  reflected  in  all  directions, 
and  which  is  called  scattered  or  diffused  heat. 

In  order  to  determine  the  absorbing  power  of  bodies,  Leslie  used  the 
apparatus  which  he  employed  in  determining  the  reflecting  powers  (423). 
But  he  suppressed  the  plate  <z,  and  placed  the  bulb  of  the  thermometer  in 
the  focus  of  the  reflector.  This  bulb  being  then  covered  successively  with 
lampblack,  or  varnish,  or  with  gold,  silver,  or  copper  foil,  &c.,  the  thermo- 
meter exhibited  a  higher  temperature  under  the  influence  of  the  source  of 
heat,  M,  according  as  the  substance  with  which  the  bulb  was  covered 
absorbed  more  heat.  Leslie  found  in  this  way  that  the  absorbing  power  of 
a  body  is  greater  the  less  its  reflecting  power.  In  these  experiments,  how- 
ever, the  relation  of  the  absorbing  powers  cannot  be  deduced  from  that  of 
the  temperatures  indicated  by  the  thermometer,  for  Newton's  law  is  not 
exactly  applicable  in  this  case,  as  it  only  prevails  for  bodies  whose  substance 
does  not  vary,  and  here  the  covering  of  the  bulb  varied  with  each  observa- 
tion. But  we  shall  presently  show  (426)  how  the  comparative  absorbing 
powers  may  be  deduced  from  the  ratios  of  the  emissive  powers. 

Taking,  as  a  source  of  heat,  a  canister  filled  with  water  at  100°,  Melloni 
found,  by  means  of  the  thermomultiplier,  the  following  relative  absorbing 
powers  : — 

Lampblack       .         .         .100         Indian  ink     .         .         .         .85 

White  lead        .         .         .     100         Shellac 72 

Isinglass  .         .         .         .       91         Metals 13 

425.  Radiating-  power. — The  radiating  or  emissive  power  of  a  body  is 
its  capability  of  emitting,  at  the  same  temperature,  and  with  the  same  extent 
of  surface,  greater  or  less  quantities  of  heat. 

The  apparatus  represented  in  fig.  361  was  also  used  by  Leslie  in  deter- 
mining the  radiating  power  of  bodies.  For  this  purpose  the  bulb  of  the 
thermometer  was  placed  in  the  focus  of  the  reflector,  and  the  faces  of  the 
canister  M  were  formed  of  different  metals,  or  covered  with  different 
substances  such  as  lampblack,  paper,  &c.  The  cube  being  filled  with  hot 
water,  at  100°,  and  all  other  conditions  remaining  the  same,  Leslie  turned 
each  face  of  the  cube  successively  towards  the  reflectors,  and  noted  the 
temperature  each  time.  That  face  which  was  coated  with  lampblack  caused 
the  greatest  elevation  of  temperature,  and  the  metal  faces  the  least.  Applying 
Newton's  law,  and  representing  the  heat  emitted  by  lampblack  as  100,  Leslie 
formed  the  following  table  of  radiating  powers  : — 


3/8  On  Heat.  [425- 

Lampblack       .         .         .100  Tarnished  lead  .         .         -45 

White  lead        .         .         .100  Mercury     .         .         .         .20 

Paper        .        •;"»'.       98  Polished  lead     .     ;  .'        .     19 

Ordinary  white  glass         .       90  Polished  iron      .     "".."-.     15 

Isinglass.         .         .   .  '.       80  Tin, gold, silver, copper, &c.     12 

It  will  be  seen  that,  in  this  table,  the  order  of  the  bodies  is  exactly  the 
reverse  of  that  in  the  tables  of  reflecting  powers. 

The  radiating  powers  of  several  substances  were  determined  by  Desains 
and  De  la  Provostaye,  who  used  the  thermomultiplier.  They  found  in  this 
manner,  the  following  numbers  compared  with  lampblack  as  100  : — 

Platinum  foil    ....       -.  >  '    ,  .  .  io-So 

Burnished  platinum      -   .  ;..     .     <    .         .  .  *•  9*50 

Silver  deposited  chemically     ,'ih     .  M*v,  .  .  5-36 

Copper  foil       .       >..        .         .         ,         .  .  .  4-90 

Gold  leaf          .         .       •  -.-;:'  .<;  ;  ' :  ..  .:  ;     .  .  .  4-28 

Pure  silver  laminated       .         .        .  r-<     .-  .  .  3-00 

„            burnished       .         .    '•'  .  '      .  .  .  2*50 

„           deposited  chemically  and  burnished  .  2-25 

It  appears,  therefore,  that  the  radiating  power  found  by  Leslie  for  the 
metals  is  too  large. 

426.  Identity  of  the  absorbing:  and  radiating  powers. — The  absorb- 
ing power  of  a  body  cannot  be  accurately  deduced  from  its  reflecting  power, 
because  the  two  are  not  exactly  complementary.  But  the  absorbing  power 
would  be  determined  if  it  could  be  shown  that  in  the  same  body  it  is  equal 
to  the  radiating  power.  This  conclusion  has  been  drawn  by  Dulong  and 
Petit  from  the  following  experiments  :— In  a  large  glass  globe,  blackened  on 
the  inside,  was  placed  a  thermometer  at  a  certain  temperature,  1 5°  for  ex- 
ample ;  the  globe  was  kept  at  zero  by  surrounding  it  with  ice,  and  having 
been  exhausted  by  means  of  a  tubulure  connected  with  the  air-pump,  the  time 
was  noted  which  elapsed  while  the  thermometer  fell  through  5°.  The  experi- 
ment was  then  made  in  the  contrary  direction  :  that  is,  the  sides  of  the  globe 
were  heated  to  1 5°,  while  the  thermometer  was  cooled  to  zero  :  the  time  was 
then  observed  which  the  thermometer  occupied  in  rising  through  5°.  It  was 
found  that  this  time  was  exactly  the  same  as  that  which  the  thermometer 
had  taken  in  sinking  through  5°,  and  it  was  thence  concluded  that  the 
radiating  power  is  equal  to  the  absorbing  power  for  the  same  body,  and  for 
the  same  difference  between  its  temperature  and  the  temperature  of  the  sur- 
rounding medium,  because  the  quantities  of  heat  emitted  or  absorbed  in  the 
same  time  are  equal. 

This  point  may  also  be  demonstrated  by  means  of  the  following  apparatus 
devised  by  Ritchie.  Fig.  362  represents  what  is  virtually  a  differential 
thermometer,  the  two  glass  bulbs  of  which  are  replaced  by  two  cylindrical 
reservoirs  B  and  C,  of  metal,  and  full  of  air.  Between  them  is  a  third  and 
larger  one  A,  which  can  be  filled  with  hot  water  by  means  of  a  tubulure. 
The  ends  of  B  and  of  A,  which  face  the  right,  are  coated  with  lampblack  ; 
those  of  C  and  of  A,  which  face  the  left,  are  either  painted  white,  or  are 


-427]         Reflecting,  Absorbing,  and  Radiating  Powers. 


#A  C 


Fig.  362. 


379 

coated  with  silver  foil.  Thus  one  of  the  two  faces  opposite  each  other  is 
black,  and  the  other  white  ;  hence  when  the  cylinder  A  is  filled  with  hot 
water,  its  white  face  radiates  towards  the  black  face  of  B,  and  its  black  face 
towards  the  white  face  of  C.  In  these  circum- 
stances the  liquid  in  the  stem  does  not  move, 
indicating  that  the  two  reservoirs  are  at  the 
same  temperature.  On  the  one  hand,  the 
greater  emissive  power  of  the  black  face  of  A 
is  compensated  by  the  smaller  absorptive  power 
of  the  white  face  of  C  ;  while,  on  the  other 
hand,  the  feebler  radiating  power  of  the  white 
face  of  A  is  compensated  by  the  greater 
absorbing  power  of  the  black  face  of  B. 

The  experiment  may  be  varied  by  replacing 
the  two  white  faces  by  discs,  of  paper,  glass, 
porcelain,  &c. 

427.  Causes  which  modify  the  reflecting:, 
absorbing1,  and  radiating1  powers. — As  the 
radiating  and  absorbing  powers  are  equal,  any 
cause  which  affects  the  one  affects  the  other 
also.  And  as  the  reflecting  power  varies  in 
.an  inverse  manner,  whatever  increases  it  dimi- 
nishes the  radiating  and  absorbing  powers,  and 
vice  versa. 

It  has  been  already  stated  that  these  different  powers  vary  with  different 
bodies,  and  that  metals  have  the  greatest  reflecting  power,  and  lampblack 
the  least.  In  the  same  body  these  powers  are  modified  by  the  degree  of 
polish,  the  density,  the  thickness  of  the  radiating  substance,  the  obliquity  of 
the  incident  or  emitted  rays,  and,  lastly,  by  the  nature  of  the  source  of  heat. 

It  has  been  usually  assumed  that  the  reflecting  power  increases  with  the 
polish  of  the  surface,  and  that  the  other  powers  diminish  therewith.  But 
Melloni  showed  that  by  scratching  a  polished  metallic  surface  its  reflecting 
power  was  sometimes  diminished  and  sometimes  increased.  This  pheno- 
menon he  attributed  to  the  greater  or  less  density  of  the  reflecting  surface. 
If  the  plate  had  been  originally  hammered,  its  homogeneity  would  be 
destroyed  by  this  process,  the  molecules  would  be  closer  together  on  the 
surface  than  in  the  interior,  and  the  reflecting  power  would  be  increased. 
But  if  the  surface  is  scratched,  the  internal  and  less  dense  mass  becomes 
exposed,  and  the  reflecting  power  diminished.  On  the  contrary,  in  a  plate 
which  has  not  been  hammered,  and  which  is  homogeneous,  the  reflecting 
power  is  increased  when  the  plate  is  scratched,  because  the  density  at  the 
surface  is  increased  by  the  scratches. 

Melloni  found  that  when  the  faces  of  a  cube  filled  with  water  at  a  constant 
temperature  were  varnished,  the  emissive  power  increased  with  the  number 
•of  layers  up  to  16  layers,  while  above  that  point  it  remained  constant, 
whatever  the  number.  The  thickness  of  the  16  layers  was  calculated  to  be 
0-04  mm.  With  reference  to  metals,  gold  leaves  of  0-008,  0-004,  and  0-002 
of  a  millimetre  in  thickness,  having  been  successively  applied  on  the  sides 
•of  a  cube  of  glass,  the  diminution  of  radiant  heat  was  the  same  in  each  case. 


380 


On  Heat. 


[427- 


It  appears,  therefore,  that,  beyond  certain  limits,  the  thickness  of  the  ra- 
diating layer  of  metal  is  without  influence. 

The  absorbing  power  is  greatest  when  the  rays  are  at  right  angles,  and 
it  diminishes  in  proportion  as  the  incident  rays  deviate  from  the  normal. 
This  is  one  of  the  reasons  why  the  sun  is  hotter  in  summer  than  in  winter, 
because,  in  the  former  case,  the  sun's  rays  are  less  oblique. 

The  radiating  power  of  gaseous  bodies  in  a  state  of  combustion  is  very 
weak,  as  is  seen  by  bringing  the  bulb  of  a  thermometer  near  a  hydrogen 
flame,  the  temperature  of  which  is  very  high.  But  if  a  platinum  spiral  be 
placed  in  this  flame,  it  assumes  the  temperature  of  the  flame,  and  radiates 
a  great  amount  of  heat,  as  is  shown  by  the  thermometer.  For  a  similar 
reason  the  flames  of  oil  and  of  gas  lamps  radiate  more  than  a  hydrogen 
flame  in  consequence  of  the  excess  of  carbon  which  they  contain,  and 
<  which,  not  being  entirely  burned,  becomes  incandescent  in  the  flame. 
^  428.  XVXelloni's  researches  on  radiant  heat. — For  our  knowledge  of 
the  phenomena  of  the  reflection,  emission,  and  absorption  of  heat  which 
have  up  to  now  been  described,  science  is  indebted  mainly  to  Leslie.  But 
since  his  time  the  discovery  of  other  and  far  more  delicate  modes  of  de- 
tecting and  measuring  heat,  has  not  only  extended  and  corrected  our 
previous  knowledge,  but  has  led  to  the  discovery  of  other  phenomena  of 
radiant  heat,  which,  without  such  improved  means,  must  have  remained 
unknown. 

This  advance  in  science  is  due  to  an  Italian  philosopher,  Melloni,  who 
first  applied  the  thermo-electric  pile,  invented  by  Nobili,  to  the-measurement 
of  very  small  differences  of  temperature  ;  a  method  of  which  a  preliminary 
account  has  already  been  given  (412). 

In  his  ex- 
periments Mel- 
loni used  five 
sources  of  heat 
— ist,  a  Loca- 
telli;s  lamp— 
one,  that  is, 
without  a  glass 
chimney,  but 
provided  with 
a  reflector  (fig. 
363)  ;  2nd,  an 
Argand  lamp, 
that  is,  one  with 
a  chimney  and  a 

double  draught ;  3rd,  a  platinum  spiral,  kept  red-hot  by  a  spirit  lamp  (fig. 
364)  ;  4th,  a  blackened  copper  plate,  kept  at  a  temperature  of  about  400° 
by  a  spirit  lamp  (fig.  365) ;  5th,  a  copper  tube,  blackened  on  the  outside 
and  filled  with  water  at  100°  (fig.  366). 

429.  Dynamical  theory  of  heat. — Before  describing  the  results  arrived 
at  by  Melloni  and  others,  it  will  be  convenient  to  explain  here  the  view  now 
generally  taken  as  to  the  mode  in  which  heat  is  propagated.  For  additional 
information  the  chapter  on  the  Mechanical  Theory  of  Heat  and  the  book  on 


Fig.  363- 


Fig.  365- 


Fig.  366. 


-429]  Dynamical  Theory  of  Heat.  381 

Light  should  be  read.  According  to  what  has  already  been  stated  (292),  a 
hot  body  is  nothing  more  than  one  whose  particles  are  in  a  state  of  vibration. 
The  higher  the  temperature  of  the  body,  the  more  rapid  are  these  vibrations, 
and  a  diminution  in  temperature  is  but  a  diminished  rapidity  of  vibration  of 
the  particles.  The  propagation  of  heat  through  a  bar  is  due  to  a  gradual 
communication  of  this  vibratory  motion  from  the  heated  part  to  the  rest  of 
the  bar.  A  good  conductor  is  one  which  readily  takes  up  and  transmits  the 
vibratory  motion  from  particle  to  particle,  while  a  bad  conductor  is  one  which 
takes  up  and  transmits  the  motion  with  difficulty.  But  even  through  the  best 
conductors  the  propagation  of  this  motion  is  comparatively  slow.  How  then 
are  we  to  explain  the  instantaneous  perception  of  heat  experienced  when  a 
screen  is  removed  from  a  fire,  or  when  a  cloud  drifts  from  the  face  of  the 
sun  ?  In  this  case,  the  heat  passes  from  one  body  to  another  without  affect- 
ing the  temperature  of  the  medium  which  transmits  it.  In  order  to  explain 
these  phenomena,  it  is  imagined  that  all  space,  the  interplanetary  spaces  as  well 
as  the  interstices  in  the  hardest  crystal  or  the  heaviest  metal — in  short,  matter 
of  any  kind — is  permeated  by  a  medium  having  the  properties  of  a  fluid  of 
infinite  tenuity,  called  ether.  The  particles  of  a  heated  body  being  in  a  state  of 
intensely  rapid  vibration,  communicate  their  motion  to  the  ether  around  them, 
throwing  it  into  a  system  of  waves  which  travel  through  space  and  pass  from 
one  body  to  another  with  the  velocity  of  light.  When  the  undulations  of  the 
ether  reach  a  given  body,  the  motion  is  again  delivered  up  to  the  particles  of 
that  body,  which  in  turn  begin  to  vibrate  ;  that  is,  the  body  becomes  heated. 
This  passage  of  motion  through  the  hypothetical  ether  is  termed  radiation, 
and  what  is  called  a  ray  of  heat  is  merely  the  direction  of  the  motion  of  one 
series  of  waves. 

It  will  facilitate  the  understanding  of  this  to  consider  the  analogous  mode 
in  which  sound  is  produced  and  propagated.  A  sounding  body  is  one  whose 
entire  mass  is  in  a  state  of  vibration  (222)  ;  the  more  rapid  the  rate  of  vibra- 
tion, the  more  acute  the  sound  ;  the  slower  the  rate  of  vibration,  the  deeper 
the  sound.  This  vibratory  motion  is  communicated  to  the  surrounding  air,  by 
means  of  which  the  vibrations  reach  the  auditory  nerve,  and  there  produce 
the  sensation  of  sound.  If  a  metal  ball  be  heated,  say,  to  the  temperature 
of  boiling  water,  we  can  ascertain  that  it  radiates  heat,  although  we  cannot 
see  any  luminosity  ;  and  if  its  temperature  be  gradually  raised,  we  see  it 
become  successively  of  a  dull  red,  bright  red,  and  dazzling  white.  At  each 
particular  temperature  the  heated  body  emits  waves  of  a  definite  length  ;  in 
other  words,  its  particles  vibrate  in  a  certain  period.  As  its  temperature 
rises  it  sends  out  other  and  more  rapid  vibrations,  which  coexist,  however, 
with  all  those  which  it  had  previously  emitted.  Thus  the  motion  at  each 
successive  temperature  is  compounded  of  all  preceding  ones. 

It  has  been  seen  that  vibrations  of  the  air  below  and  above  a  certain  rate 
do  not  affect  the  auditory  nerve  (244) ;  it  can  only  take  up  and  transmit  to  the 
brain  vibrations  of  a  certain  periodicity.  So  too  with  the  vibrations  which 
produce  light.  The  optic  nerve  is  insensible  to  a  large  number  of  wave- 
lengths. It  can  apprehend  only  those  waves  that  form  the  visible  spectrum. 
If  the  rate  of  undulation  be  slower  than  the  red  or  faster  than  the  violet, 
though  intense  motion  may  pass  through  the  humours  of  the  eye  and  fall 
upon  the  retina,  yet  we  shall  be  utterly  unconscious  of  the  fact,  for  the 


382  On  Heat.  [429- 

optic  nerve  cannot  take  up  and  respond  to  the  rate  of  vibrations  which  exist 
beyond  the  visible  spectrum  in  both  directions.  Hence,  these  are  termed 
invisible  or  obscure  rays.  A  vast  quantity  of  these  obscure  rays  is  emitted 
by  flames  which,  though  intensely  hot,  are  yet  almost  non-luminous,  such 
as  the  oxy-hydrogen  flame,  or  that  of  a  Bunsen's  burner  ;  for  the  vibra- 
tions which  these  emit,  though  capable  in  part  of  penetrating  the  media 
of  the  eye,  are  incapable  of  exciting  in  the  optic  nerve  the  sensation  of 
light. 

430.  Thermal  analysis  of  solar  light. — When  a  beam  of  sunlight  (fig. 
367),  admitted  through  an  aperture  in  a  dark  room,  is  concentrated  on  a 


Fig.  367. 

prism  of  rock  salt  by  means  of  a  lens  of  the  same  material,  and  then,  after 
emerging  from  the  prism,  is  received  on  a  screen,  it  will  be  found  to  present 
a  band  of  colours  in  the  following  order :  red,  orange,  yellow,  green,  blue, 
and  violet.  This  is  called  the  spectrum  (564). 

If  now  a  narrow  and  delicate  thermopile  be  placed  successively  on  the 
space  occupied  by  each  of  the  colours,  it  will  be  scarcely  affected  on  the 
violet,  but  in  passing  over  the  other  colours  it  will  indicate  a  gradual  rise  of 
temperature,  which  is  greatest  at  the  red.  Painters,  thus  guided  by  a  cor- 
rect but  unconscious  feeling,  always  speak  of  blue  and  green  colours  as  cold, 
and  of  red  and  orange  as  warm  tones.  If  the  pile  be  now  moved  in  the 
same  direction  beyond  the  limits  of  the  luminous  spectrum,  the  temperature 
will  gradually  rise  up  to  CP,  at  which  it  attains  its  maximum.  From  this 
point  the  pile  indicates  a  decrease  of  temperature  until  it  reaches  a  point,  O, 
where  it  ceases  to  be  affected.  This  point  is  about  as  distant  from  R  as  the 
latter  is  from  V  :  that  is,  there  is  a  region  in  which  thermal  effects  are  pro- 
duced extending  as  far  beyond  the  red.  end  of  the  spectrum  in  one  direction 
as  the  entire  length  of  the  visible  spectrum  is  in  the  other.  In  accordance 
with  what  we  have  stated,  the  sun's  light  consists  of  rays  of  different  rates  of 
vibration  ;  by  their  passage  through  the  prism  they  are  unequally  broken  or 
refracted  ;  those  of  greatest  wave  length  or  slowest  vibrating  period  are  least 
bent  aside,  or  are  said  to  be  the  least  refrangible,  while  those  with  shorter 
wavelengths  are  the  most  refrangible. 

These  non-luminous  rays  outside  the  red  are  called  the  extra  or  ultra-red 
rays,  or  sometimes  the  Herschelian  rays,  from  Sir  W.  Herschel,  who  first 
discovered  their  existence. 


-431] 


TyndaWs  Researches. 


333 


If,  in  the  above  case,  prisms  of  other  materials  than  rock  salt  be  used, 
the  position  of  the  maximum  heat  will  be  found  to  vary  with  the  nature  of 
the  prism,  a  fact  first  noticed  by  Seebeck.  Thus  with  a  prism  of  water  it  is 
in  the  yellow,  with  one  of  crown  glass,  in  the  middle  of  the  red,  and  so  on. 
These  changes  are  due  to  the  circumstance  that  prisms  of  different  materials 
absorb  rays  of  different  refrangibility  to  unequal  extents.  But  rock  salt 
practically  allows  heat  of  all  kinds  to  pass  with  equal  facility,  and  thus  gives 
a  normal  spectrum. 

431.  Tyndall' s  researches. — Tyndall  investigated  the  spectrum  pro- 
duced by  the  electric  light,  by  the  following  mode  of  experimenting  : — The 
electric  light  was  produced  between  charcoal  points  by  a  Grove's  battery  of 
fifty  cells.  The  beam,  rendered  parallel  by  a  double  rock  salt  lens,  was 
caused  to  pass  through  a  narrow  slit,  and  then  through  a  second  lens  of  rock 
salt  ;  the  slices  of  white  light  thus  obtained  being  decomposed  by  a  prism 
of  the  same  material.  To  investigate  the  thermal  conditions  of  the  spec- 
trum a  linear  thermo-electric  pile  was  used  ;  that  is,  one  consisting  of  a 
number  of  elements  arranged  in  a  line,  and  in  front  of  which  was  a  slit  that 
could  be  narrowed  to  any  extent.  The  instrument  was  mounted  on  a 
movable  bar  connected  with  a  fine  screw,  so  that  by  turning  a  handle  the 
pile  could  be  pushed  forward  through  the  smallest  space.  On  placing  this 
apparatus  successively  in  each  part  of  the  spectrum  of  the  electric  light,  the 
heating  effected  at  various  points  near  each  other  was  determined  by  the 
indications  of  a  very  delicate  galvanometer.  As  in  the  case  of  the  solar 
spectrum,  the  heating  effect  gradually  increased  from  the  violet  end  towards 
the  red,  and  was  greatest  in  the  dark  space  beyond  the  red.  The  position 
of  the  greatest  heat  was  about  as  far  from  the  limit  of  the  visible  red  as  the 
latter  was  from  the  green,  and  the  total  extent  of  the  invisible  spectrum  was 
found  to  be  twice  that  of  the  visible. 

The  increase  of  temperature  in  the  dark  space  is  very  considerable.  If 
thermal  intensities  are  represented  by  perpendicular  lines  of  proportionate 
length,  erected 
at  those  parts  of 
the  spectrum  to 
which  they  cor- 
respond, on  pass- 
ing beyond  the 
red  end  these 
lines  increase 
rapidly  and 

greatly  in  length, 
reach  a  maxi- 
mum, and  then 
fall  somewhat 
more  suddenly. 
If  these  lines  are 

connected,  they  form  a  curve  (fig.  368),  which  beyond  the  red  represents 
a  peak,  quite  dwarfing  that  of  the  visible  spectrum.  In  fig.  369,  the  dark 
parts  at  the  end  represent  the  obscure  radiation.  The  curve  is  based,  in  the 
manner  above  stated, 'on  the  results  obtained  by  Tyndall  with  the  electric 


Fig.  368. 


On  Heat.  [431- 

light.  The  upper  curve  in  fig.  369  represents  the  spectrum  of  sunlight  from 
the  experiments  of  Miiller  with  a  rocksalt  prism,  while  the  lower  curve 
represents  the  results  obtained  with  the  use  of  a  flintglass  prism,  which  is 
thus  seen  to  absorb  some  of  the  ultra-red  radiation. 

Tyndall  found  that  by  interposing  various  substances,  more  especially 
water,  in  certain  thicknesses,  in  the  path  of  the  electric  light,  the  ultra-red 
radiation  was  greatly  diminished.  Now  aqueous  vapour,  like  water,  absorbs 
the  obscure  rays.  And  probably  the  reason  why  the  obscure  part  of  the 
spectrum  of  sunlight  is  not  so  intense  as  in  the  case  of  the  electric  light  is 
that  the  obscure  rays  have  been  already  partially  absorbed  by  the  aqueous 
vapour  of  the  atmosphere.  If  a  solar  spectrum  could  be  produced  out- 
side the  atmosphere,  it  doubtless  would  give  a  spectrum  more  like  that  of 
the  electric  light,  which  is  unaffected  by  the  atmospheric  absorption. 

This  has  been  confirmed  in  other  ways.  Melloni  observed  that  the 
position  of  the  maximum  in  the  solar  spectrum  differs  on  different  days ; 
which  is  probably  due  to  the  varying  absorption  of  the  atmosphere,  in  con- 
sequence of  its  vaiying  hygrometric  state.  Secchi,  in  Rome,  found  the 

same  shifting  of 
the  maximum 
to  occur  in  the 
different  seasons 
of  the  year  ; 
for  in  winter, 
when  there  is 
least  moisture 
in  the  atmo- 
sphere, the 
maximum  is 
farther  from  the 
red  than  in  sum- 


Fig.  369. 


mer,  when  the  aqueous  vapour  in  the  air  is  most  abundant.  An  important 
observation  on  the  luminous  rays  has  also  been  made  by  Cooke,  in  America, 
who  found  that  the  faint  black  lines  in  the  solar  spectrum  attributed  to  the 
absorption  of  light  by  our  atmosphere  (see  book  on  Optics)  are  chiefly  caused 
by  the  presence  of  aqueous  vapour. 

432.  luminous  and  obscure  radiation. — The  radiation  from  a  luminous 
object,  a  gas  flame  for  example,  is  of  a  composite  character  ;  a  portion  con- 
sists of  what  we  term  light,  but  a  far  greater  part  consists  of  heat  rays, 
which  are  insensible  to  our  eyes,  being  unable  to  affect  the  optic  nerve. 
When  this  mixed  radiation  falls  upon  the  blackened  face  of  a  thermo-electric 
pile,  the  whole  of  it  is  taken  to  be  absorbed,  the  light  by  this  act  being 
converted  into  heat,  and  affecting  the  instrument  proportionally  with  the 
purely  calorific  rays.  The  total  radiation  of  a  luminous  source,  expressed 
in  units  of  heat  or  force,  can  thus  be  measured.  By  introducing  into  the 
path  of  the  rays  a  body  capable  of  stopping  either  the  luminous  or  the 
obscure  radiation,  we  can  ascertain  by  the  comparative  action  on  the  pile 
the  relative  quantities  of  heat  and  light  radiated  from  the  source.  Melloni 
sought  to  do  this  by  passing  a  luminous  beam  through  a  layer  of  water 
containing  alum  in  solution  ;  a  liquid  which  he  found  in  previous  experi- 


-433]  Transmutation  of  Obscure  Rays.  385 

ments  absorbed  all  the  radiation  from  bodies  heated  under  incandescence. 
Comparing  the  transmission  through  this  liquid — which  allowed  the  luminous 
part  of  the  beam  to  pass,  but  quenched  the  obscure  portion — with  the  trans- 
mission through  a  plate  of  rock  salt — which  affected  neither  the  luminous  nor 
the  obscure  radiation,  but  gave  the  loss  due  o  reflection — Melloni  found 
that  90  per  cent,  of  the  radiation  from  an  oil  flame  and  99  per  cent,  of  the 
radiation  from  an  alcohol  flame  consist  of  invisible  calorific  rays.  This  pro- 
portion has  been  still  further  increased  by  the  experiments  of  Tyndall,  who 
employed  a  solution  of  iodine  in  bisulphide  of  carbon,  which  he  found  to  be 
impervious  to  the  most  intense  light,  but  very  pervious  to  radiant  heat  ;  only 
a  slight  absorption  being  affected  by  the  bisulphide.  By  successively  coin- 
paring  the  transmission  through  the  transparent  bisulphide,  and  the  trans- 
mission through  the  same  liquid  rendered  opaque  by  iodine,  the  value  of  the 
luminous  radiation  from  various  sources  was  found  to  be  as  follows  : — 

Source  Luminous          Obscure 

Red-hot  spiral o  100 

Hydrogen  flame o  100 

Oil  flame         ......  3  97 

Gas  flame        ......  4  96 

White-hot  spiral 4-6  95-4 

Electric  light  ....*.  jo  90 

Here  by  direct  experiment  the  ratio  of  luminous  to  obscure  rays  in  the 
electric  light  is  found  to  be  10  per  cent,  of  the  total  radiation.  By  prismatic 
analysis,  the  curve  shown  in  fig.  368  was  obtained,  graphically  representing 
the  proportion  of  luminous  to  obscure  rays  in  the  electric  light ;  by  calculating 
the  areas  of  the  two  spaces  in  the  diagram,  the  obscure  portion,  DCBA,  is 
found  to  be  nearly  10  times  as  large  as  the  luminous  one,  DCE. 

433.  Transmutation  of  obscure  rays. — We  shall  find,  in  speaking  of 
the  luminous  spectrum,  that  beyond  the  violet  there  are  rays  which  are  in- 
visible to  the  eye,  but  which  are  distinguished  by  their  chemical  action,  and 
are  spoken  of  as  the  actinic  or  chemical  rays  ;  they  are  also  known  as  the 
Ritteric  rays,  from  the  philosopher  who  first  discovered  their  existence. 

As  we  shall  afterwards  see  in  the  book  on  Optics,  Stokes  has  succeeded 
in  converting  these  rays  into  rays  of  lower  refrangibility,  which  then  become 
visible  ;  so  Tyndall  has  effected  the  corresponding  but  inverse  change,  and 
has  increased  the  refrangibility  of  the  Herschelian  or  extra  red  rays,  and 
thus  rendered  them  visible.  The  charcoal  points  of  the  electric  light  were 
placed  in  front  of  a  concave  silvered  glass  mirror  in  such  a  manner  that 
the  rays  from  the  points  after  reflection  were  concentrated  to  a  focus  about 
6  inches  distant.  On  the  path  of  the  beam  was  interposed  a  cell  full  of  a 
solution  of  iodine  in  bisulphide  of  carbon,  which  (432)  has  the  power  of  com- 
pletely stopping  all  luminous  radiation,  but  gives  free  passage  to  the  non- 
luminous  rays.  On  now  placing  in  the  focus  of  the  beam,  thus  sifted,  a  piece 
of  platinum,  it  was  raised  to  incandescence  by  the  impact  of  perfectly  invisible 
rays.  In  like  manner  a  piece  of  charcoal  in  vacuo  was  heated  to  redness. 

By  a  proper  arrangement  of  the  charcoal  points  a  metal  may  be  raised 
to  whiteness,  and  the  light  now  emitted  by  the  metal  yields  on  prismatic 
analysis  a  brilliant  luminous  spectrum,  which  is  thus  entirely  derived  from 

C  C 


386 


On  Heat. 


[433- 


the  invisible  rays  beyond  the  red.  This  transmutation  of  non-luminous  into 
luminous  heat,  Tyndall  calls  calorescence. 

When  the  eye  was  cautiously  placed  in  the  focus,  guarded  by  a  small 
hole  pierced  in  a  metal  screen,  so  that  the  converged  rays  should  only  enter 
the  pupil  and  not  affect  the  surrounding  part  of  the  eye,  no  impression  of 
light  was  produced,  and  there  was  scarcely  any  sensation  of  heat.  A  con- 
siderable portion  was  absorbed  by  the  humours  of  the  eye,  but  yet  a  power- 
ful beam  undoubtedly  reached  the  retina  ;  for,  as  Tyndall  showed  by  a 
separate  experiment,  about  18  per  cent,  of  the  obscure  radiation  from  the 
electric  light  passed  through  the  humours  of  an  ox's  eye. 

434.  Transmission  of  thermal  rays. — Melloni  was  the  first  who  ex- 
amined extensively  and  accurately  the  absorption  of  heat  by  solids  and 
liquids.  The  apparatus  he  employed  is  represented  in  fig.  370,  where  AB  is 


Fig.  370. 

the  thermo-electric  pile  ;  a  is  a  support  for  the  source  of  heat,  in  this  case  a 
Locatelli's  lamp  ;  F  and  E  are  screens,  and  C  is  a  support  for  the  body  ex- 
perimented on  ;  while  m  is  the  support  for  the  pile,  and  D  the  galvanometer. 
To  express  the  power  which  bodies  have  of  transmitting  heat,  Melloni 
used  the  term  diathermancy :  diathermancy  bears  the  same  relation  to- 
radiant  heat  that  transparency  does  to  light ;  and  in  like  manner  the  power 
of  stopping  radiant  heat  is  called  athermancy,  which  thus  corresponds  to 
opacity  for  light.  In  experimenting  on  the  diathermancy  of  liquids,  Melloni 
used  glass  troughs  with  parallel  sides,  the  thickness  of  the  liquid  layer  being 
0-36  in.  The  radiant  heat  of  an  Argand  lamp  with  a  glass  chimney  was 
first  allowed  to  fall  directly  on  the  face  of  the  pile,  and  the  deflection  pro- 
duced in  the  galvanometer  taken  as  the  total  radiation  ;  the  substance  under 
examination  was  then  interposed,  and  the  deflection  noted.  This  corre- 
sponded to  the  quantity  of  heat  transmitted  by  the  substance.  If  /  indicate 
this  latter  number,  and  t'  the  total  radiation,  then 

f  :  /:  :  100  :  x, 

which  is  the  percentage  of  rays  transmitted.     Thus  calling  the  total  radia- 
tion 100,  Melloni  found  that 


-434] 


Transmission  of  Thermal  Rays. 


387 


Bisulphide  of  carbon  transmitted 

Olive  oil  „ 

Ether  „ 

Sulphuric  acid  „ 

Alcohol  „ 

Solution  of  alum  or  sugar  „ 
Distilled  water 


63 
30 

21 
17 
15 
12 
II 


In  experimenting  with  solids  they  were  cut  into  plates  o'l  inch  in  thick- 
ness, and  it  was  found  that  of  every  100  rays  there  was  transmitted  by 

Rock  salt  «;;;r^,;;  •.-,..  92  Selenite  .  .  .  20 
Smoky  quartz  >.*,>.'  .  .  67  Alum  .  .  .  .12 
Transparent  carbonate  of  lead  52  Sulphate  of  copper  .  o 

The  transmission  of  heat  through  liquids  has  been  re-examined  by  Tyndall, 
who  used  a  cell  consisting  of  parallel  plates  of  rock  salt  separated  by  a  ring 
of  brass  with  an  aperture  on  the  top  through  which  the  liquid  could  be 
poured.  As  this  ring  could  be  changed  at  will,  liquid  layers  of  various 
thicknesses  were  easily  obtainable,  the  apparatus  being  merely  screwed 
together  and  made  liquid-tight  by  paper  washers.  The  instrument  was 
mounted  on  a  support  before  an  opening  in  a  brass  screen  placed  in  front 
of  the  pile.  The  source  of  heat  employed  was  a  spiral  of  platinum  wire 
raised  to  incandescence  by  an  electric  current,  the  spiral  being  enclosed  in  a 
small  glass  globe  with  an  aperture  in  front,  through  which  the  radiation 
passed  unchanged  in  its  character,  a  point  of  essential  importance  overlooked 
by  Melloni.  The  following  table  contains  the  results  of  experiments  made 
with  liquids  in  the  various  thicknesses  indicated,  the  numbers  expressing 
the  absorption  per  cent,  of  the  total  radiation.  The  transmission  per  cent, 
can  be  found  in  each  case  by  subtracting  the  absorption  from  100.  Thus  a 
layer  of  water  0-2  inch  thick  absorbs  807  and  transmits  19-3  per  cent,  of  the 
radiation  from  a  red-hot  spiral. 

Absorption  of  heat  by  liquids. 


Thickness  of  liquid  in  parts  of  an  inch 

0*02 

o'o4                 0*07 

0-14 

0-27 

Bisulphide  of  carbon 

5*5 

8-4          12-5 

15-2 

173 

Chloroform        .         .  •      ,  . 

1  6-6 

25-0 

35'o 

40*0 

44-8 

Iodide  of  methyl       .    .;,.. 

36T 

46-5 

53'2 

65-2 

68-6 

Benzole     ... 

43  "4 

557 

62-5 

71-5 

73-6 

Amylene  .         .      '  . 

58-3 

65-2 

73-6 

777 

82-3 

Ether        .        .;  -;;;  *   ';;-''J 

633 

73'5 

76-1 

78-6 

85-2 

Alcohol     .         *-'-•..  :M.  # 

67-3 

78-6 

83-6 

85-3 

89-1 

Water       .   ..-.-'.  -••,->.  .-;.,:!*1 

807 

86-1 

88-8 

91-0 

91-0 

It  appears  from  these  tables  that  there  is  no  connection  between  diather- 
mancy and  transparency.  The  liquids,  except  olive  oil,  are  all  colourless 
and  transparent,  and  yet  vary  as  much  as  75  per  cent,  in  the  amount  of  heat 
transmitted.  Among  solids,  smoky  quartz,  which  is  nearly  opaque  to  light 

c  c  2 


388 


On  Heat. 


[434- 


transmits  heat  very  well  ;  while  alum,  which  is  perfectly  transparent,  cuts  off 
88  per  cent,  of  heat  rays.  As  there  are  different  degrees  of  transparency,  so 
there  are  different  degrees  of  diathermancy  ;  and  the  one  cannot  be  predi- 
cated from  the  other. 

By  studying  the  transmission  of  heat  from  different  parts  of  the  spec- 
trum separately,  the  connection  between  light  and  heat  becomes  manifest. 
With  this  view  Masson  and  Jamin  received  the  spectrum  of  the  solar  light 
given  by  a  prism  of  rock  salt  on  a  movable  screen  provided  with  an  aperture, 
so  that  by  raising  or  lowering  the  screen  the  action  of  any  given  part  of  the 
spectrum  on  different  plates  could  be  investigated.  They  thus  found — 

That  glass,  rock  crystal,  ice,  and  generally  substances  transparent  for 
light,  are  also  diathermanous  for  all  kinds  of  luminous  heat ; 

That  a  coloured  glass,  red,  for  instance,  which  only  transmits  the  red  rays 
of  the  spectrum,  and  extinguishes  the  others,  also  extinguishes  every  kind  of 
luminous  heat,  excepting  that  of  the  red  rays  ; 

That  glass  and  rock  crystal,  which  are  diathermanous  for  luminous  heat, 
also  transmit  the  obscure  heat  near  the  red — that  is,  the  most  refrangible — 
but  extinguish  the  extreme  obscure  rays,  or  those  which  are  the  least  de- 
flected by  the  prism.  Alum  extinguishes  a  still  greater  proportion  of  the 
obscure  spectrum,  and  ice  stops  it  altogether. 

Knoblauch  has  shown  that  very  thin  layers  of  gold,  silver,  and  platinum, 
which  are  known  to  transmit  luminous  rays  of  a  definite  colour,  also  allow 
rays  of  heat  to  pass  ;  so  that  these  substances  are  diathermanous,  though  in 
4a  small  degree.  This  is  also  the  case  with  thin  sheets  of  ebonite. 

435.  Influence  of  the  nature  oi  the  heat. — The  diathermanous  power 
differs  greatly  with  the  heat  from  different  sources,  as  is  seen  from  the 
following  table,  in  which  the  numbers  express  what  proportion  of  every 
100  rays  from  the  different  sources  of  heat  incident  on  the  plates  is  trans- 
mitted : — 


Locatelli's 
lamp 

Incandescent 
platinum  wire 

Copper  at  400° 

Copper  at  100° 

Rock  salt   . 

92 

92 

92 

92 

Fluor  spar  .       .  ;    :    .  • 

78 

69 

42 

33 

Plate  glass 

39 

24 

6 

0 

Black  glass 

26 

55 

12 

o 

Selenite      . 

14 

5 

O 

0 

Alum  .         *  i      .       '•.  ™ 

9 

2 

0 

0 

Ice     .        v  •••    .       -if 

6 

0-5 

0 

0 

These  different  sources  of  heat  correspond  to  light  from  different  sources. 
Rock  salt  is  here  stated  to  transmit  all  kinds  of  heat  with  equal  facility,  and 
to  be  the  only  substance  which  does  so.  It  is  analogous  to  white  glass, 
which  is  transparent  for  light  from  all  sources.  Fluor  spar  transmits  78  per 
cent,  of  the  rays  from  a  lamp,  but  only  33  of  those  from  a  blackened  surface 
at  100°.  A  piece  of  plate  glass  only  one-tenth  of  an  inch  thick,  and  perfectly 
transparent  to  light,  is  opaque  to  all  the  radiation  from  a  source  of  100°, 
transmits  only  6  per  cent,  of  the  heat  from  a  source  at  400°,  and  but  39  of 
the  radiation  from  the  lamp.  Black  glass,  on  the  contrary,  though  it  cuts 


-435] 


Influence  of  the  Nature  of  the  Heat. 


389 


off  all  heat  from  a  source  at  100°,  allows  12  per  cent,  of  the  heat  at  400°  to 
pass,  and  is  equally  transparent  to  the  heat  from  the  spiral,  but  on  account 
of  its  blackness  is  more  opaque  to  the  heat  from  the  lamp.  As  we  have 
already  seen,  every  luminous  ray  is  a  heat  ray  ;  now  as  several  of  the  sub- 
stances in  this  table  are  pervious  to  all  the  luminous  rays,  and  yet,  as  in  the 
case  of  ice,  transmit  about  6  per  cent,  of  luminous  heat,  we  have  an  apparent 
anomaly  ;  which,  however,  is  only  a  confirmation  of  the  remarkably  small 
proportion  which  the  luminous  rays  of  a  lamp  bear  to  the  obscure. 

From  these  experiments  Melloni  concluded  that  as  the  temperature  of 
the  spurce  rose,  more  heat  was  transmitted.  This  has  been  confirmed  by 
some  experiments  of  Tyndall.  The  platinum  lamp  (434)  was  used  as  the 
source,  the  temperature  of  which  could  be  varied  from  a  dark  to  a  brilliant 
white  heat,  by  a  gradual  augmentation  of  the  strength  of  the  electric  current 
which  heated  the  platinum  spiral.  Instead  of  liquids,  vapours  were  examined 
in  a  manner  to  be  described  subsequently  ;  the  measurements  are  given  in 
the  following  table  : — 

Absorption  of  heat  by  vapours. 


Source,  platinum  spiral 

Name  of  vapour 

Barely  visible 

Bright  red 

White  hot 

Near  fusion 

Bisulphide  of  carbon 

6-5 

47 

2'9 

2'5 

Chloroform 

9-1 

6'3 

5-6 

3'9 

Iodide  of  methyl        .         * 

12-5 

9-6 

7-8 

Benzole 

26-4 

20'6 

I6'5 

Ether         ...         ._" 

43  '4 

31-4 

25-9 

237 

Formic  ether 

45-2 

31*9 

25-1 

21-3 

Acetic  ether       .         . 

49-6 

34'6 

27-2 

The  percentage  of  rays  absorbed  is  here  seen  to  diminish  in  each  case 
as  the  temperature  of  the  source  rises.  Mere  elevation  of  temperature  does 
not,  however,  invariably  produce  a  high  penetrative  power  in  the  rays 
emitted  ;  the  rays  from  sources  of  far  higher  temperature  than  any  of  the 
foregoing  are  more  largely  absorbed  by  certain  substances  than  are  the  rays 
emitted  from  any  one  of  the  sources  as  yet  mentioned.  Thus,  the  radia- 
tion from  a  hydrogen  flame  was  completely  intercepted  by  a  layer  of  water 
only  0-27  of  an  inch  thick,  the  same  layer  transmitting  9  per  cent,  of  the 
radiation  from  the  red-hot  spiral,  a  source  of  much  lower  temperature.  The 
explanation  of  this  is,  that  those  rays  which  heated  water  emits  (and  water, 
the  product  of  combustion,  is  the  main  radiant  in  a  hydrogen  flame)  are  the 
very  ones  which  this  substance  most  largely  absorbs.  This  statement,  which 
will  become  clearer  after  reading  the  analogous  phenomena  in  the  case  of 
light,  was  exemplified  by  the  powerful  absorption  of  the  heat  from  a 
carbonic  oxide  flame  by  carbonic  acid  gas.  It  will  be  seen  presently  (438) 
that  of  the  rays  from  a  heated  plate  of  copper,  defiant  gas  absorbs  10  times 
the  quantity  intercepted  by  carbonic  acid,  whilst  of  the  rays  from  a  carbonic 
oxide  flame  Tyndall  found  carbonic  acid  absorbed  twice  as  much  as  olefiant 
gas.  A  tenth  of  an  atmosphere  of  carbonic  acid,  inclosed  in  a  tube  4  feet 
long,  absorbs  60  per  cent,  of  the  radiation  from  a  carbonic  oxide  flame. 


390  On  Heat.  [435- 

Radiant  heat  of  this  character  can  thus  be  used  as  a  delicate  test  for  the 
presence  of  carbonic  acid,  the  amount  of  which  may  even  be  accurately 
measured  by  the  same  means.  Prof.  Barrett  made  in  this  way  a  physical 
analysis  of  the  human  breath.  In  one  experiment,  the  carbonic  acid  con- 
tained in  breath  physically  analysed  was  found  to  be  4-65  per  cent.,  whilst 
the  same  breath  chemically  analysed  gave  4-66  per  cent. 

436.  Influence  of  the  thickness  and  nature  of  screens. — It  will  be 
seen  from  the  table  (435)  that  of  every  100  rays  rock  salt  transmits  92.  The 
other  8  may  either  have  been  absorbed  or  reflected  from  the  surface  of  the 
plate.  According  to  Melloni,  the  latter  is  the  case  ;  for  if,  instead  of  on  one 
plate,  heat  be  allowed  to  fall  on  two  or  more  plates  whose  total  thickness 
does  not  exceed  that  of  the  one,  the  quantity  of  heat  arrested  will  be  propor- 
tional to  the  number  of  reflecting  surfaces.  He  therefore  concluded  that 
rock  salt  was  quite  diathermanous. 

The  experiments  of  later  observers  show  that  this  conclusion  is  not 
strictly  correct ;  rock  salt  does  absorb  a  very  small  proportion  of  obscure 
rays. 

The  quantity  of  heat  transmitted  through  rock  salt  is  practically  the 
same,  whether  the  plate  be  I,  2,  or  4  millimetres  thick.  But  with  other  bodies 
absorption  increases  with  the  thickness,  although  by  no  means  in  direct 
proportion.  This  is  seen  to  be  the  case  in  the  table  of  absorption  by  liquids 
at  different  thicknesses.  The  following  table  tells  what  proportion  of 
1,000  rays  from  a  Locatelli's  lamp  pass  through  a  glass  plate  of  the  given 
thickness  : — 

Thickness  in  millimetres      0-512345678 
Rays  transrhJtted     .         -775    733   682   653   634   620  609   600    592 

The  absorption  takes  place  in  the  first  layers  ;  the  rays  which  have  passed 
these  possess  the  property  of  passing  through  other  layers  in  a  higher  degree, 
so  that  beyond  the  first  layers  the  heat  transmitted  approaches  a  certain 
constant  value.  If  a  thin  glass  plate  be  placed  behind  another  glass  plate 
a  centimetre  thick,  the  ^former  diminishes  the  transmission  by  little  more 
than  the  reflection  from  its  surface.  But  if  a  plate  of  alum  were  placed  be- 
hind the  glass  plate,  the  result  would  be  different,  for  the  latter  is  opaque  for 
much  of  the  heat  transmitted  by  glass. 

Heat,  therefore,  which  has  traversed  a  glass  plate  traverses  another 
plate  of  the  same  material  with  very  slight  loss,  but  is  very  greatly  diminished 
by  a  plate  of  alum.  Of  100  rays  which  had  passed  through  green  glass 
or  tourmaline,  only  5  and  7  were  respectively  transmitted  by  the  same 
plate  of  alum.  A  plate  of  blackened  rock  salt  only  transmits  obscure  rays, 
while  alum  extinguishes  them.  Consequently,  when  these  two  substances 
are  superposed,  a  system  impervious  to  light  and  heat  is  obtained. 

These  phenomena  find  their  exact  analogies  in  the  case  of  light.  The 
different  sources  of  heat  correspond  to  flames  of  different  colours,  and  the 
screens  of  various  materials  to  glasses  of  different  colours.  A  red  flame 
looked  at  through  a  red  glass  appears  quite  bright,  but  through  a  green  glass 
it  appears  dim  or  is  scarcely  visible.  So  in  like  manner  heat  which  has 
traversed  a  red  glass  passes  through  another  red  glass  with  little  diminu- 
tion but  it  is  almost  completely  stopped  by  a  green  glass.  Rock  salt  at  1 50° 


-437] 


Diffusion  of  Heat. 


391 


emits  only  one  kind  of  heat ;  it  is  monothermal,  just  as  sodium  vapour  is 
monochromatic. 

Different  luminous  rays  being  distinguished  by  their  colours,  to  these 
different  obscure  calorific  rays  Melloni  gives  the  name  of  thermocrose  or  heat 
colouration.  The  invisible  portion  of  the  spectrum  is  accordingly  mapped 
out  into  a  series  of  spaces,  each  possessing  its  own  peculiar  feature  corre- 
sponding to  the  coloured  spaces  which  are  seen  in  that  portion  of  the  spec- 
trum visible  to  our  eyes. 

Besides  thickness  and  colour,  the  polish  of  a  substance  influences  the 
transmission.  Glass  plates  of  the  same  size  and  thickness  transmit  more 
heat  as  their  surface  is  more  polished.  Bodies  which  transmit  heat  of  any 
kind  very  readily  are  not  heated.  Thus  a  window  pane  is  not  much  heated 
by  the  strongest  sun's  heat ;  but  a  glass  screen  held  before  a  common  fire 
stops  most  of  the  heat,  and  is  itself  heated  thereby.  The  reason  of  this  is 
that  by  far  the  greater  part  of  the  heat  from  a  fire  is  obscure,  and  to  this  kind 
of  heat  glass  is  opaque. 

437.  Diffusion  of  heat. — When  a  ray  of  light  falls  upon  an  unpolished 
surface  in  a  definite  direction,  it  is  decomposed  into  a  variety  of  rays  which 
are  reflected  from  the  surface  in  all  directions.  This  irregular  reflection  is 
called  diffusion,  and  it  is  in  virtue  of  it  that  bodies  are  visible  when  light 
falls  upon  them.  A  further  peculiarity  is,  that  all  solar  rays  are  not  equally 
diffused  from  the  surface  of  bodies.  Certain  bodies  diffuse  certain  rays  and 
absorb  others,  and  accordingly  appear  coloured.  The  red  colour  of  a  gera- 
nium is  caused  by  its  absorbing  all  the  rays,  excepting  the  red,  which  are 
irregularly  reflected.  Just  as  is  the  case  with  transmitted  light  in  transparent 
bodies,  so  with  diffused  light  in  opaque  ones  ;  for  if  a  red  body  is  illuminated 
by  red  light  it  appears  of  a  bright  red  colour,  but  if  greeiflfight  fall  upon  it 
it  is  almost  black.  We  shall  now  see  that  here  again  analogous  phenomena 
prevail  with  heat. 

Various  substances  diffuse  different  thermal  rays  to  a  different  extent ; 
each  possesses  a  peculiar  thermocrose.  Melloni  placed  a  number  of  strips 
of  brass  foil  between  the  source  of  heat  and  the  thermo-pile.  They  were 
coated  on  the  side  opposite  to  the  pile  with  lampblack,  and  on  the  other 
side  with  the  substances  to  be  investigated.  Representing  the  quantity  of 
heat  absorbed  by  the  lampblack  by  100,  the  absorption  of  the  other  bodies 
was  as  follows  : — 


Incandescent 
platinum 

Copper  at  400° 

Copper  at  100° 

Lampblack        .    i!  -w!  r.  -,.     '    . 

100 

100 

100 

White  lead        .     >,  ^  -.-,*•        . 

56 

89 

100 

Isinglass  .   ..  ,*•-,,  -v-    .  f;i;  ,   . 

54 

64 

91 

Indian  ink    .     ..,'     ,  .-  !t  T. 

95 

87 

85 

Shellac      .         .         .  "  r'.' 

47 

70 

72 

Polished  metal          .         .  "'      ... 

I3-5 

13 

13 

Hence  white  lead  absorbs  far  less  of  the  heat  radiated  from  incandescent 
platinum  than  lampblack,  but  it  absorbs  the  obscure  rays  from  copper  at 
100°  as  completely  as  lampblack.  Indian  ink  is  the  reverse  of  this  ;  it 


392 


On  Heat. 


[437- 


absorbs  obscure  rays  less  completely  than  luminous  rays.  Lampblack 
absorbs  the  heat  from  all  sources  in  equal  quantities,  and  very  nearly  com- 
pletely. In  consequence  of  this  property  all  thermoscopes  which  are  used 
for  investigating  radiant  heat  are  covered  with  lampblack,  as  it  is  the  best- 
known  absorbent  of  heat.  The  behaviour  of  metals  is  the  reverse  of  that  of 
lampblack.  They  reflect  the  heat  of  different  sources  in  the  same  degree. 
They  are  to  heat  what  white  bodies  are  to  light. 

As  coloured  light  is  altered  by  diffusion  from  several  bodies,  so  Knoblauch 
has  shown  that  the  different  kinds  of  heat  are  altered  by  reflection  from  dif- 
ferent surfaces.  The  heat  of  an  Argand  lamp  diffused  from  white  paper 
passes  more  easily  through  calcspar  than  when  it  has  been  diffused  from 
black  paper. 

The  rays  of  heat,  like  the  rays  of  light,  are  susceptible  of  polarisation 
and  double  refraction.  These  properties  will  be  better  understood  after 
treating  of  light. 

438.  Relation  of  gases  and  vapours  to  radiant  neat. — This  subject 
has  been  investigated  by  Tyndall  ;  the  apparatus  he  used  is  represented  in 
the  adjacent  figure,  the  arrangement  being  looked  upon  from  above. 

A  (fig.  371)  is  a  cylinder  about  4  feet  in  length  and  2|  inches  in  diameter, 
placed  horizontally,  the  ends  of  which  can  be  closed  with  rock-salt  plates  : 


r 


Fig.  371- 


by  means  of  a  lateral  tube  at  r  it  can  be  connected  with  an  air-pump  and 
exhausted  ;  while  at  t  is  another  tube  which  serves  for  the  introduction  of 
gases  and  vapours.  T  is  a  sensitive  thermo-pile  connected  with  an  extremely 
delicate  galvanometer,  M. 

The  deflections  of  this  galvanometer  were  proportional  to  the  degrees  of 
heat  up  to  about  30° ;  beyond  this  point  the  proportionality  no  longer  held 
good,  and  accordingly,  for  the  higher  degrees,  a  table  was  empirically  con- 
structed, in  which  the  value  of  the  higher  deflections  was  expressed  in  units ; 
the  unit  being  the  amount  of  heat  necessary  to  move  the  needle  through  one 
of  the  lower  degrees, 

C  was  a  source  of  heat,  which  usually  was  either  a  Leslie's  cube  filled  with 
boiling  water,  or  else  a  sheet  of  blackened  copper  heated  by  gas.  Now, 
when  the  source  of  heat  was  permitted  to  radiate  through  the  exhausted 
tube,  the  needle  made  a  great  deflection  ;  and  in  this  position  a  very  con- 
siderable degree  of  absorption  would  have  been  needed  to  produce  an 
alteration  of  i°  of  the  galvanometer.  And  if  to  lessen  this  deflection  a  lower 
source  of  heat  had  been  used,  the  fraction  absorbed  would  be  correspondingly 
less,  and  might  well  have  been  insensible.  Hence  Tyndall  adopted  the  fol- 
lowing device,  by  which  he  was  enabled  to  use  a  powerful  flux  of  heat,  and  at 
the  same  time  to  discover  small  variations  in  the  quantity  falling  on  the  pile. 


-439] 


A  bsorption  of  Heat  by  Gases. 


393 


The  source  of  heat  at  C  was  allowed  to  radiate  through  the  tube  at  the 
end  of  which  the  pile  was  placed  ;  a  deflection  was  produced  of,  say,  70°  ;. 
a  second  source  of  heat,  D,  was  then  placed  near  the  other  face  of  the  pile, 
the  amount  of  heat  falling  on  the  pile  from  this  compensating  cube  being 
regulated  by  means  of  a  movable  screen  S.  When  both  faces  of  the  pile 
are  warmed,  two  currents  are  produced,  which  are  in  opposite  directions,, 
and  tend,  therefore,  to  neutralise  each  other  :  when  the  heat  on  both  faces 
is  precisely  equal,  the  neutralisation  is  perfect,  and  no  current  at  all  is  pro- 
duced, however  high  may  be  the  temperature  on  both  sides.  In  the  arrange- 
ment just  described,  by  means  of  the  screen  S,  the  radiation  from  the 
compensating  cube  was  caused  to  neutralise  exactly  the  radiation  from  the 
source  C  ;  the  needle  consequently  was  brought  down  from  70°  to  zero,  and 
remained  there  so  long  as  both  sources  were  equal.  If  now  a  gas  or  vapour 
be  admitted  into  the  exhausted  tube,  any  power  of  absorption  it  may  possess 
will  be  indicated  by  the  destruction  of  this  equilibrium,  and  preponderance 
of  the  radiation  from  the  compensating  cube,  by  an  amount  corresponding 
to  the  heat  cut  off  by  the  gas.  Examined  in  this  way,  air,  hydrogen,  and 
nitrogen,  when  dried  by  passing  through  sulphuric  acid,  were  found  to  exert 
an  almost  inappreciable  effect ;  their  presence  as  regards  radiant  heat  being 
but  little  different  to  a  vacuum.  But  with  olefiant  and  other  complex  gases 
the  case  was  entirely  different.  Representing  by  the  number  I  the  quantity 
of  radiant  heat  absorbed  by  air,  olefiant  gas  absorbs  970  times,  and  am- 
moniacal  gas  1,195  times,  this  amount.  In  the  following  table  is  given  the 
absorption  of  obscure  heat  by  various  gases,  referred  to  air  as  unity  : — 


Absorption 

Absorption 

Name  of  gas 

under  30  inches 

Name  of  gas 

under  30  inches 

of  pressure     ! 

of  pressure 

Air          .         . 

I 

Carbonic  acid      .         . 

90 

Oxygen  .... 

I 

Nitrous  oxide 

335 

Nitrogen 

I 

Marsh  gas  . 

403 

Hydrogen 

I 

Sulphurous  acid  .         . 

710 

Chlorine 

39 

Olefiant       .        .     -    . 

970 

Hydrochloric  acid 

62 

Ammonia    .         .   '      ,  , 

1195 

If,  instead  of  comparing  the  gases  at  a  common  pressure  of  one  atmo- 
sphere, they  are  compared  at  a  common  pressure  of  an  inch,  their  differences 
in  absorption  are  still  more  strikingly  seen.  Thus,  assuming  the  absorption 
by  i  inch  of  dry  air  to  be  i,  the  absorption  by  I  inch  of  olefiant  gas  is  7,950,. 
and  by  the  same  amount  of  sulphurous  acid  8,800. 

439.  Influence  of  pressure  and  thickness  on  the  absorption  of  heat 
by  gases. — The  absorption  of  heat  by  gases  varies  with  the  pressure  ;  this 
variation  is  best  seen  in  the  case  of  those  gases  which  have  considerable 
absorptive  power.  Taking  the  total  absorption  by  atmospheric  air  under 
ordinary  pressure  at  unity,  the  numbers  of  olefiant  gas  under  a  pressure  of  ir 
3,  5,  7,  and  10  inches  of  mercury  are  respectively  90,  142,  168,  182,  and  193. 
Thus  one-thirtieth  of  an  atmosphere  of  olefiant  gas  exerts  90  times  the 
absorption  of  an  entire  atmosphere  of  air.  And  the  absorption,  it  is  seen,, 
increases  with  the  density,  though  not  in  a  direct  ratio.  Tyndall  showed,, 


394 


On  Heat. 


[439- 


however,  by  special  experiments,  that  for  very  low  pressures  the  absorption 
does-increase  with  the  density.  Employing  as  a  unit  volume  of  the  gas  a 
quantity  which  measured  only  i  of  a  cubic  inch,  and  admitting  succes- 
sive measures  of  olefiant  gas  into  the  experimental  tube,  it  was  found  that 
up  to  15  measures  the  absorption  was  directly  proportionate  to  the  density 
in  each  case. 

In  these  experiments  the  length  of  the  experimental  tube  remained  the 
same  whilst  the  pressure  of  the  gas  within  it  was  caused  to  vary  ;  in  subse- 
quent experiments  the  pressure  of  the  gas  was  kept  constant,  whilst  the 
length  of  the  tube  was,  by  suitable  means,  varied  from  O-QI  of  an  inch  up  to 
50  inches.  The  source  was  a  heated  plate  of  copper  ;  of  the  total  radiation 
from  this  nearly  2  per  cent,  was  absorbed  by  a  film  of  olefiant  gas  -01  of  an 
inch  thick,  upwards  of  9  per  cent,  by  a  layer  of  the  same  gas  o-i  of  an  inch 
thick,  33  per  cent,  by  a  layer  2  inches  thick,  68  per  cent,  by  a  column  20 
inches  long,  and  77  per  cent,  by  a  column  rather  more  than  4  feet  long. 

440.  Absorptive  power  of  vapours.—  The  absorptive  power  of  olefiant 
gas  is  exceeded  by  that  of  several  vapours.  The  liquid  from  which  the 
vapours  were  to  be  produced  was  inclosed  in  a  small  flask,  which  could  be 
attached  with  a  stop-cock  to  the  exhausted  experimental  tube.  The  absorp- 
tion was  then  determined  after  admitting  the  vapours  into  the  tube  in 
quantities  measured  by  the  pressure  of  the  barometer  gauge  attached  to  the 
air-pump. 

The  following  table  shows  the  absorption  of  vapours  under  pressures 
varying  from  o-  1  to  I  -o  inch  of  mercury  :  — 


Absorption  under  pressure  in  inches  of  mercury 

O'l 

o'S 

I*O 

Bisulphide  of  carbon         .         . 

15 

47 

62 

Benzole     .         .         .         .         . 

66 

182 

267 

Chloroform       .         .         ,         . 

85 

182 

236 

Ether        .         .        V      '.  ,.     . 

300 

710 

870 

Alcohol     .         .         .         .         , 

325 

622 

Acetic  ether     .        .        , 

590 

980 

1195 

These  numbers  refer  to  the  absorption  of  a  whole  atmosphere  of  dry  air 
as  their  unit,  and  it  is  thus  seen  that  a  quantity  of  bisulphide  of  carbon 
vapour,  the  feeblest  absorbent  yet  examined,  which  only  exerts  a  pressure  of 
j1^  of  an  inch  of  mercury,  or  the  g~  of  an  atmosphere,  gave  fifteen  times  the 
absorption  of  an  entire  atmosphere  of  air ;  and  i  of  an  inch  of  acetic  ether 
590  times  as  much.  Comparing  air  at  a  pressure  of  cri  with  acetic  ether  of 
the  same  pressure,  the  absorption  of  the  latter  would  be  more  than  17-500 
times  as  great  as  that  of  the  former. 

Tyndall  found  that  the  odours  from  the  essential  oils  exercised  a  marked 
influence  on  radiant  heat.  Perfectly  dry  air  was  allowed  to  pass  through  a 
tube  containing  dried  paper  impregnated  with  various  essential  oils,  and 
then  admitted  into  the  experimental  tube.  Taking  the  absorption  of  dry  air 
as  unity,  the  following  were  the  numbers  respectively  obtained  for  air  scented 
with  various  oils  : — Patchouli  31,  otto  of  roses  37,  lavender  60,  thyme  68, 


-442]  Dynamic  Radiation  and  Absorption.  395 

rosemary  74,  cassia  109,  aniseed  372.  Thus  the  perfume  of  a  flower- 
bed absorbs  a  large  percentage  of  the  heat  of  low  refrangibility  emitted 
from  it. 

Ozone  prepared  by  electrolysing  water  was  also  found  to  have  a  remark- 
able absorptive  effect.  The  small  quantity  of  ozone  present  in  electrolytic 
oxygen  was  found  in  one  experiment  to  exercise  136  times  the  absorption  of 
the  entire  mass  of  the  oxygen  itself. 

But  the  most  important  results  are  those  which  follow  from  his  experi- 
ments on  the  behaviour  of  aqueous  vapour  to  radiant  heat.  The  experimental 
tube  was  filled  with  air,  dried  as  perfectly  as  possible,  and  the  absorption 
it  exercised  was  found  to  be  one  unit.  Exhausting  the  tube,  and  admitting 
the  ordinary  undried,  but  not  specially  moist,  air  from  the  laboratory,  the 
absorption  now  rose  to  72  units.  The  difference  between  dried  and  undried 
air  can  only  be  ascribed  to  the  aqueous  vapour  the  latter  contains.  Thus  on 
a  day  of  average  humidity  the  absorptive  effect  due  to  the  transparent  aqueous 
vapour  present  in  the  atmosphere  is  72  times  as  great  as  that  of  the  air 
itself,  though  in  quantity  the  latter  is  about  200  times  greater  than  the  former. 
Analogous  results  were  obtained  on  different  days,  and  with  specimens  of 
air  taken  from  various  localities.  When  air  which  had  been  specially  purified 
and  dried  was  allowed  to  pass  though  a  tube  filled  with  fragments  of  moistened 
glass  and  examined,  it  was  found  to  exert  an  absorption  90  times  that  of 
pure  air. 

In  some  other  experiments  Tyndall  suppressed  the  use  of  rock-salt  plates 
in  his  experimental  tube,  and  even  the  tube  itself,  and  yet  in  every  case  the 
results  were  such  as  to  show  the  great  power  which  aqueous  vapour  possesses 
as  an  absorbent  of  radiant  heat. 

The  absorptive  action  which  the  aqueous  vapour  in  the  atmosphere  exerts 
on  the  sun's  heat  has  been  established  by  a  series  of  actinometrical  observa- 
tions made  by  Soret  at  Geneva  and  on  the  summit  of  Mont  Blanc  ;  he  finds 
that  the  intensity  of  the  solar  heat  on  the  top  of  Mont  Blanc  is  f  of  that 
at  Geneva  ;  in  other  words,  that  of  the  heat  which  is  radiated  at  the  height 
of  Mont  Blanc,  about  \  is  absorbed  in  passing  through  a  vertical  layer  of 
the  atmosphere  14*436  feet  in  thickness.  The  same  observer  has  found  that 
with  virtually  equal  solar  heights  there  is  the  smallest  transmission  of  heat 
on  those  days  on  which  the  tension  of  aqueous  vapour  is  greatest ;  that  is, 
when  there  is  most  moisture  in  the  atmosphere. 

441.  Radiating-  power  of  gases. — Tyndall  also  examined  the  radiating 
power  of  gases.     A  red-hot  copper  ball  was  placed  so  that  the  current  of 
heated  air  which  rose  from  it  acted  on  one  face  of  a  thermo-pile  ;  this  action 
was  compensated  by  a  cube  of  hot  water  placed  in  front  of  the  opposite  face. 
On  then  allowing  a  current  of  dry  olefiant  gas  from  a  gasholder  to  stream 
through  a  ring  burner  over  the  heated  ball  and  thus  supplant  the  ascending 
current  of  hot  air,  it  was  found  that  the  gas  radiated  energetically.     By  com- 
paring in  this  manner  the  action  of  many  gases  it  was  discovered  that,  as  is 
the  case  with  solids,  those  gases  which  are  the  best  absorbers  are  also  those 
which  radiate  most  freely. 

442.  Dynamic  radiation  and  absorption. — A  gas  when  permitted  to 
enter  an  exhausted  tube  is  heated  in  consequence  of  the  collision  of  its  par- 
ticles against  the  sides  of  the  vessel ;  it  thus  becomes  a  source  of  heat,  which 


396  On  Heat.  [442- 

is  perfectly  capable  of  being  measured.  Tyndall  calls  this  dynamic  heating. 
In  like  manner,  when  a  tube  full  of  gas  or  vapour  is  rapidly  exhausted,  a 
chilling  takes  place  owing  to  the  loss  of  heat  in  the  production  of  motion  ; 
this  he  calls  dynamic  chilling  or  absorption. 

He  could  thus  determine  the  radiation  or  absorption  of  a  gas  without 
any  source  of  heat  external  to  the  gas  itself.  An  experimental  tube  was 
taken,  one  end  of  which  was  closed  with  a  polished  metal  plate,  and  the 
other  with  a  plate  of  rock  salt  ;  in  front  of  the  latter  was  the  face  of  the  pile. 
The  needle  being  at  zero,  and  the  tube  exhausted,  a  gas  was  allowed  quickly 
to  enter  until  the  tube  was  full,  the  effect  on  the  galvanometer  being  noted. 
This  being  only  a  transitory  effect,  the  needle  soon  returned  to  zero  ;  the 
tube  was  then  rapidly  pumped  out,  by  which  a  sudden  chilling  was  produced 
and  the  needle  exhibited  a  deflection  in  the  opposite  direction.  Comparing 
in  this  way  the  dynamic  heating  and  chilling  of  various  gases,  those  gases 
which  are  the  best  absorbers  were  also  found  to  be  the  best  radiators. 

Polished  metallic  surfaces  are,  as  we  have  seen  (427),  bad  radiators, 
but  radiate  freely  when  covered  with  varnish.  Tyndall  made  the  curious 
experiment  of  varnishing  a  metallic  surface  by  a  film  of  gas.  A  Leslie's 
cube  was  placed  with  its  polished  metal  side  in  front  of  the  pile,  and  its  effect 
neutralised  by  a  second  cube  placed  before  the  other  face  of  the  pile.  On 
allowing  a  stream  of  defiant  or  coal  gas  to  flow  from  a  gasholder  over  the 
metallic  face  of  the  first  cube,  a  copious  radiation  from  that  side  was  pro- 
duced as  long  as  the  flow  of  gas  continued.  Acting  on  the  principle  indi- 
cated in  the  foregoing  experiment,  Tyndall  determined  the  dynamic  radiation 
and  absorption  of  vapours.  The  experimental  tube  containing  a  vapour 
under  a  small  known  pressure,  air  was  allowed  to  enter  until  the  pressure 
inside  the  tube  was  the  same  as  that  of  the  atmosphere.  In  this  way  the 
entering  air,  by  its  impact  against  the  tube,  became  heated  ;  and  its  particles 
mixing  with  those  of  the  minute  quantity  of  vapour  present,  each  of  them 
became,  so  to  speak,  coated  with  a  layer  of  the  vapour.  The  entering  air 
was  in  this  case  a  source  of  heat,  just  as  in  the  above  experiments  the 
Leslie's  cube  was.  Here,  however,"  one  gas  varnished  another  ;  the  radia- 
tion and  subsequently  the  absorption  of  various  vapours  could  thus  be 
determined. 

It  was  found  that  vapours  differed  very  materially  in  their  power  of 
radiating  under  these  circumstances  ;  of  those  which  were  tried  bisulphide 
of  carbon  vapour  was  the  worst  and  boracic  ether  the  best  radiator.  And  in 
all  cases  those  which  were  the  best  absorbents  were  also  the  best  radiators. 

443.  Relation  of  absorption  to  molecular  state. — After  examining  the 
absorption  of  heat  by  vapours,  Tyndall  tried  the  same  substances  in  a  liquid 
form.  The  conditions  of  the  experiments  were  in  both  cases  the  same  ; 
the  source  of  heat  was  a  spiral  of  platinum  heated  to  redness  by  an  electric 
current  of  known  strength  ;  and  plates  of  rock  salt  were  invariably  employed 
to  contain  both  vapours  and  liquids.  Finally,  the  absorption  by  the  vapours 
was  re-measured  ;  in  this  case  introducing  into  the  experimental  tube,  not, 
as  before,  equal  quantities  of  vapour,  but  amounts  proportional  to  the 
density  of  the  liquid.  When  this  last  condition  had  been  attained,  it  was 
found  that  the  order  of  absorption  by  a  series  of  liquids,  and  by  the  same 
series  when  turned  into  vapour,  was  precisely  the  same.  Thus  the  sub- 


-443]  Relation  of  Absorption  to  Molecular  State.  397 

stances  tried  stood  in  the  following  order  as  liquid  and  as  vapour,  beginning 
with  the  feeblest  absorbent,  and  ending  with]the  most  powerful  : — 

Liquids  Vapours 

Bisulphide  of  carbon  .  '.  .".  "V  .  Bisulphide  of  carbon. 

Chloroform      %.  .  '   .         ....  Chloroform. 

Iodide  of  ethyl  .  '  \  '    ".'       '.  .  Iodide  of  ethyl. 

Benzole      .         .  .'  V  ;,    .,  ,'  Benzole. 

Ether          ..        .  ..  ..'        .  .  Ether. 

Alcohol      .   '     .  .  '    .      '   .  .  Alcohol. 
Water. 

A  direct  determination  of  aqueous  vapour  could  not  be  made,  on  account 
of  its  low  tension,  and  the  hygroscopic  nature  of  the  rock  salt.  But  the  unde- 
viating  regularity  of  the  absorption  by  all  the  other  substances  in  the  list, 
both  as  liquid  and  vapour,  establishes  the  fact,  which  is  corroborated  by 
the  experiments  already  mentioned,  that  aqueous  vapour  is  one  of  the  most 
energetic  absorbents  of  heat. 

In  this  table  it  will  be  noticed  that  those  substances.j&l«eh— h£ve  the 
simplest  chemical  constitution  stand  first  in  the  list,  with  one  anomalous 
exception,  namely  that  of  water.  In  the  absorption  of  heat  by  gases,  Tyndall 
found  that  the  elementary  gases  were  the  feeblest  absorbents,  while  the 
gases  of  most  complex  constitution  were  the  most  powerful  absorbents.  Thus 
it  may  be  inferred  that  absorption  is  mainly  dependent  on  chemical  consti- 
tution ;  that  is  to  say,  that  absorption  and  radiation  are  molecular  acts 
independent  of  the  physical  condition  of  the  body. 

But  this  conclusion  seemed  to  be  contradicted  by  the  experiments  of 
Masson  and  Courtepee  on  powders.  Tyndall  repeated  these  experiments, 
avoiding  certain  sources  of  error  into  which  they  had  fallen,  and  discovered 
that  the  radiation  of  powders  is  similar  to  that  of  the  solids  from  which 
they  were  derived,  and  therefore  differs  greatly  inter  se.  The  absorbent 
power  of  powders  was  also  found  to  correspond  with  their  radiative  power — 
as  we  have  shown  to  be  the  case  with  solids  and  gases,  and,  though  as  yet 
we  have  no  experiments  on  the  subject,  is  doubtless  also  true  for  liquids. 
The  powders  were  attached  to  the  tin  surfaces  of  a  Leslie's  cube,  in  such  a 
manner  that  radiation  took  place  from  the  surface  of  the  powder  alone.  The 
following  table  gives  the  radiation  in  units  from  some  of  the  powders  ex- 
amined by  Tyndall  ;  the  metal  surface  of  the  cube  giving  a  deflection  of  15 
units  :— 

Radiation  from  powders. 

Rock  salt        it  :•••»-;•;       .     35-3  Sulphate  of  calcium  .  777 

Biniodide  of  mercury      .     397  Red  oxide  of  iron     .  .  78-4 

Sulphur  ....     40-6  Hydrated  oxide  of  zinc  .  80-4 

Carbonate  of  calcium      .     70*2  Sulphide  of  iron       .  .  817 

Red  oxide  of  lead    .         .74*0  Lampblack      .         .  .  84*0 

These  substances  are  of  various  colours.  Some  are  white,  such  as  rock 
salt,  carbonate  and  sulphate  of  calcium,  and  hydrated  oxide  of  zinc  ;  some 
are  red,  such  as  biniodide  of  mercury  and  oxide  of  lead  ;  whilst  others  are 
black,  as  sulphide  of  iron  and  lampblack  ;  we  have  besides  other  colours. 


398  On  Heat.  [443- 

The  colours,  therefore,  have  no  influence  on  the  radiating  power  :  rock  salt, 
for  example,  is  the  feeblest  radiator,  and  hydrated  oxide  of  zinc  one  of  the 
most  powerful  radiators. 

Nearly  a  century  ago  Franklin  made  experiments  on  coloured  pieces  of 
cloth,  and  found  their  absorption,  indicated  by  their  sinking  into  snow  on 
which  they  were  placed,  to  increase  with  the  darkness  of  the  colour.  But 
all  the  cloths  were  equally  powerful  absorbents  of  obscure  heat,  and  the 
effects  noticed  were  only  produced  by  their  relative  absorptions  of  light.  In 
fact,  the  conclusions  to  be  drawn  from  Franklin's  experiment  only  hold  good 
for  luminous  heat,  especially  sunlight,  such  as  he  employed. 

444.  Applications. — The  properties  which  bodies  possess  of  absorbing, 
emitting,  and  reflecting  heat  meet  with  numerous  applications  in  domestic 
economy  and  in  the  arts.  Leslie  stated  in  a  general  manner  that  white 
bodies  reflect  heat  very  well,  and  absorb  very  little,  and  the  contrary  is 
the  case  with  black  substances.  As  we  have  seen,  this  principle  is  not 
generally  true,  as  Leslie  supposed  ;  for  example,  white  lead  has  as  great  an 
absorbing  power  for  non-luminous  rays  as  lampblack  (437).  Leslie's  principle 
applies  to  powerful  absorbents  like  cloth,  cotton,  wool,  and  other  organic 
substances  when  exposed  to  luminous  heat.  Accordingly,  the  most  suitable 
coloured  clothing  for  summer  is  just  that  which  experience  has  taught  us  to 
use,  namely,  white,  for  it  absorbs  less  of  the  sun's  rays  than  black  clothing, 
and  hence  feels  cooler. 

The  polished  fire-irons  before  a  fire  are  cold,  whilst  the  black  fender  is 
often  unbearably  hot.  If,  on  the  contrary,  a  liquid  is  to  be  kept  hot  as  long 
as  possible,  it  must  be  placed  in  a  brightly  polished  metallic  vessel,  for 
then,  the  emissive  power  being  less,  the  cooling  is  slower.  Hence  it  is 
advantageous  that  .the  steam  pipes,  &c.,  of  locomotives  should  be  kept 
bright.  In  the  Alps,  the  mountaineers  accelerate  the  fusion  of  the  snow  by 
covering  it  with  earth,  which  increases  the  absorbing  power. 

In  our  dwellings,  the  outsides  of  stoves  and  of  hot-water  apparatus 
ought  to  be  black,  and  the  insides  of  fireplaces  ought  to  be  lined  with  fire- 
brick, in  order  to  increase  the  radiating  power  towards  the  apartment. 

It  is  in  consequence  of  the  great  diathermaneity  of  dry  atmospheric  air 
that  the  higher  regions  of  the  atmosphere  are  so  cold,  notwithstanding  the 
great  heat  which  traverses  them  ;  whilst  the  intense  heat  of  the  sun's  direct 
rays  on  high  mountains  is  probably  due  to  the  comparative  absence  of 
aqueous  vapour  at  these  elevations. 

As  nearly  all  the  luminous  rays  of  the  sun  pass  through  water,  and  the 
sun's  radiation  as  we  receive  it  on  the  surface  of  the  earth  consists  of  a 
large  proportion  of  luminous  rays,  accidents  have  often  arisen  from  the  con- 
vergence of  these  luminous  rays  by  bottles  of  water  which  act  as  lenses.  In 
this  way  gunpowder  could  be  fired  by  the  heat  of  the  sun's  rays  concen- 
trated by  a  water  lens  ;  and  the  drops  of  water  on  leaves  in  greenhouses 
have,  it  is  said,  been  found  to  act  as  lenses,  and  burn  the  leaves  on  which 
they  rest. 

Certain  bodies  can  be  used  (436)  to  separate  the  heat  and  light  radiated 
from  the  same  source.  Rock  salt  covered  with  lampblack,  or  still  better 
with  iodine,  transmits  heat,  but  completely  stops  light.  On  the  other  hand 
alum,  either  as  a  plate  or  in  solution,  or  a  thin  layer  of  water,  is  permeable 


-445]     Attraction  and  Repulsion  arising  from  Radiation.        399 

to  light,  but  stops  all  the  heat  from  obscure  sources.  This  property  is  made 
use  of  in  apparatus  which  are  illuminated  by  the  sun's  rays,  in  order  to  sift 
the  rays  of  their  heating  power;  and  a  vessel  full  of  water,  or  a  solution  of 
alum,  is  used  with  the  electric  light  when  it  is  desirable  to  avoid  too  intense 
a  heat. 

In  gardens,  the  use  of  shades  to  protect  plants  depends  partly  on  the 
diathermancy  of  glass  for  heat  from  luminous  rays  and  its  athermancy  for 
obscure  rays.  The  heat  which  radiates  from  the  sun  is  largely  of  the  former 
quality,  but  by  contact  with  the  earth  it  is  changed  into  obscure  heat,  which, 
as  such,  cannot  retraverse  the  glass.  This  explains  the  manner  in  which 
greenhouses  accumulate  their  warmth,  and  also  the  great  heat  experienced 
in  summer  in  rooms  having  glass  roofs,  for  the  glass  in  both  cases  acts,  as 
it  were,  as  a  valve  which  effectually  entraps  the  solar  rays.  On  the  same 
principle  plates  of  glass  are  frequently  used  as  screens  to  protect  us  from  the 
heat  of  a  fire  ;  the  glass  allows  us  to  see  the  cheerful  light  of  the  fire,  but 
intercepts  the  larger  part  of  the  heat  radiated  from  the  fire.  Though  the 
screens  thus  become  warm  by  the  heat  they  have  absorbed,  yet,  as  they 
radiate  this  heat  in  all  directions  towards  the  fire  as  well  as  towards  us,  we 
finally  receive  less  heat  when  they  are  interposed. 

445.  Attraction  and  repulsion  arising:  from  radiation. — Crookes  has 
discovered  a  highly  remarkable  class  of  phenomena  which  are  due  to  the 
radiant  action  of  heated  and  of  luminous  bodies.  These  phenomena  are 
most  conveniently  illustrated  by  means  of  an  instrument  which  he  has 
devised  and  which  is  called  the  radiometer,  the  construction  of  which  is  as 
follows  : — A  glass  tube  (fig.  372),  with  a  bulb  blown  on  it,  is  fused  at  the 
bottom  to  a  glass  tube  which  at  one  end  serves  to  rest  the  whole  ^apparatus 
in  a  wooden  support.  In  the  other  end  is  fused  a  fine  steel  point.  On  this 
rests  a  small  vane  or  fly,  consisting  of  four  arms  of  aluminium  wire  fixed  at 
one  end  to  a  small  cap,  while  at  the  others  are  fixed  small  discs  or  lozenges 
of  thin  mica,  coated  on  one  side  with  lampblack.  The  weight  of  the  fly  is 
not  more  than  two  grains. 

In  order  to  keep  the  fly  on  the  pivot  a  tube  is  fused  in  the  upper  part  of 
the  bulb  which  reaches  down  to  and  just  surrounds  the  top  of  the  cap,  with- 
out, however,  touching  it  ;  the  other  end  of  this  tube  is  drawn  out  and  con- 
nected with  an  arrangement  for  exhausting  the  air  by  the  Sprengel  pump 
(205)  or  by  chemical  means  ;  when  the  desired  degree  of  exhaustion  has  been 
attained  this  can  be  sealed.  By  keeping  the  apparatus  during  exhaustion  in 
a  hot  air  bath  at  a  temperature  of  300°,  the  gases  occluded  on  the  inner  surface 
of  the  glass,  and  by  the  vanes,  are  got  rid  of. 

If  a  source  of  light  or  of  heat,  a  candle  for  instance,  is  brought  near  the 
fly,  it  is  attracted,  and  the  fly  rotates  slowly  in  a  direction  showing  that  the 
blackened  side  moves  towards  the  light;  this  movement,  indicating  an 
attraction,  depends  on  a  certain  state  of  rarefaction.  If,  however,  the  appa- 
ratus be  connected  with  an  arrangement  which  allows  the  pressure  to  be 
varied,  this  rotation  gradually  diminishes  in  rapidity,  as  the  air  within  is 
further  rarefied,  until  a  certain  point  is  reached  at  which  it  ceases.  If 
now  the  rarefaction  is  pushed  further,  the  highly  remarkable  phenomenon 
is  observed  that  repulsion  succeeds  to  attraction,  and  that  the  fly  now  rotates 
in  the  direction  of  the  blackened  sides  away  from  the  source  of  heat.  In 


400 


On  Heat. 


[445- 


a  double  radiometer,  in  which  two  flys  are  pivoted  independently  one  over 
the  other,  having  their  blackened  sides  opposite  each  other,  the  flys  rotate 

in  opposite  directions  on  the  approach 
of  a  lighted  candle.  When  a  cold  body, 
such  as  a  piece  of  ice,  is  brought  near, 
instead  of  a  hot  one,  exactly  the  opposite 
effects  are  observed ;  when  the  vessel 
contains  air  the  pith  ball  is  repelled,  the 
neutral  point  is  observed,  and  at  high 
degrees  of  rarefaction  attraction  ensues. 

One  of  the  most  important  facts 
brought  to  light  by  these  experiments 
is,  that  what  has  hitherto  been  looked 
upon  as  a  complete  vacuum  is  not  so 
in  reality  ;  the  most  perfect  vacuum  ob- 
tainable still  contains  a  certain  residue 
of  gas,  as  has  been  proved  by  the  ex- 
periments of  Crookes  and  others,  among 
whom  that  of  Kundt  may  be  mentioned. 
The  latter  placed  on  the  vanes  a  light 
disc  of  mica,  and  at  a  little  distance 
above  it  a  similar  disc  was  arranged  so 
as  to  rotate  freely,  in  a  horizontal  plane 
independently  of  the  first.  When  the 
lower  vane  was  made  to  rotate  by  bring- 
ing a  light  near,  it  was  found  that  the 
upper  disc  was  also  put  in  rotation  in  the 
same  direction,  being  dragged  by  the 
viscosity  of  the  residual  air.  Accordingly 
the  explanation  of  the  phenomena  of  the 
radiometer  must  take  into  account  the 
existence  of  this  gaseous  residue. 

The  nature  of  the  gas  seems  to  have 
no  special  influence  on  the  pheno- 
mena ;  whether  the  vacuum  be  one  of 
hydrogen,  of  aqueous  vapour,  or  of 
iodine  vapour,  seems  immaterial ;  though 
with  hydrogen  the  exhaustion  need  not 
be  pushed  so  far  as  with  air.  The  repulsion  takes  place  with  all  the  rays 
of  the  spectrum,  the  intensity  diminishing  from  the  ultra  red  to  the  ultra 
violet.  When  the  chemical  rays  act,  the  interposition  of  a  plate  of  alum  has 
no  effect,  while  a  solution  of  iodine  in  bisulphide  of  carbon  diminishes  the 
repulsion.  The  rate  at  which  the  vane  rotates  depends  on  the  intensity  of 
the  source  of  light.  With  a  strong  light  the  rotation  is  so  rapid  that  its  rate 
cannot  be  determined.  With  two  candles  at  the  same  distance  the  rotation 
is  twice  as  rapid  as  with  one.  Two  sources  of  light  which,  successively  placed 
at  the  same  distance,  produce  the  same  rate  of  rotation,  are  equal  in  inten- 
sity. If,  when  placed  at  different  distances,  they  produce  the  same  speed 
of  rotation,  their  intensities  are  directly  as  the  squares  of  these  distances  from 


Fig.  372. 


-445]     Attraction  and  Repulsion -arising  from  Radiation.        401 

the  radiometer.  On  this  is  based  the  use  of  the  instrument  as  a  photometer 
(509)  for  comparing  together  various  sources  of  artificial  light.  It  may  likewise 
be  used  for  making  comparative  measurements  of  the  intensity  of  sunlight, 
and  the  distribution  of  heat  in  the  solar  spectrum  may  be  investigated  by  its 
means. 

It  is  not  difficult  to  understand  that  the  attraction  observed  in  the  experi- 
ments, as  long  as  the  apparatus  still  contains  air,  may  be  explained  by  the 
action  of  convection  currents.  For  heat  falling  upon  this  blackened  disc 
would  raise  its  temperature,  and  the  temperature  of  a  layer  of  air  in  im- 
mediate contact  with  the  disc  would  be  raised  too  ;  it  would  expand  and 
rise,  flowing  over  into  the  space  behind  the  disc,  and  would  thus  increase  the 
pressure  there. 

On  the  other  hand  the  repulsion  observed  at  the  higher  degrees  of  ex- 
haustion, approaching  a  vacuum,  is  explained  by  reference  to  the  modern 
views  as  to  the  constitution  of  gases,  of  which  it  is  at  once  an  illustration 
and  a  proof. 

The  general  nature  of  this  theory  is  that  a  gas  is  an  assemblage  of  in- 
dependent molecules,  which  are  perfectly  elastic,  and  which  move  with  great 
rapidity ;  their  impacts  against  the  sides  of  the  vessel  in  which  the  gas  is 
contained  are  the  cause  of  the  pressure.  The  impact  of  the  molecules 
against  each  other  is  the  mechanism  by  which  the  equal  transmission  of 
pressure  in  gases  is  effected  (294). 

Crookes  has  calculated  that  the  mechanical  effect  of  the  force  of  repulsion 
iis  equal  to  about  the  ^  of  a  milligramme  on  a  square  centimetre,  and  Stoney 
has  shown  that  this  force  is  sufficient  to  account  for  the  effects  observed,  by 
reference  to  admitted  principles  of  the  mechanical  theory  of  gases. 

The  rays  of  heat  pass  through  the  thin  glass  without  raising  its  tempera- 
ture, and,  falling  on  the  blackened  side  of  the  vane,  are  absorbed  by  it ;  the 
consequence  of  this  is,  that  it  will  become  slightly  hotter.  The  layer  of  ex- 
tremely rarefied  air  in  immediate  contact  with  the  blackened  disc  will  also 
become  somewhat  hotter,  and  the  molecules  will  fly  from  the  disc  with 
greater  velocity.  Under  ordinary  pressures  or  even  at  moderate  degrees  of 
rarefaction  these  more  rapid  motions  would  be  equalised  by  their  impacts 
.against  other  molecules,  and  a  uniformity  of  pressure — lhat  is,  of  temperature 
— would  be  established.  But  the  frequency  of  these  intramolecular  shocks 
•  diminishes  rapidly  with  the  increase  of  rarefaction  ;  and  the  consequence  is, 
that  a  great  number  of  molecules,  after  having  been  heated  by  contact  with 
-the  blackened  side  of  the  palette,  will  strike  against  the  cold  glass.  The  effect 
of  this  will  be  to  cool  these  molecules — that  is,  to  diminish  their  velocity  ;  it 
will  be  chiefly  molecules  of  this  kind  which  fall  on  the  back  of  the  disc,  and 
on  the  regions  behind  it.  An  excess  of  force  equal  and  opposite  to  that  on 
the  glass  acts  against  the  front  of  the  disc,  and  is  sufficient  to  account  for 
-the  phenomena  exhibited  by  Crookes. 

It  follows  from  this  explanation  that,  other  things  being  equal,  a  fly  will 
rotate  more  rapidly  in  a  small  than  in  a  large  bulb.  This  has  been  con- 
clusively proved  by  Crookes,  who  constructed  a  double-bulb  radiometer,  the 
two  bulbs  being  very  different  in  size,  and  so  connected  that,  by  dexterous 
.manipulation,  the  fly  could  be  transferred  from  the  pivot  of  the  one  to  that 
.of  the  other  bulb. 

D  D 


402  On  Heat.  [445- 

The  radiometer  is  well  adapted  for  the  lecture  demonstration  of  many 
phenomena  in  heat.  Thus  the  law  of  the  inverse  square  (414)  may  be  illustrated 
by  counting  the  number  of  rotations  when  the  instrument  is  placed  at  varying 
distances  from  the  source  of  heat. 

446.  Internal  friction  or  viscosity  of  gases.— In  some  recent  experi- 
ments in  connection  with  the  radiometer,  Crookes  used  an  arrangement  con- 
sisting of  a  long  but  light  arm  of  straw  suspended  by  a  delicate  glass  fibre 
in  a  sort  of  T  tube  turned  upside  down ;  in  this  way  even  a  greater  degree 
of  delicacy  was  obtained  than  with  the  radiometer.  Thus  he  was  able  to 
get  a  deflection  by  moonlight,  which  does  not  move  the  fly  of  the  radiometer. 
He  examined  the  internal  friction  or  viscosity  of  the  residual  gas  by  causing 
the  arm  to  oscillate,  and  then  observing  the  rate  at  which  the  oscillations 
diminish  under  various  pressures.  He  thus  found  that  from  ordinary  pres- 
sures down  to  a  pressure  of  0-19  mm.,  or  what  may  be  called  a  Torricellian 
vacuum,  the  viscosity  is  practically  constant,  only  diminishing  from  0*126  to 
0-112.  It  now  begins  to  fall  off,  and  at  a  pressure  of  0*000076 mm.  it  has 
diminished  to  cvoi,  or  about  ^  •  Simultaneously  with  this  decrease  in 
viscosity  the  force  of  repulsion  excited  by  a  standard  light  on  a  blackened 
surface  varies.  It  increases  as  the  pressure  diminishes  until  the  exhaus- 
tion is  about  0-05  mm.,  and  attains  its  maximum  at  about  0-03  mm.  It  then 
sinks  very  rapidly  until  it  is  at  0*000076  mm.,  when  it  is  less  than  ^  of  its 
maximum. 

The  viscosity  varies  in  different  gases  ;  it  is  considerably  less  in  hydrogen 
than  in  air  ;  and  hence  it  is  not  necessary  to  drive  the  exhaustion  so  far  to 
produce  a  considerable  degree  of  repulsion. 

The  researches  of  Crookes  have  opened  the  way  to  an  entirely  new  field 
of  experimental  inquiry  into  the  phenomena  which  occur  in  what  is  called 
the  ultra-gaseous  state  of  matter,  or  that  in  which  the  rarefaction  of  gases  is 
pushed  to  its  utmost  limits.  The  state  in  which  molecular,  as  distinguished 
from  molar,  actions  come  into  play,  has  been  aptly  termed  Crookes's  'vacuum. 
A  further  account  of  the  researches  requires  too  great  an  amount  of  detail 
for  the  purposes  of  this  work  ;  and  it  must  also  be  added  that  the  explana- 
tions which  have  been  given  are  still  not  beyond  the  range  of  controversy. 

446(2.  Relation  of  radiant  heat  to  sound. — This  subject  has  of  late 
engaged  the  attention  of  several  physicists,  among  whom  may  be  particular- 
ised Bell  and  Tainter,  Tyndall,  Preece,  and  Mercadier.  A  convenient  way 
of  showing  the  phenomena  is  by  means  of  an  apparatus  constructed  by 
Duboscq,  the  essential  features  of  which  are  represented  in  fig.  374.  It  is 
an  arrangement  by  which  an  intermittent  beam  of  radiant  heat  may  be  made 
to  act  on  various  bodies,  and  consists  of  a  disc  D  mounted  on  a  horizontal 
axis,  and  which,  by  means  of  the  multiplying  wheels  P  and  P',  may  be 
rotated  at  any  desired  speed.  In  the  disc  is  a  series  of  holes  the  numbers 
of  which  are  in  some  multiple  of  the  ratio  4:5:6:8.  This  apparatus  con- 
stitutes in  fact  a  syren  (242),  and  is  very  convenient  for  lecture  purposes. 
If,  while  the  disc  is  rotating  with  uniform  speed,  a  current  of  air  be  succes- 
sively directed  against  the  rows  of  holes  from  the  inside  to  the  outside,  we 
get  the  fundamental  note,  the  third,  the  fifth,  and  the  octave. 

On  the  stand  is  a  support  on  which  the  arrangement  o  may  be  fixed  in 
any  position  by  means  of  the  screw  s  ;  it  consists  of  a  screen  and  wide  tube 


-446a] 


Relation  of  Radiant  Heat  to  Sound. 


403 


behind  which  is  the  source  of  radiant  heat,  not  represented  in  the  figure. 
To  this  support  may  be  fitted  a  double  convex  lens,  if  the  rays  are  to  be 
concentrated  on  one  line  of  holes,  or  a  cylindrical  lens  when  a  slice  of 
thermal  rays  is  to  be  used  ;  or  the  rays  may  be  concentrated  by  a  mirror,  to 
get  rid  of  the  effects  of  absorption  by  glass.  The  support  s  is  for  holding 
various  pieces  of  apparatus. 

Tyndall  found  that  when  a  flask  like  that  represented  in  fig.  373,  con- 
taining a  small  quantity  of  ether,  was  placed  so  that  the  intermittent  beam 
arising  from  a  lime-light  could  fall  on  it,  and  the  top  was  connected  with  a 
flexible  tube,  a  distinct  musical  note  was  heard  when  the  ear-trumpet  was 
held  to  the  ear.  Other  liquids  being  tried  it  was  found  that  those  which  his 
other  experiments  had  revealed  as  the  best  absorbers  of  heat  (440)  gave  the 
loudest  sounds.  The  vapour  was  the  operative  cause,  for  when  the  beam 
was  caused  to  strike  against  the  liquid  instead  of  against  the  vapour  no 
sound  was  heard  ;  this  was  also  the  case  when  the  rays  fell  on  a  rock  salt 
cell  filled  with  the  liquid.  The  pitch  of  the  note  depended  on  the  velocity 
of  rotation. 

Dry  air  gave  no  sound.,  but  air  containing  moisture  did  so  ;  and  the 
more  moisture  was  present  the  louder  was  the  sound.  Other  gases  gave 
sounds  in  the  order  of  their  absorption  for  heat ;  and,  indeed,  all  Tyndall's 
results  in  this  direction  are  most  strikingly  confirmed. 

The  investigations  of  the  other  experimenters,  Preece,  Bell  and  Tainter, 
and  Mercadier,  were  chiefly  directed  to  the  effects  produced  when  the 
intermittent  beam  is  allowed  to  fall  on  solid  bodies.  A  sort  of  an  acoustic 


Fig.  375- 


Fig.  373- 


Fig.  374- 

trumpet  (fig.  375)  was  used  by  Mercadier,  consisting  of  a  movable  piece  ab 
fitting  over  cd  so  that  plates  L  of  various  materials  could  be  experimented 

D  D  2 


404  On  Heat.  [446a- 

upon.     The  other  end/ is  fitted  with  a  flexible  tube  and  bell  so  that  it  could 
be  applied  to  the  ear. 

When  the  intermittent  beam  is  allowed  to  act  on  this  plate  it  is  set  in 
vibration  and  a  sound  is  produced.  This  is  not  due  at  any  rate  mainly  to 
transverse  vibrations  of  the  plate,  for  neither  the  pitch  nor  quality  of  the  note 
was  altered  when  the  thickness  and  nature  of  the  plate  was  changed  (282) 
nor  was  it  altered  when  the  plate  was  slit.  The  best  effects  were  obtained 
when  the  diaphragm  was  of  thin  metal  foil  coated  with  lampblack  on  the 
side  next  the  rays.  Marked  effects  were  also  obtained  when  a  transparent 
plate  was  used  blackened  on  the  side  away  from  the  rays.  The  effect  is  one 
of  radiant  heat,  and  is  essentially  due  to  alternate  expansions  and  contrac- 
tions of  the  layer  of  air  in  contact  with  the  surfaces  which  absorb  the  radiant 
heat.  The  phenomenon  may  be  very  simply  exhibited  by  blackening  hah 
the  inside  of  a  test  tube  R,  the  open  end  of  which  is  provided  with  a  flexible 
tube  which  can  be  placed  to  the  ear.  When  the  rays  fall  on  the  blackened 
part  a  loud  sound  is  heard,  but  very  little  when  the  bright  side  is  exposed. 
The  effect  is  also  obtained  when  a  blackened  piece  of  foil  is  placed  in  the 
tube. 


-448]  Specific  Heat.  405 


CHAPTER    IX. 

CALORIMETRY. 

447.  Calorimetry.       Thermal   unit. — The  object  of  calorimetry  is  to 
measure  the  quantity  of  heat  which  a  body  parts  with  or  absorbs,  when  its 
temperature  sinks  or  rises  through  a  certain  number  of  degrees,  or  when  it 
changes  its  condition. 

Quantities  of  heat  may  be  expressed  by  any  of  its  directly  measurable 
effects,  but  the  most  convenient  is  the  alteration  of  temperature,  and  quan- 
tities of  heat  are  usually  defined  by  stating  the  extent  to  which  they  are 
capable  of  raising  a  known  weight  of  a  known  substance,  such  as  water. 
The  unit  chosen  for  comparison,  and  called  the  thermal  unit,  is  not  every- 
where the  same.  In  France  it  is  the  quantity  of  heat  necessary  to  raise  the 
temperature  of  one  kilogramme  of  water  through  one  degree  Centigrade  ;  this 
is  called  a  calorie.  In  this  book  we  shall  adopt,  as  a  thermal  unit,  the 
quantity  of  heat  necessary  to  raise  one  pound  of  water  through  one  degree 
Centigrade  :  i  calorie  =  2-2  thermal  units,  and  one  thermal  unit  =  0-45  calorie. 

On  the  centimetre-gramme-second  system  of  units  the  heat  required  to 
raise  one  gramme  of  water  through  one  degree  is  taken  as  the  unit.  This  is 
called  the  gramme  degree  or  water  gramme  degree. 

448.  Specific  heat. — When  equal  weights  of  two  different  substances,  at 
the  same  temperature,  placed  in  similar  vessels,  are  subjected  for  the  same 
length  of  time  to  the  heat  of  the  same  lamp,  or  are  placed  at  the  same 
distance  in  front  of  the  same  fire,  it  is  found  that  their  temperatures  will  vary 
considerably  ;  thus  mercury  will  be  much  hotter  than  water.     But  as,  from 
the  conditions  of  the  experiment,  they  have  each  been  receiving  the  same 
amount  of  heat,  it  is  clear  that  the  quantity  of  heat  which  is  sufficient  to 
raise  the  temperature  of  mercury  through  a  certain  number  of  degrees,  will 
only  raise  the  temperature  of  the  same  quantity  of  water  through  a  less 
number  of  degrees  ;  in  other  words,  that  it  requires  more  heat  to  raise  the 
temperature  of  water  through  one  degree  than  it  does  to  raise  the  temperature 
of  mercury  by  the  same  extent.     Conversely,  if  the  same  quantities  of  water 
and  of  mercury  at  100°  C.  be  allowed  to  cool  down  to  the  temperature  of  the 
air,  the  water  will  require  a  much  longer  time  for  the  purpose  than  the 
mercury  ;  hence,   in  cooling  through  the  same   number  of  degrees,  water 
gives  out  more  heat  than  does  mercury. 

It  is  readily  seen  that  all  bodies  have  not  the  same  specific  heat.  If  a 
pound  of  mercury  at  100°  is  mixed  with  a  pound  of  water  at  zero,  the  tem- 
perature of  the  mixture  will  only  be  about  3°  ;  that  is  to  say,  that  while  the 
mercury  has  cooled  through  97°,  the  temperature  of  the  water  has  only  been 
raised  3°.  Consequently  the  same  weight  of  water  requires  about  32  times  as 
much  heat  as  mercury  does,  to  produce  the  same  elevation  of  temperature. 


406  On  Heat.  [448- 

If  similar  experiments  are  made  with  other  substances  it  will  be  found 
that  the  quantity  of  heat  required  to  effect  a  certain  change  of  temperature 
is  different  for  almost  every  substance,  and  we  speak  of  the  specific  heat,  or 
thermal  or  calorific  capacity  of  a  body  as  the  quantity  of  heat  which  it  absorbs 
when  its  temperature  rises  through  a  given  range  of  temperature,  from  zero 
to  i°  for  example,  compared  with  the  quantity  of  heat  which  would  be 
absorbed,  in  the  same  circumstances,  by  the  same  weight  of  water  ;  that  is, 
water  is  taken  as  the  standard  for  the  comparison  of  specific  heats.  Thus, 
to  say  that  the  specific  heat  of  lead  is  0-0314,  means  that  the  quantity  of 
heat  which  would  raise  the  temperature  of  any  given  weight  of  lead  through 
i°  C.  would  only  raise  the  temperature  of  the  same  weight  of  water  through 
0-0314°  C. 

Temperature  is  the  vis  viva  of  the  smallest  particles  of  a  body  ;  in 
bodies  of  the  same  temperature  the  atoms  have  the  same  vis  viva,  the 
smaller  mass  of  the  lighter  atoms  being  compensated  by  their  greater 
velocity.  The  heat  absorbed  by  a  body  not  only  raises  its  temperature — that 
is,  increases  the  vis  viva  of  the  progressive  motion  of  the  atoms— but  in  over- 
coming the  attraction  of  the  atoms  it  moves  them  further  apart,  and  along 
with  the  expansion  which  this  represents,  some  external  pressure  is  overcome. 
In  the  conception  of  specific  heat  is  included,  not  merely  that  amount  of  heat 
which  goes  to  raise  the  temperature,  but  also  that  necessary  for  the  internal 
work  of  expansion,  and  that  required  for  the  external  work.  If  these  latter 
could  be  separated,  we  should  get  the  true  heat  of  temperature,  that  which  is 
used  solely  in  increasing  the  vis  viva  of  the  atoms.  This  is  sometimes 
called  the  true  specific  heat. 

Three  methods  have  been  employed  for  determining  the  specific  heats  of 
bodies  :  (i.)  the  method  of  the  melting  of  ice,  (ii.)  the  method  of  mixtures, 
and  (iii.)  that  of  cooling.  In  the  latter,  the  specific  heat  of  a  body  is  deter- 
mined by  the  time  which  it  takes  to  cool  through  a  certain  temperature. 
Previous  to  describing  these  methods,  it  will  be  convenient  to  explain  the 
expression  for  the  quantity  of  heat  absorbed  or  given  out  by  a  body  of  known 
weight  and  specific  heat,  when  its  temperature  rises  or  falls  through  a  certain 
number  of  degrees. 

449.  Measure  of  the  sensible  heat  absorbed  by  a  body.— Let  m  be 
the  weight  of  a  body  in  pounds,  c  its  specific  heat,  and  /  its  temperature. 
The  quantity  of  heat  necessary  to  raise  a  pound  of  water  through  one  degree 
being  taken  as  unity,  m  of  these  units  would  be  required  to  raise  m  pounds 
of  water  through  one  degree,  and  to  raise  it  through  t  degrees,  t  times  as 
much,  or  mt.  As  this  is  the  quantity  of  heat  necessary  to  raise  through  / 
degrees  m  pounds  of  water,  whose  specific  heat  is  unity,  a  body  of  the  same 
weight,  only  of  different  specific  heat,  would  require  mtc.  Consequently, 
when  a  body  is  heated  through  /  degrees,  the  quantity  of  heat  which  it 
absorbs  is  the  product  of  its  weight,  into  the  range  of  temperature,  into  its 
specific  heat.  This  principle  is  the  basis  of  all  the  formulae  for  calculating 
specific  heats. 

If  a  body  is  heated  or  cooled  from  /  to  f  degrees,  the  heat  absorbed  or 
disengaged  will  be  represented  by  the  formula 

m(t'-£}c, 


-450] 


Method  of  the  Fusion  of  Ice. 


407 


450.  Method  of  the  fusion  of  ice. — This  method  of  determining  specific 
heats  is  based  on  the  fact  that  to  melt  a  pound  of  ice  80  thermal  units  are 
necessary,  or  more  exactly  79*25.     Black's  calorimeter  (fig.  376)  consists  of 
a  block  of  ice   in  which  a  cavity  is  made, 
and  which  is  provided  with  a  cover  of  ice. 
The  substance  whose  specific  heat  is  to  be 
determined  is  heated  to  a  certain  tempera- 
ture, and  is  then  placed  in  the  cavity,  which 
is  covered.     After  some  time  the  body  be- 
comes cooled  to  zero.    It  is  then  opened,  and 
both  the  substance  and  the  cavity  wiped  dry 
with   a   sponge  which  has  been  previously 
weighed.      The    increase  of  weight  of  this 
sponge  obviously  represents  the  ice  which 
has  been  converted  into  water. 

Now,  since  one  pound  of  ice  at  o°  in  melting  to  water  at  o°  absorbs  80 
thermal  units,  P  pounds  absorbs  80  P  units.  On  the  other  hand  this  quan- 
tity of  heat  is  equal  to  the  heat  given  out  by  the  body  in  cooling  from  /°  to 
zero,  which  is  mlc,  for  it  may  be  taken  for  granted  that  in  cooling  from  t°  to 
zero  a  body  gives  out  as  much  heat  as  it  absorbs  in  being  heated  from  zero 
to  t°.  Consequently  from 


mtc  =  80  P 


mt 


It  is  difficult  to  obtain  blocks  of  ice  as  large  and  pure  as  those  used  by 
Black  in  his  experiments,  and  Lavoisier  and  Laplace  replaced  the  block  of 
ice  by  a  more  complicated 
.  apparatus  which  is  called 
the  ice  calorimeter.  Fig. 
377  gives  a  perspective 
view  of  it,  and  fig.  378 
represents  a  section.  It 
consists  of  three  concen- 
tric tin  vessels  ;  in  the 
central  one  is  placed  the 
body  M,  whose  specific 
heat  is  to  be  determined, 
while  the  two  others  are 
filled  with  pounded  ice. 
The  ice  in  the  compart- 
ment A  is  melted  by  the 
heated  body,  while  the 
ice  in  the  compartment  B 
cuts  off  the  heating  influ-  Fig-  37?-  Fig  ^ 

ence   of  the  surrounding 

atmosphere.     The  two  stopcocks  E  and  D  give  issue  to  the  water  which 
arises  from  the  liquefaction  of  the  ice. 

In  order  to  find  the  specific  heat  of  a  body  by  this  apparatus,  its  weight, 
m,  is  first  determined ;  it  is  then  raised  to  a  given  temperature,  /,  by  keeping 


408 


On  Heat. 


[450- 


it  for  some  time  in  an  oil  or  water  bath,  or  in  a  current  of  steam.  Having 
been  quickly  brought  into  the  central  compartment,  the  lids  are  replaced 
and  covered  with  ice,  as  represented  in  the  figure.  The  water  which  flows 
out  by  the  stopcock  D  is  collected.  Its  weight,  P,  is  manifestly  that  of  the 
melted  ice.  The  calculation  is  then  made  as  in  the  preceding: 
case. 

There  are  many  objections  to  the  use  of  this  apparatus. 
From  its  size  it  requires  some  quantity  of  ice,  and  a  body,  M, 
of  large  mass  ;  while  the  experiment  lasts  a  considerable  time. 
A  certain  weight  of  the  melted  water  remains  adhering  to  the 
ice,  so  that  the  water  which  flows  out  from  D  does  not  exactly 
represent  the  weight  of  the  melted  ice. 

451.  Bunsen's  ice  calorimeter. — On  the  very  considerable 
diminution  of  volume  which  ice   experiences  on  passing  into- 
water  (347),  Bunsen  has  based  a  calorimeter  which  is  particu- 
larly suitable  when  only  small  quantities  of  a  substance  can 
be  used   in   determinations.     A   small   test   tube   a  (fig.    379) 
intended  to  receive  the  substance  experimented  upon  is  fused 
in    the   wider   tube    B.      The   part   ab   contains    pure   freshly 
boiled   distilled  water,  and  the  prolongation  of  this  tube  BC,, 
together   with   the   capillary   tube   d,    contains    pure   mercury. 
This  tube  d  is  firmly  fixed  to  the  end  of  the    tube    C  ;  it  is 
graduated,  and  the  value  of  each  division  of  the  graduation  is 
specially  determined  by  calibration.     When  the  apparatus  is 
immersed    in    a   freezing   mixture,    the   water   in    the   part   ab 
freezes.     Hence,  if  afterwards,  while  the  apparatus  is  protected 
against  the  excess  of  heat  from  without,  a  weighed  quantity  of 
a  substance  at  a  given  temperature  is  • 
introduced   into  the   tube,   it  imparts 
its  heat  to  this  in  sinking  to  zero.     In 
doing   so  it  melts  a  certain  quantity 
of  ice,  which  is  evidenced  by  a  cor- 
responding depression  of  the  mercury 
in   the  tube  d.     Thus  the  weight   of 
ice  melted,  together  with  the  weight 
and  original  temperature  of  the  sub- 
stance experimented  upon,  furnish  all 
the  data  for  calculating  the  specific 
heat. 

For  heating  the  substance  in  this, 
and  also  in  other  calorimetrical  ex- 
periments, the  apparatus  fig.  380  is 
well  adapted.  The  cylindrical  metal 
vessel  G  is  narrower  at  the  top,  and 
a  glass  test-tube  R  is  fitted  into  a 
cork  which  closes  G.  In  this  glass  tube, 
which  is  also  closed  by  a  cork  K,  the 
substance  is  placed  which  is  to  be  heated.  The  greater  part  of  the  vessel  is 
covered  by  a  thick  mantle  of  felt,  B.  The  water  in  the  vessel  is  boiled  the 


Fig-  379- 


Fig.  380. 


-453]  Corrections.  409 

steam  emerging  at  d,  until  the  substance  has  acquired  the  temperature  of 
boiling  water,  for  which  about  twenty  minutes  is  required.  The  mantle  and 
the  lamp  having  been  taken  away,  the  tube  R  is  rapidly  removed,  and  its 
contents  tipped  into  the  tube  a  of  the  calorimeter  (fig.  378). 

For  this  method  of  determining  specific  heat  a  new  determination  of  the 
latent  heat  of  ice  was  made,  and  was  found  to  be  80*025.  It  was  also  in  con- 
nection with  these  experiments  that  Bunsen  made  his  determination  of  the 
specific  gravity  of  ice,  which  he  found  to  be  in  the  mean  0-91674. 

By  the  above  method  Bunsen  determined  the  specific  heat  of  several  of 
the  rare  metals  for  which  a  weight  of  only  a  few  grains  could  be  used. 

452.  method  of  mixtures. — In  determining  the  specific  heat  of  a  solid 
body  by  this  method,  it  is  weighed  and  raised  to  a  known  temperature,  by 
keeping  it,  for  instance,  for  some  time  in  a  closed  place  heated  by  steam ; 
it  is  then  immersed  in  a  mass  of  cold  water,  the  weight  and  temperature  of 
which  are  known.     From  the  temperature  of  the  water  after  mixture  the 
specific  heat  of  the  body  is  determined. 

Let  M  be  the  weight  of  the  body,  T  its  temperature,  c  its  specific  heat ; 
and  let  m  be  the  weight  of  the  cold  water,  and  t  its  temperature. 

As  soon  as  the  heated  body  is  plunged  into  the  water,  the  temperature  of 
the  latter  rises  until  both  are  at  the  same  temperature.  Let  this  temperature 
be  6.  The  heated  body  has  been  cooled  by  T  —  6  ;  it  has,  therefore,  lost  a 
quantity  of  heat,  W  (T  -  6}c.  The  cooling  water  has,  on  the  contrary,  ab- 
sorbed a  quantity  of  heat  equal  to  m(B  —  t\  for  the  specific  heat  of  water  is 
unity.  Now  the  quantity  of  heat  given  out  by  the  body  is  manifestly  equal  to 
the  quantity  of  heat  absorbed  by  the  water  ;  that  is,  M(T  —  6}c  =  7n(6  —  /),  from 

which 

c==  m(6-t] 

An  example  will  illustrate  the  application  of  this  formula.  A  piece  of 
iron  weighing  60  ounces,  and  at  a  temperature  of  100°  C.,  is  immersed  in 
1 80  ounces  of  water,  whose  temperature  is  19°  C.  After  the  temperatures 
have  become  uniform,  that  of  the  cooling  water  is  found  to  be  22°  C.  What 
is  the  specific  heat  of  the  iron  ? 

Here  the  weight  of  the  heated  body,  M,  is  60,  the  temperature,  T,  is  100°, 
c  is  to  be  determined  ;  the  temperature  of  mixture,  6,  is  22°,  the  weight  of 
the  cooling  water  is  180,  and  its  temperature  12°.  Therefore 

180(22-19)  _  9 
~6o(ioo-22y-78  = 

453.  Corrections. — The  vessel  containing  the  cooling  water  is  usually 
a  small  cylinder  of  silver  or  brass,  with  thin  polished  sides,  and  is  supported 
by  some  badly  conducting  arrangement.     It  is  obvious  that  this  vessel,  which 
is  originally  at  the  temperature  of  the  cooling  water,  shares  its  increase  of 
temperature,  and  in  accurate  experiments  this  must  be  allowed  for.     The 
decrease  of  temperature  of  the   heated   body  is  equal  to  the  increase  of 
temperature  of  the  cooling  water,  and  of  the  vessel  in  which  it  is  contained. 
If  the  weight  of  this  latter  be  m',  and  its  specific  heat  <r',  its  temperature,  like 
that  of  the  water,  is  /  :  consequently  the  previous  equation  becomes 

<9)  =  m(6  -t}  +  m'c'(6  - 1} ; 


410  On  Heat.  [453- 

from  which,  by  obvious  transformations, 

=  (m  +  m'c'}  (6  -  t] 
~ 


,  Generally  speaking,  the  value  m'c'  is  put  =  /i  ;  that  is  to  say,  p.  is  the 
weight  of  water  which  would  absorb  the  same  quantity  of  heat  as  the  vessel. 
This  is  said  to  be  the  reduced  value  in  water  of  the  vessel,  or  the  water  equi- 
valent. This  expression  accordingly  becomes 


In  accurate  experiments  it  is  necessary  to  allow  also  for  the  heat  absorbed 
by  the  glass  and  mercury  of  the  thermometer,  by  introducing  into  the  equa- 
tion their  values  reduced  on  the  same  principle. 

In  order  to  allow  for  the  loss  of  heat  due  to  radiation,  a  preliminary  experi- 
ment is  made  with  the  body  whose  specific  heat  is  sought,  the  only  object 
of  which  is  to  ascertain  approximately  the  increase  of  temperature  of  the 
cooling  water.  If  this  increase  be  10°,  for  example,  the  temperature  of  the 
water  is  reduced  by  half  this  number  —  that  is  to  say,  5°  below  the  tempera- 
ture of  the  atmosphere  —  and  the  experiment  is  then  carried  out  in  the 
ordinary  manner. 

By  this  method  of  compensation,  first  introduced  by  Rumford,  the  water 
receives  as  much  heat  from  the  atmosphere,  during  the  first  part  of  the  ex- 
periment, as  it  loses  by  radiation  during  the  second  part. 

454-  Regnault's  apparatus  for  determining1  specific  heats.  —  Fig.  381 
represents  one  of  the  forms  of  apparatus  used  by  Regnault  in  determining 
specific  heats  during  the  method  of  mixtures. 

The  principal  part  is  a  water  bath,  AA,  of  which  fig.  382  represents  a 
section.  It  consists  of  three  concentric  compartments  ;  in  the  central  one 
there  is  a  small  basket  of  brass  wire,  c,  containing  fragments  of  the  substance 
whose  specific  heat  is  to  be  determined,  in  the  middle  of  which  is  placed  a 
thermometer,  T.  The  second  compartment  is  heated  by  a  current  of  steam 
coming  through  the  tube,  e,  from  a  boiler  B,  and  passing  into  a  worm,  a. 
where  it  is  condensed.  The  third  compartment,  zY,  is  an  air  chamber,  to 
hinder  the  loss  of  heat.  The  water  bath,  AA,  rests  on  a  chamber,  K,  with 
double  sides,  EE,  forming  a  jacket,  which  is  kept  full  of  cold  water,  in  order 
to  exclude  the  heat  from  AA,  and  from  the  boiler,  B.  The  central  compart- 
ment of  the  water  bath  is  closed  by  a  damper,  r,  which  can  be  opened  at 
pleasure,  so  that  the  basket,  c,  can  be  lowered  into  the  chamber,  K. 

On  the  left  of  the  figure  is  represented  a  small  and  very  thin  brass  vessel, 
D,  suspended  by  silk  threads  on  a  small  carriage,  which  can  be  moved  out 
of,  or  into,  the  chamber,  K.  This  vessel,  which  serves  as  a  calorimeter,  con- 
tains water,  in  which  is  immersed  a  thermometer,  /.  Another  thermometer 
at  the  side,  t\  gives  the  temperature  of  the  air. 

When  the  thermometer  T  shows  that  the  temperature  of  the  substance 
in  the  bath  is  stationary,  the  screen,  h,  is  raised,  and  the  vessel,  D,  moved  to 
just  below  the  central  compartment  of  the  water  bath.  The  damper,  r,  is 
then  -withdrawn,  and  the  basket,  c,  and  its  contents  are  lowered  into  the  water 
in  the  vessel,  D,  the  thermometer,  T,  remaining  fixed  in  the  cork.  The 


-454] 


Apparatus  for  Determining  Specific  Heats. 


411 


carriage  and  the  vessel,  D,  are  then  moved  out,  and  the  water  agitated  until 
the  thermometer,  T,  becomes  stationary.  The  temperature  which  it  indicates 
is  6.  This  temperature  known,  the  rest  of  the  calculation  is  made  in  the 
manner  described  in  art.  449,  care  being  taken  to  make  all  the  necessary 
corrections. 

In  determining  the  specific  heat  of  substances — phosphorus,  for  instance 
— which  could  not  be  heated  without  causing  them  to  melt,  or  undergo  some 
change  which  would  interfere  with  the  accuracy  of  the  result,  Regnault 
adopted  an  inverse  process  :  he  cooled  them  down  to  a  temperature  con- 
siderably below  that  of  the  water  in  the  calorimeter,  and  then  observed  the 
diminution  in  the  temperature  of  the  latter,  which  resulted  from  immersing 
the  cooled  substance  in  it. 

In  determining  the  specific  heat  of  substances,  which,  like  potassium, 
would  decompose  water,  some  other  liquid,  such  as  turpentine  or  benzole, 


Fig.  381. 

must  be  used.  These  liquids  have  the  additional  advantage  of  having  a 
lower  specific  heat  than  water,  which  has  the  highest  of  any  liquid,  so  that 
an  error  in  determining  the  temperature  of  the  cooling  liquid  has  a  less 
influence  on  the  value  of  the  specific  heat.  With  this  view  use  has  been 
made  of  mercury,  the  specific  heat  of  A^hich  is  only  one-thirtieth  that  of 
water. 


412  On  Heat.  [455- 

455.  Method    of    cooling-. — Equal   weights  of  different   bodies   whose 
specific  heats  are  different,  will  occupy  different  times  in  cooling  through 
the  same  number  of  degrees.     Dulong  and  Petit  applied  this  principle  in 
determining  the  specific  heats  of  bodies  in  the  following  manner  :— A  small 
polished  silver  vessel  is  filled  with  the  substance  in  a  state  of  fine  powder, 
and  a  thermometer  placed  in  the  powder,  which  is  pressed  down.     This 
vessel  is  heated  to  a  certain  temperature,  and  is  then   introduced   into   a 
copper  vessel,  in  which  it  fits  hermetically.     This  copper  vessel  is  exhausted, 
and  maintained  at  the  constant  temperature  of  melting  ice,  and  the  time 
noted  which  the  substance  takes  in  falling  through  a  given  range  of  tem- 
perature, from  15°  to  5°  for  example.     The  times  which  equal  weights  of  dif- 
ferent bodies  require  for  cooling,  through  the  same  range  of  temperature,  are 
directly  as  their  specific  heats. 

Regnault  has  proved  that  with  solids  this  method  does  not  give  trust- 
worthy results  ;  it  assumes,  which  is  not  quite  the  case,  that  the  cooling  in 
all  parts  is  equal,  and  that  all  substances  part  with  their  heat  to  the  silver 
case  with  equal  facility.  The  method  may,  however,  be  employed  with 
success  in  the  determination  of  the  specific  heat  of  liquids. 

In  an  investigation  of  the  specific  heats  of  various  soils,  Pfaundler  found 
that  a  soil  of  low  specific  heat  heats  and  cools  rapidly,  while  earth  of  higher 
specific  heat  undergoes  slow  heating  and  slow  cooling ;  that  moist  earths 
rich  in  humus  have  a  high  specific  heat,  amounting  in  the  case  of  turf  to  as 
much  as  0-5  ;  while  dry  soils  free  from  humus,  such  as  lime  and  sand,  have 
a  low  specific  heat,  not  more  than  about  0-2. 

456.  Specific  heat    of  liquids. — The  specific   heat  of  liquids  may  be 
determined  either  by  the  method  of  cooling,  by  that  of  mixtures,  or  by  that 
of  the  ice  calorimeter.     In  the  latter  case  they  are   contained  in  a  small 
metal  vessel,  or  a  glass  tube,  which  is  placed  in  the  central  compartment 
(fig.  382),  and  the  experiment  then  made  in  the  usual  manner. 

A  method  devised  by  Pfaundler  of  determining  the  specific  heat  of 
liquids,  which  under  certain  circumstances  is  advantageous,  depends  on  a 
property  of  the  electrical  current  of  heating  any  conductor  through  which 
it  passes. 

In  two  equal  calorimeters  containing  the  liquids  to  be  tested,  together 
with  suitable  thermometers  and  stirrers,  two  equal  spirals  of  fine  platinum 
wire  are  placed.  These  are  connected  with  a  voltaic  battery  by  means  of 
copper  wires,  and  if  the  same  current  of  electricity  be  simultaneously 
passed  through  each  of  them,  which  can  be  very  accurately  done,  the  heat 
produced  in  the  wires  will  be  equal,  and  the  rise  in  temperature  in  the 
liquids  will  then  be  inversely  as  the  specific  heats.  One  of  the  liquids  is 
usually  water. 

It  will  be  seen  from  the  table  in  the  following  article  that  water  and  oil  of 
turpentine  have  a  much  greater  specific  heat  than  other  substances,  and  more 
especially  than  the  metals.  It  is  from  its  great  specific  heat  that  water  re- 
quires a  long  time  in  being  heated  or  cooled,  and  that  for  the  same  weight 
and  temperature  it  absorbs  or  gives  out  far  more  heat  than  other  substances. 
This  double  property  is  applied  in  the  hot-water  apparatus,  of  which  we 
shall  presently  speak,  and  it  plays  a  most  important  part  in  the  economy  of 
nature. 


-457]  Specific  Heats  of  Bodies.  413 

457.  Specific  heats  of  bodies. — The  list  contained  in  the  next  article 
(458)  gives  the  specific  heats  of  a  great  number  of  elementary  substances. 
We  give  here  the  specific  heats  of  a  few  substances,  mostly  liquids  : — 

Specific  heat  Specific  heat 

Turpentine  .  >  "     .  0*426  Bisulphide  of  carbon  .  0-245 

Alcohol.  .  ;.  .  0-062  Thermometer  glass  .  0-198 

Ether     .  *  _.  .  0-516  Steel      .        .         .  '  .  0-118 

Glycerine  .  .  .  0-555  Brass     .         .  ',''    ". '/'  .  0-094 

The  specific  heat  of  water  is  commonly  taken  at  unity,  which  is  not 
strictly  correct.  According  to  the  most  recent  determinations  the  mean 
specific  heat  between  o°  and  /  is  expressed  by  the  formula  I  +  0-0001 5/. 

These  numbers,  as  well  as  the  numbers  in  (458),  represent  the  mean 
specific  heats  between  o°  and  100°.  It  was  shown  by  Dulong  and  Petit 
that  the  specific  heats  increase  with  the  temperature.  Those  of  the 
metals,  for  instance,  are  greater  between  100°  and  200°  than  between  o°  and 
100°,  and  are  still  greater  between  200°  and  300°  ;  that  is  to  say,  a  greater 
amount  of  heat  is  required  to  raise  a  body  from  200°  to  250°,  than  from  100° 
to  150°,  and  still  more  than  from  o°  to  50°.  For  silver,  the  mean  specific 
heat  between  o°  and  100°  is  0-057,  while  between  o°  and  200°  it  is  0-0611. 
The  following  table  gives  the  specific  heats  at  various  temperatures  : — 

Copper         <vro'«>          •          •          •          •      .   -.  0*0910  +  0-000046^ 

Zinc 0-0865  -f  o-oooo88/ 

Lead   ........  0*0286  +  o-oooo38/ 

Platinum     .         w:  ;  •<••;'•.    •     .         .  -       .  0-0317 +  0-0000062^ 
Water          .         .  :  -  ;•:••        .         .         ,rr       .  1+0-00030^ 

The  increase  of  specific  heat  with  the  temperature  is  greater  as  bodies 
are  nearer  their  fusing  point.  Any  action  which  increases  the  density  and 
molecular  aggregation  of  a  body,  diminishes  its  specific  heat.  The  specific 
heat  of  copper  is  diminished  by  its  being  hammered,  but  it  regains  its  original 
value  after  the  metal  has  been  again  heated. 

The  specific  heat  of  a  liquid  increases  with  the  temperature  much  more 
rapidly  than  that  of  a  solid.  Water  is,  however,  an  exception  :  its  specific 
heat  increases  less  rapidly  than  does  that  of  solids. 

The  most  remarkable  examples  of  the  influence  of  temperature  on  the 
specific  heat  are  afforded  by  carbon,  boron,  and  silicon.  Weber  has  found 
that  at  6oou  the  specific  heat  of  carbon  is  7  times,  and  that  of  boron  2^  times 
as  great  as  their  respective  specific  heats  at  -  50°.  The  specific  heat  of 
diamond  is  0-0635  at  -  5°°>  0-1318  at  33°,  0-2218  at  140°,  and  0-3026  at  247°. 
Although  the  specific  heat  increases  thus  rapidly  between  —  50°  and  250° 
beyond  that  point  the  rate  of  increase  is  slower ;  and  beyond  600°,  or  at  an 
incipient  red  heat,  it  seems  to  be  pretty  constant,  or  at  any  rate  to  exhibit 
no  greater  variations  with  the  temperature  than  are  afforded  by  other  sub- 
stances. Thus  while  at  600°  the  specific  heat  is  0-441,  at  985°  it  is  0-459. 
Graphite  also  has  at  22°  the  specific  heat  0-168  ;  this  increases,  but  at  a 
gradually  diminishing  rate,  to  642°,  where  its  specific  heat  is  0-445.  Like 
diamond,  an  incipient  red  heat  seems  to  be  a  limiting  temperature  beyond 
which  graphite  exhibits  only  the  ordinary  variation  with  the  temperature. 


4I4  On  Heat.  [457- 

Weber  has  also  found  that,  in  their  thermal  deportment,  there  are  only  two 
essentially  different  modifications  of  carbon  —  the  transparent  one  (diamond), 
and  the  opaque  ones  (graphite,  dense  amorphous  carbon,  and  porous  amor- 
phous carbon). 

Crystallised  boron  is  similar  in  its  deportment  to  carbon  ;  its  specific 
heat  increases  from  0*1915  at  —40°  to  0*2382  at  27°,  and  to  0-3663  at  233°. 
The  rate  of  increase  is  very  rapid  up  to  80°  ;  it  increases  beyond  that 
temperature,  but  at  a  gradually  diminished  rate,  and,  no  doubt',  tends  to  an 
almost  constant  value  of  0*5. 

The  specific  heat  of  silicon  also  varies  with  the  temperature  ;  between 
—  40°  and  200°  it  increases  from  0-136  to  0-203  5  the  rate  of  increase  is  less 
rapid  with  higher  temperatures,  being  at  200°  only  Ta¥  what  it  is  at  10°.  At 
200°  it  reaches  its  limiting  value. 

The  specific  heat  of  substances  is  greater  in  the  liquid  than  in  the  solid 
state,  as  will  be  seen  by  the  following  table  :  — 

Solid  Liquid 

Water  .  .       ,.         .         .  .  .  .  0-489,  rooo 

Sulphur  .....  .  .  .  0-203'  0-234 

Bromine  .         .         ,  .  .  .  0-084  o-iio 

Iodine  .  ,         .  .     \         .  .  .  .  0-054  0-008 

Mercury  ,         ..       '.         .  .  .  .  0-031  0-033 

Phosphorus  ....  .  V  .  0-190  0*202 

Tin       .  .        '.         .         ...  .  .  0-056  0*064 

Lead     .  .         .         .     •    .  .     -   .  .  0-031  0*040 

It  also  differs  with  the  allotropic  modification  ;  thus  the  specific  heat  of 
red  phosphorus  is  0-19,  and  that  of  white  0*17  -  of  crystallised  arsenic 
0-083,  and  of  amorphous  0*058  ;  of  crystallised  selenium  0-084,  and  of 
amorphous  0-0953;  of  wood  charcoal  0-241;  of  graphite  0-202;  and  of 
diamond  0-147. 

Pouillet  used  the  specific  heat  of  platinum  for  measuring  high  degrees  of 
heat.  Supposing  200  ounces  of  platinum  had  been  heated  in  a  furnace,  and 
had  then  been  placed  in  1,000  ounces  of  water,  the  temperature  of  which  it 
had  raised  from  13°  to  20°.  From  the  formula  we  have  M  =  200,  m  =  1000  ; 
6  is  20,  and  /is  13.  The  specific  heat  of  platinum  is  0-033,  an^  we  have 
therefore,  from  the  equation  — 


7000+J32  =  7132 
Me  6-6  6-6 

It  is  found,  however,  that  the  mean  specific  heat  of  platinum  at  tempera- 
tures up  to  about  1200°  is  0-0377  ;  if  this  value,  therefore,  be  substituted  for 
c  in  the  above  equation,  we  have  — 

T  =  7150*8  =     8o  c 
7'54 

By  this  method,  which  requires  great  skill  in  the  experimenter,  Pouillet 
determined  a  series  of  high  temperatures.  He  found,  for  example,  the  tem- 
perature of  melting  iron  to  be  1  500°  to  1  600°  C. 


-458] 


Dulong  and  Petifs  Law. 


415 


458.  Dulong  and  Petit's  law. — A  knowledge  of  the  specific  heat  of 
bodies  has  become  of  great  importance,  in  consequence  of  Dulong  and  Petit's 
discovery  of  the  remarkable  law,  that  the  product  of  the  specific  heat  of  any 
solid  element  into  its  atomic  weight  is  approximately  a  constant  number,  as 
will  be  seen  from  the  following  table  : — - 


Specific  heat 

Atomic  weight 

Atomic  heat 

Aluminium     . 

0-2143 

27-4 

5-87 

Antimony 

0-0513 

122 

6-26 

Arsenic  .... 

0-0822 

75 

6-I7 

Bismuth 

0-0308 

210 

6-47 

Bromine 

0-0843 

80 

674 

Cadmium 

0-0567 

112 

6-35 

Cobalt    .... 

0-1067 

587 

6-26 

Copper  
Gold       .... 

0-0939 
0-0324 

63-5 
197 

5'99 
6-38 

Iodine    .... 

0-0541 

127 

6-87 

Iron        . 

0-1138 

56 

6-37 

Lead      .... 

0-0314 

207 

6-50 

Magnesium    .         .         .            0*2475 

24 

5'94 

Mercury         .         .         .           0-0332 

200 

6-64 

Nickel    ....           0-1092 

587 

6-41 

Phosphorus    .         .         .  .          0*1740 

31'0 

5'39 

Platinum         .         .         .  ;         0-0324 

I97-5 

6-40 

Potassium       .         .         .            0-1655 

39'i 

6  -47 

Silver     .         .         .         .  :         0-0570 

1  08-0 

6-16 

Salphur.         .         .         .  i         0-178 

32 

570 

Tin         .         .         .         .            0-0555 

118 

6-55 

Zinc        .         .         .         .|         0-0950 

65-2 

6-23 

It  will  be  seen  that  the  number  is  not  a  constant,  but  varies  between  5-39 
and  6-87.  These  variations  may  depend  partly  on  the  difficulty  of  getting 
the  elements  in  a  state  of  perfect  purity,  and  partly  on  errors  incidental  to 
the  determination  of  the  specific  heats,  and  of  the  atomic  weights.  Againr 
the  specific  heats  of  bodies  vary  with  the  state  of  aggregation  of  the  bodies, 
and  also  with  the  temperatures  at  which  they  are  determined  ;  some,  such 
as  potassium,  have  been  determined  at  temperatures  very  near  their  fusing 
points  ;  others,  like  platinum,  at  temperatures  much  removed  from  them.  A 
prominent  cause,  therefore,  of  the  discrepancies  is  doubtless  to  be  found  in 
the  fact  that  all  the  determinations  have  not  been  made  under  corresponding 
physical  conditions. 

The  atomic  weights  of  the  elements  represent  the  relative  weights  of  equal 
numbers  of  atoms  of  these  bodies,  and  the  product,/^,  of  the  specific  heat, 
c,  into  the  atomic  weight,  /,  is  the  atomic  heal,  or  the  quantity  of  heat 
necessary  to  raise  the  temperature  of  the  same  number  of  atoms  of  different 
substances  by  one  degree  ;  and  Dulong  and  Petit's  law  may  be  thus  ex- 
pressed :  the  same  quantity  of  heat  is  needed  to  heat  an  atom  of  all  simple 
bodies  to  the  same  extent. 

The  atomic  heat  of  a  body,  when  divided  by  its  specific  heat,  gives  the 


416  On  Heat.  [458- 

atomic  weight  of  a  body.  Regnault  even  proposed  to  use  this  relation  as  a 
means  of  determining  the  atomic  weight,  and  it  certainly  is  of  great  service 
in  deciding  on  the  atomic  weight  of  a  body  in  cases  where  the  chemical 
relations  permit  a  choice  between  two  or  more  numbers. 

According  to  modern  views,  the  heat  imparted  to  a  body  is  partly  ex- 
pended in  external  work,  which  in  the  case  of  a  solid  would  be  extremely 
small,  being  only  that  required  for  the  pressure  of  the  atmosphere  raised 
through  a  distance  representing  the  expansion  ;  secondly,  the  internal  work, 
or  the  heat  used  in  overcoming  the  attraction  of  the  atoms,  and  forcing 
them  apart ;  and  thirdly,  there  is  the  true  specific  heat,  or  the  heat  applied  in 
increasing  the  temperature — that  is,  in  increasing  the  vis  viva  of  the  molecules 
(448).  By  far  the  most  considerable  of  these  is  the  latter  ;  the  amount  of 
heat  consumed  in  the  two  former  operations  is  small,  and  the  variations 
with  different  bodies  must  be  inconsiderable.  Until,  however,  the  relation 
between  the  various  factors  is  made  out,  absolute  identity  in  the  numbers 
for  the  atomic  specific  heat  cannot  be  expected.  Weber  holds  that  even 
when  due  allowance  has  been  made  for  these  circumstances,  the  variations 
are  too  great  to  be  accounted  for,  and  he  considers  that  they  point  for  their 
explanation  to  an  alteration  in  the  constitution  of  the  atom,  and  render 
probable  a  changing  valency  of  the  atom  of  carbon. 

459.  Specific  heat  of  compound  bodies.- — In  compound  bodies  the  law 
also  prevails  :  the  product  of  the  specific  heat  into  the  equivalent  is  an  al- 
most constant  number,  which  varies,  however,  with  different  classes  of  bodies. 
Thus,  for  the  class  of  oxides  of  the  general  formula  RO,  it  is  11-30  ;  for  the 
sesquioxides  R2O3  it  is  27-15  ;  for  the  sulphides  RS,  it  is  18-88  ;  and  for  the 
carbonates  RCO3,  it  is  21-54.  The  law,  which  is  known  as  Neumanris  l^yu, 
may  be  expressed  in  the  following  general  manner  : —  With  compounds  of 
the  same  formula,  and  of  a  similar  chemical  constitution,  the  product  of  the 
atomic  weight  into  the  specific  heat  is  a  constant  quantity.  This  includes 
Dulong  and  Petit's  law  as  a  particular  case. 

Kopp  propounded  the  following  law,  which  is  an  extension  of  that  of 
Neumann  : — The  molecular  heats  of  all  solid  bodies  are  equal  to  the  sum  of 
the  molecular  heats  of  the  elements  contained  in  tJiem.  Dulong  and  Petit's 
law  that  all  elements  have  the  same  atomic  heat  he  does  not  consider  uni- 
versally valid.  He  assigns  the  number  6-4  to  all  elements  excepting  the  fol- 
lowing ;  with  sulphur  and  phosphorus  it  is  5-4,  fluorine  5*0,  oxygen  4-0, 
silicon  3-8,  boron  27,  hydrogen  2*3,  and  carbon  r8. 

Even  with  this  modification  it  is  found  that  the  calculated  heats  of  com- 
pounds differ  more  from  the  observed  ones  than  can  be  ascribed  to  errors  in 
the  determination  of  the  specific  heats.  This  is  probably  due  to  the  fact  that 
some  of  the  heat  is  expended  in  internal  work,  and  that  it  is  this  which  brings 
about  the  discrepancies. 

With  mixtures  of  alcohol  and  water  in  certain  proportions,  the  specific 
heat  is  greater  than  that  of  the  water  ;  thus,  that  of  a  mixture  containing  20 
per  cent,  of  alcohol  was  found  by  Duprd  and  Page  to  be  rc>456.  No  general 
law  can  be  laid  down  for  solutions  of  acids  or  of  salts  in  water  ;  though  the 
specific  heat  is  most  frequently  less  than  that  calculated  from  the  consti- 
tuents. 


-460]  Specific  Heat  of  Gases.  417 

460.  Specific  Heat  of  grases.— The  specific  heat  of  a  gas  may  be  re- 
ferred either  to  that  of  water  or  to  that  of  air.  In  the  former  case  it  repre- 
sents the  quantity  of  heat  necessary  to  raise  a  given  weight  of  the  gas  through 
one  degree,  as  compared  with  the  heat  necessary  to  raise  the  same  weight 
of  water  one  degree.  In  the  latter  case  it  represents  the  quantity  of  heat 
necessary  to  raise  a  given  volume  of  the  gas  through  one  degree,  compared 
with  the  quantity  necessary  for  the  same  volume  of  air  treated  in  the  same 
manner. 

De  la  Roche  and  Berard  determined  the  specific  heats  of  gases  in  re- 
ference to  water  by  causing  known  volumes  of  a  given  gas  under  constant 
pressure,  and  at  a  given  temperature,  to  pass  through  a  spiral  glass  tube 
placed  in  water.  From  the  increase  in  temperature  of  this  water,  and  from 
the  other  data,  the  specific  heat  was  determined  by  a  calculation  analogous 
to  that  given  under  the  method  of  mixtures.  They  also  determined  the 
specific  heats  of  different  gases  relatively  to  that  of  air,  by  comparing  the 
quantities  of  heat  which  equal  volumes  of  a  given  gas,  and  of  air  at  the  same 
pressure  and  temperature,  imparted  to  equal  weights  of  water.  Subsequently 
to  these  researches,  De  la  Rive  and  Marcet  applied  the  method  of  cooling  to 
the  same  determination  ;  and  more  recently  Regnault  made  a  series  of  in- 
vestigations on  the  calorific  capacities  of  gases  and  vapours,  in  which  he 
adopted,  but  with  material  improvements,  the  method  of  De  la  Roche  and 
Berard.  •  He  thus  obtained  the  following  results  for  the  specific  heats  of  the 
various  gases  and  vapours,  compared  first  with  an  equal  weight  of  water 
taken  as  unity  ;  secondly,  with  that  of  an  equal  volume  of  air,  referred,  as 
before,  to  its  own  weight  of  water  taken  as  unity  : — 

Specific  heats 


Simple 
gases 


Equal  Equal 

weights  volumes 

Air          .         .        ,.  .     0-2374  0-2374 

Oxygen.         .     '"'-'J         .  '       .         .     0-2174  0-2405 

Nitrogen         .     f  :  '"-'^ ;"  ^     .     0-2438  0-2370 


Compound 


Hydrogen  ."'.  .  3*4°9°  0-2359 

Chlorine         .         .         .  .   -     .  0-1210  0-2962 

Binoxide  of  nitrogen  \.::  .'  '    .  0-2315  0-2406 

Carbonic  oxide       .         ,-  .  0-2450  0*2370 

Carbonic  acid         .     |CT  .  0-2163  0-3307 

gases  Hydrochloric  acid      i-!;-r  •••'.•      .  0-1845  0-2333 

Ammonia       .         .      .'.  .  0-5083  0-2966 

Olefiant  gas  .     i;  •"    '  ^1\  •         •  0-4040  0-4106 

Water    .         .         .     :  :  :•  '  .         .  0-4805  0-2984 

Ether     .  .  0-4810  1-2296 

Alcohol.         .    :I  V    -  .  0-4534  o-7i7t 

1  Turpentine     .     -r;.  "  .  0-5061  2-3776 

I  Bisulphide  of  carbon      .  .  0-1570  0-4140 

\Benzole..  •' ":i).C:i;':-lj'i  : •    •.  .         .  0-3754  1-0114 


Vapours 


In  making  these  determinations  the  gases  were  under  a  constant  pressure, 
but  variable  volume  ;  that  is,  the  gas  as  it  was  heated  could  expand,  and 
this  is  called  the  specific  heat  under  constant  pressure.  But  if  the  gas  when 
being  heated  is  kept  at  a  constant  volume,  its  pressure  or  elastic  force  then 

E  E 


41 8  On  Heat.  [460- 

necessarily  increasing,  it  has  a  different  capacity  for  heat ;  this  latter  is 
spoken  of  as  the  specific  heat  under  constant  volume.  That  this  latter  is  less 
than  the  former  is  evident  from  the  following  considerations  : — 

Suppose  a  given  quantity  of  gas  to  have  had  its  temperature  raised  t° 
while  the  pressure  remained  constant,  this  increase  of  temperature  will  have 
been  accompanied  by  a  certain  increase  in  volume.  Supposing  now  that 
the  gas  is  so  compressed  as  to  restore  it  to  its  original  volume,  the  result  of 
this  compression  will  be  to  raise  its  temperature  again  to  a  certain  extent, 
say  f°.  The  gas  will  now  be  in  the  same  condition  as  if  it  had  been  heated 
and  had  not  been  allowed  to  expand.  Hence,  the  same  quantity  of  heat  which 
is  required  to  raise  the  temperature  of  a  given  weight  of  gas,  /°,  while  the 
pressure  remains  constant  and  the  volume  alters,  will  raise  the  temperature 
t  + 1'  degrees  if  it  is  kept  at  a  constant  volume  but  variable  pressure.  The 
specific  heat,  therefore,  of  a  gas  at  constant  pressure,  c,  is  greater  than  the 
specific  heat  under  constant  volume,  c,,  and  they  are  to  each  other  as  /+/':/, 

that  is  C.J^JL. 
c,       t 

It  is  not  possible  to  determine  by  direct  means  the  specific  heat  of  gases 
under  constant  volume  with  much  approach  to  accuracy  ;  and  it  has  been 
determined  by  some  indirect  method,  of  which  the  most  accurate  is  based 
on  the  theory  of  the  propagation  of  sound  (229).  A  critical  comparison  of 
the  most  accurate  recent  determinations  gives  the  number  1*405  for  the 

value  of  — ,  which  is  usually  designated  by  the  symbol  k. 

C4 

461.  Latent  heat  of  fusion. — Black  was  the  first  to  observe  that  during 
the  passage  of  a  body  from  the  solid  to  the  liquid  state,  a  quantity  of  heat 
disappears,  so  far  as  thermometric  effects  are  concerned,  and  which  is  ac- 
cordingly said  to  become  latent. 

In  one  experiment  he  suspended  in  the  room  at  a  temperature  8-5°  two 
thin  glass  flasks,  one  containing  water  at  o°,  and  the  other  the  same  weight 
of  ice  at  o°.  At  the  end  of  half  an  hour  the  temperature  of  the  water  had 
risen  4°,  that  of  the  ice  being  unchanged,  and  it  was  10^  hours  before  the 
ice  had  melted  and  attained  the  same  temperature.  Now  the  temperature 
of  the  room  remained  constant,  and  it  must  be  concluded  that  both  vessels 
received  the  same  amount  of  heat  in  the  same  time.  Hence  21  times  as 
much  heat  was  required  to  melt  the  ice  and  raise  it  to  4°  as  was  sufficient 
to  raise  the  same  weight  of  water  through  4°.  So  that  the  total  quantity  of 
heat  imparted  to  the  ice  was  21x4  =  84;  and  as  only  4  of  this  was  used  in 
raising  the  temperature,  the  remainder,  80,  was  used  in  simply  melting  the 
ice. 

He  also  determined  the  latent  heat  by  immersing  119  parts  of  ice  at  o° 
in  135  parts  of  water  at  87*7°  C.  He  thus  obtained  254  parts  of  water  at 
1 1 -6°  C.  Taking  into  account  the  heat  received  by  the  vessel  in  which 
the  liquid  was  placed,  he  obtained  the  number  79-44  as  the  latent  heat  of 
liquefaction  of  ice. 

We  may  thus  say 

Water  at  o°  =  Ice  at  o°  +  latent  heat  of  liquefaction. 
The  method  which  Black  adopted  is  essentially  that  which  is  now  used 


-461]  Latent  Heat  of  Fusion.  419 

for  the  determination  of  latent  heats  of  liquids  ;  it  consists  in  placing  the 
substance  under  examination  at  a  known  temperature  in  the  water  (or  other 
liquid)  of  a  calorimeter,  the  temperature  of  which  is  sufficient  to  melt  the 
substance  if  it  is  solid,  and  to  solidify  it  if  liquid  ;  and  when  uniformity  of 
temperature  is  established  in  the  calorimeter,  this  temperature  is  determined. 
Thus,  to  take  a  simple  case,  suppose  it  is  required  to  determine  the  latent 
heat  of  the  liquidity  of  ice.  Let  M  be  a  certain  weight  of  ice  at  zero,  and  m 
a  weight  of  water  at  t°  sufficient  to  melt  the  ice.  The  ice  is  immersed  in 
the  water,  and  as  soon  as  it  has  melted,  the  final  temperature  6°  is  noted. 
The  water,  in  cooling  from  t°  to  0°,  has  parted  with  a  quantity  of  heat, 
m  (t-6).  If  x  be  the  latent  heat  of  the  ice,  it  absorbs,  in  liquefying,  a 
quantity  of  heat  M.r  ;  but,  besides  this,  the  water  which  it  forms  has  risen 
to  the  temperature  0°,  and  to  do  so  has  required  a  quantity  of  heat,  repre- 
sented by  M0°.  We  thus  get  the  equation 


from  which  the  value  x  is  deduced. 

By  this  method  Desains  and  De  la  Provostaye  found  that  the  latent  heat 
of  the  liquefaction  of  ice  is  79-25  :  that  is,  a  pound  of  ice,  in  liquefying, 
absorbs  the  quantity  of  heat  which  would  be  necessary  to  raise  79*25  pounds 
of  water  i°,  or,  what  is  the  same  thing,  one  pound  of  water  from  zero  to 
79-25°.  Bunsen's  most  recent  determination  gives  80-025  (451). 

This  method  is  thus  essentially  that  of  the  method  of  mixtures  :  the  same 
apparatus  may  be  used,  and  the  same  precautions  are  required,  in  the  two 
cases.  In  determining  the  latent  heat  of  liquefaction  of  most  solids,  the  differ- 
ent specific  heats  of  the  substance  in  the  solid  and  in  the  liquid  state  require 
to  be  taken  into  account.  In  such  a  case,  let  m  be  the  weight  of  the  water 
in  the  calorimeter  (the  water  equivalents  of  the  calorimeter  and  thermometer 
supposed  to  be  included)  ;  M  the  weight  of  the  substance  worked  with  ;  /the 
original  and  6  the  final  temperature  of  the  calorimeter  ;  T  the  original  tem- 
perature of  the  substance  ;  C  its  melting  (or  freezing)  point  ;  C  the  specific 
heat  of  the  substance  in  the  solid  state  between  the  temperature  C  and  6  ;  c 
its  specific  heat  in  the  liquid  state  between  the  temperatures  T  and  C  ;  and 
let  L  be  the  latent  heat  sought. 

If  the  experiment  be  made  on  a  melted  substance  which  gives  out  heat 
to  the  calorimeter  and  is  thereby  solidified  (it  is  taken  for  granted  that  a 
body  gives  out  as  much  heat  in  solidifying  as  it  absorbs  in  liquefying),  it  is 
plain  that  the  quantity  of  heat  absorbed  by  the  calorimeter,  m(6  -  /),  is  made 
up  of  three  parts  :  first,  the  heat  lost  by  the  substance  in  cooling  from  its 
original  temperature  T  to  the  solidifying  point  C  ;  secondly,  the  heat  given 
out  in  solidification,  L  ;  and,  thirdly,  the  heat  it  loses  in  sinking  from  its 
solidifying  point  C,  to  the  temperature  of  the  water  of  the  calorimeter. 
That  is  : 


whence, 


. 
M 

The  following  numbers   have   been   obtained   for  the   latent   heats   of 
fusion  :  — 

E  E  2 


420 


On  Heat. 


[461- 


Water    . 

Nitrate  of  Sodium 

„         ,,    Potassium 
Zinc 

Platinum 

Silver     .  «•:  >- 

Tin 


80-25 
62-97 

47-37 
28-13 
27-18 
21-07 
14-25 


Cadmium 
Bismuth 
Sulphur . 
Lead 

Phosphorus   . 
D'Arcet's  alloy 
Mercury 


13-66 
12-64 
9'37 
5'37 
5-03 
4-50 
2-83 


These  numbers  represent  the  number  of  degrees  through  which  a  pound 
of  water  would  be  raised  by  a  pound  of  the  body  in  question  in  passing 
from  the  liquid  to  the  solid  state  ;  or,  what  is  the  same  thing,  the  number  of 
pounds  of  water  that  would  be  raised  i°  C.  by  one  of  the  bodies  in  solidi- 
fying. 

On  modern  views  the  heat  expended  in  melting  is  consumed  in  moving 
the  atoms  into  new  positions  ;  the  work,  or  its  equivalent  in  heat  required 
for  this,  the  potential  energy  they  thus  acquire,  is  strictly  comparable  to  the 
expenditure  of  work  in  the  process  of  raising  a  weight.  When  the  liquid 
solidifies,  it  reproduces  the  heat  which  had  been  expended  in  liquefying  the 
solid  :  just  as  when  a  stone  falls  it  produces  by  its  impact  against  the 
ground  the  heat,  the  equivalent  of  which  in  work  had  been  expended  in 
raising  it,  and  a  similar  explanation  applies  to  the  latent  heat  of  gasification. 
462.  Determination  of  the  latent  heat  of  vapour. — Liquids,  as  we 
have  seen,  in  passing  into  the  state  of  vapour,  absorb  a  very  considerable 

quantity  of  heat,  which  is  termed 
latent  heat  of  vaporisation.  In  deter- 
mining the  heat  absorbed  in  liquids, 
it  is  assumed  that  a  vapour,  in  liquefy- 
ing, gives  out  as  much  heat  as  it  had 
absorbed  in  becoming  converted  into 
vapour. 

The  method  employed  is  essentially 
the  same  as  that  for  determining  the 
specific  heat  of  gases.  Fig.  383  repre- 
sents the  apparatus  used  by  Despretz. 
The  vapour  is  produced  in  a  retort, 
C,  where  its  temperature  is  indicated 
by  a  thermometer.  It  passes  into  a 
worm  SS  immersed  in  cold  water, 
where  it  condenses,  imparting  its 
latent  heat  to  the  condensing  water  in  the  vessel  B.  The  condensed  vapour 
is  collected  in  a  vessel,  A,  and  its  weight  represents  the  quantity  of  vapour 
which  has  passed  through  the  worm.  The  thermometers  in  B  give  the 
change  of  temperature. 

Let  M  be  the  weight  of  the  condensed  vapour,  T  its  temperature  on 
entering  the  worm,  which  is  that  of  its  boiling  point,  and  x  the  latent  heat  of 
vaporisation.  Similarly,  let  m  be  the  weight  of  the  condensing  water  (com- 
prising the  weight  of  the  vessel  B  and  of  the  worm  SS  reduced  in  water),  let 
/°  be  the  temperature  of  the  water  at  the  beginning,  and  6°  its  temperature 
at  the  end  of  the  experiment. 


Fig.  383- 


-462]          Determination  of  the  Latent  Heat  of  Vapour.  42  1 

It  is  to  be  observed  that,  at  the  commencement  of  the  experiment,  the 
condensed  vapour  passes  out  at  the  temperature  /°,  while  at  the  conclusion 
its  temperature  is  <9°  ;  we  may,  however,  assume  that  its  mean  temperature 

during  the  experiment  is  ±  -^~2-.     The  vapour   M   after   condensation  has 
therefore  parted  with  a  quantity  of  heat   M.(  T-          ^  c,  while   the  heat 


disengaged  in  liquefaction  ,  is  represented  by  M.r.  The  quantity  of  heat 
absorbed  by  the  cold  water,  the  worm,  and  the  vessel  is  m(6—f).  There- 
fore, 

M,r+M 


from  which  x  is  obtained.     Despretz  found  that  the  latent  heat  of  aqueous 
vapour  at  100°  is  540  ;  that  is,  a  pound  of  water  at  100°  absorbs  in  vaporising 
as  much  heat  as  would  raise  540  pounds    of  water  through   i°.     Regnault 
found  the  number  537,  and  Favre  and  Silbermann  538  -8. 
As  in  the  case  of  the  latent  heat  of  water  we  may  say, 

Steam  at  100°  -  Water  at  100°  +  latent  heat  of  gasification. 

Bertholet  uses  the  very  convenient 
apparatus  represented  in  fig.  384,  for  deter- 
mining latent  heats  of  vaporisation.  The 
liquid  in  the  flask  D  is  heated  by  the  ring 
burner  B,  and  the  vapour  which  forms  passes 
through  the  tube  ab  into  the  serpentine  S, 
where  it  condenses  and  collects  in  the  bulb 
R.  These  are  contained  in  the  calorimeter 
C,  the  top  of  which  is  ^  closed  by  a  wooden 
cover,  HH',  and  a  layer  of  felt,  NN';  they 
cut  off  any  heat  from  the  flask  D  and  from 
the  burner  B.  As  the  serpentine  SR  can 
be  detached  from  ab,  it  is  easy  to  deter- 
mine the  weight  of  the  distillate  ;  from  this, 
and  from  the  rise  in  temperature  of  the  water 
in  the  calorimeter,  the  latent  heat  can  be 
readily  calculated. 

In  the  conversion  of  a  body  from  the 
liquid  into  the  gaseous  state,  as  in  the 
analogous  process  of  fusion,  one  part  of  the 
heat  is  used  in  increasing  the  temperature 

and  another  in  internal  work.  For  vaporisation,  the  greater  portion  is  con- 
sumed in  the  internal  work  of  overcoming  the  reciprocal  attraction  of  the 
particles  of  liquid,  and  in  removing  them  to  the  far  greater  distances  apart 
in  which  they  exist  in  the  gaseous  state.  In  addition  to  this  there  is  the 
external  work  —  namely,  that  required  to  overcome  the  external  pressure, 
usually  that  of  the  atmosphere  :  and  as  the  increase  of  volume  in  vaporisa- 
tion is  considerable,  this  pressure  has  to  be  raised  through  a  greater  space. 
Vaporisation  may  take  place  without  having  external  work  to  perform, 
as  when  it  is  effected  in  vacuo  ;  but  whether  the  evaporation  is  under  a  high 


422 


On  Heat. 


[462- 


or  under  a  low  pressure,  on  the  surface  of  a  liquid  or  in  the  interior,  there 
is  always  a  great  consumption  of  heat  in  internal  work. 

463.  Favre  and  Silbermann's  Calorimeter. — The  apparatus  (fig.  385) 
furnishes  a  very  delicate  means  of  determining  the  calorific  capacity  of 
liquids,  latent  heats  of  evaporation,  and  the  heat  disengaged  in  chemical 
actions. 

The  principal  part  is  a  spherical  iron  reservoir,  A,  full  of  mercury,  of 
which  it  holds  about  50  pounds,  and  represents,  therefore,  a  volume  of  more 
than  half  a  gallon.  On  the  left  there  are  two  tubulures,  B,  in  which  are 
fitted  two  sheet-iron  tubes  or  muffles,  projecting  into  the  interior  of  the  bulb. 
Each  can  be  fitted  with  a  glass  tube  for  containing  the  substance  experi- 


Fig.  385- 

mented  upon.  In  most  cases  one  muffle  and  one  glass  tube  are  enough  ; 
the  two  are  used  when  it  is  desired  to  compare  the  quantities  of  heat  pro- 
duced in  two  different  operations.  In  a  third  vertical  tubulure,  C,  there  is 
also  a  muffle,  which  can  be  used  for  determining  calorific  capacities  by 
Regnault's  method  (455),  in  which  case  it  is  placed  beneath  the  r  of  fig.  382. 
The  tubulure  d  contains  a  steel  piston  ;  a  rod  turned  by  a  handle,  m, 
and  which  is  provided  with  a  screw  thread,  transmits  a  vertical  motion  to 
the  piston  ;  but,  by  a  peculiar  mechanism,  gives  it  no  rotatory  motion.  In 
the  last  tubulure  is  a  glass  bulb,  a,  in  which  is  a  long  capillary  glass  tube,  bo, 
divided  into  parts  of  equal  capacity. 


-463] 


Favre  and  Silbermanris  Calorimeter. 


423 


It  will  be  seen  from  this  description  that  the  mercury  calorimeter  is 
essentially  a  thermometer  with  a  very  large  bulb  and  a  capillary  stem  :  it 
is  therefore  extremely  delicate.  It  differs,  however,  from  a  thermometer  in 
the  fact  that  the  divisions  do  not  indicate  the  temperature  of  the  mercury 
in  the  bulb,  but  the  number  of  thermal  units  imparted  to  it  by  the  substances 
placed  in  the  muffle. 

This  graduation   is   effected   as   follows  :  —  By  working  the  piston   the 
mercury  can  be  made  to  stop  at  any  point  of  the  tube,  60,  at  which  it  is 
desired  the  graduation  should  commence.     Having  then  placed  in  the  iron 
tube  a  small  quantity  of  mercury,  which  is  not  afterwards  changed,  a  thin 
glass  tube,  e,  is  inserted, 
which  is  kept  fixed  against 
the  buoyancy  of  the  mer- 
cury by   a    small   wedge 
not    represented    in    the 
figure.      The  tube   being 
thus   adjusted,  the   point 
of  a   bulb  tube  (see   fig. 
386)   is   introduced,   con- 
taining   water    which    is 
raised     to     the     boiling 
point  :    turning  the  posi- 
tion of  the  pipette,  then, 
as   represented    in   //',   a 
quantity  of  the  liquid  flows 
into  the  test  tube. 

The  heat  which  is  thus  imparted  to  the  mercury  makes  it  expand  ;  the 
column  of  mercury  in  bo  is  lengthened  oy  a  number  of  divisions,  which  we 
shall  call  n.  If  the  water  poured  into  the  test  glass  be  weighed,  and  if  its 
temperature  be  taken  when  the  column  bo  is  stationary,  the  product  of  the 
weight  of  the  water  into  the  number  of  degrees  through  which  it  has  fallen 
indicates  the  number  of  thermal  units  which  the  water  gives  up  to  the  entire 
apparatus  (447).  Dividing,  by  ?z,  this  number  of  thermal  units,  the  quotient 
gives  the  number,  a,  of  thermal  units  corresponding  to  a  single  division  of 
the  tube  bo. 

In  determining  the  specific  heat  of  liquids,  a  given  weight,  M,  of  the 
liquid  in  question  is  raised  to  the  temperature  T  and  is  poured  into  the  tube 
C.  Calling  the  specific  heat  of  the  liquid  c,  its  final  temperature  0,  and  n 
the  number  of  divisions  by  which  the  mercurial  column  bo  has  advanced,  we 
have 

Mc(T  —  6}  =  na,  from  which  c  =      /^^T 


Fig.  386. 


The  boards  represented  round  the  apparatus  are  hinged  so  as  to  form  a 
box,  which  is  lined  with  eider-down  or  wadding,  to  prevent  any  loss  of  heat. 
It  is  closed  at  the  top  by  a  board,  which  is  provided  with  a  suitable  case, 
also  lined,  which  fits  over  the  tubulures  d  and  a.  A  small  magnifying  glass 
which  slides  along  the  latter,  enables  the  divisions  on  the  scale  to  be  read 
off. 


424  On  Heat.  [464- 

464.  Examples. — I.  What  weight  of  ice  at  zero  must  be  mixed  with  9 
pounds  of  water  at  20°  in  order  to  cool  it  to  5°  ? 

Let  M  be  the  weight  of  ice  necessary  ;  in  passing  from  the  state  of  ice 
to  that  of  water  at  zero,  it  will  absorb  8oM  thermal  units  ;  and  in  order  to 
raise  it  from  zero  to  5°,  5M  thermal  units  will  be  needed.  Hence  the  total 
heat  which  it  absorbs  is  8oM  +  5M  =  85M.  On  the  other  hand,  the  heat 
given  up  by  the  water  in  cooling  from  20°  to  5°  is  9  x  (20-  5)  =  135.  Con- 
sequently, 

85M  =  135  ;  from  which  M  =  1-588  pounds. 

II.  What  weight  of  steam  at  100°  is  necessary  to  raise  the  temperature 
of  208  pounds  of  water  from  14°  to  32°  ? 

Let  p  be  the  weight  of  the  steam.  The  latent  heat  of  steam  is  540°,  and 
consequently/  pounds  of  steam  in  condensing  into  water  give  up  a  quantity 
of  heat,  540/5  and  form/  pounds  of  water  at  100°.  But  the  temperature  of 
the  mixture  is  32°,  and  therefore/  gives  up  a  further  quantity  of  heat  p 
(100  — 32)  =  68/,  for  in  this  case  c  is  unity.  The  208  pounds  of  water  in 
being  heated  from  14°  to  32°  absorb  208(32  —  14)  =  3744  units.  Therefore 

54o/  +  68/  =  3744  ;  from  which  p  =  6-158  pounds. 


-466]  Steam  Boiler.  425 


CHAPTER   X. 

^  STEAM     ENGINES. 

465.  Steam    Engines. — Steam   engines  are    machines    by    which  heat 
energy,  obtained  by  the  combustion  of  some  fuel,  is  turned  into  mechanical 
work,  aqueous  vapour  being  used  as  a  working  fluid  for  effecting  the  trans- 
formation.    In  all  but  a  few  very  exceptional  cases  the  mechanical  means 
used  for  the  transformation  of  the  one  form  of  energy  into  the  other  are  as 
follows  : — the  heat  of  combustion  is,  as  far  as  possible,  imparted  to  water  in 
a  closed  vessel  called  a  boiler ;  the  water  is  thereby  converted  into  steam, 
occupying  an  enormously  greater  volume,  and  this  steam  is  allowed  to  pass 
from  the  boiler  as  fast  as  it  is  formed,  and  to  act  alternately  on  the  two  sides 
of  a  movable  piston  working  backwards  and  forwards  in  a  cylinder.     As  soon 
as  the  piston  has  been  pushed  to  either  end  of  the  cylinder  by  the  incoming 
steam  acting  on  one  side  of  it,  the  communication  between  that  side  and  the 
boiler  is  shut  off,  and  another  communication  opened  either  to  a  condenser 
or  to  the  atmosphere.     In  either  case  the  steam  rushes  out  of  the  cylinder 
and  the  pressure  against  the  piston  falls,  so  that  it  can  be  pushed  back  by 
fresh  steam  from  the  boiler  acting  on  its  opposite  side.     If  the  purpose  of 
the  engine  is  merely  to  work  pumps,  or  any  other  apparatus  requiring  only  a 
reciprocating  motion,  a  rod  from  the  piston  can  be  connected  directly,  or 
through  a  lever,  to  the  pump  to  be  worked.     If,  however,  as  in  a  majority  of 
cases,  the  engine  has  to  drive  something  having  a  rotary  motion,  a  simple 
mechanism  is  used  to  change  the  reciprocating  motion  of  the  piston  into  the 
rotation  of  a  crank.     In  this  change  itself  there  is  no  loss  of  work  or  energy 
(471),  the  work  of  the  steam  on  the  piston  being  exactly  equal  to  the  work 
done  at  the  rotating  crank-pin,  minus  only  the  lost  work  spent  in  overcoming 
the  friction  of  the  joints  of  the  mechanism. 

We  shall  first  consider  the  boiler,  or  apparatus  for  generating  steam,  and 
then  the  engine  itself. 

466.  Steam  boiler. — Figs.  387  and  388  show  one  ot  the  forms  of  boiler 
most  commonly  used  in  this  country  for  supplying  steam  to  stationary  engines. 
This  type  of  boiler  is  called  Cornish,  having  been  first  used  for  the  pumping 
engines  in  Cornwall.     Fig.  387  shows  a  longitudinal  section  of  the  boiler  and 
the  brick  flues  in  which  it  is  set,  and  fig.  388  shows  on  the  left  a  half-front 
view   of  the  boiler  and  on  the  right  a  half  cross  section.     The  boiler  consists 
of  an  outer  cylindrical  shell  A  of  wrought  iron  or  steel  plates  riveted  together, 
and  a  smaller  internal  flue  or  furnace  B.     The  latter  is  open   at  both  ends, 
and  is  crossed  by  a  series  of  vertical  tubes  C,  called  Galloway  tubes,  which 
allow  the  water  to  circulate  from  the  lower  to  the  upper  part  of  the  boiler. 
The   fire  is  placed  on  a  grate  D  in  the  front  part  of  the  flue  and  ending 
in  a  firebrick  bridge  over  which  the  gases  have  to  pass.     These  hot  gases 


426 


On  Heat. 


[466- 


find  their  way  past  the  tubes  to  the  back  of  the  boiler  and  then  are  com- 
pelled to  diverge  sideways  and  return  by  the  side  flues  K  to  nearly  the  front 
of  the  shell  where  the  flues  are  diverted  downwards,  as  shown  in  fig.  388, 
and  thence  they  return  by  the  lower  flue  L  to  the  chimney  M.  By  thus 


Fig.  387. 

encircling  the  boiler  with  flues  it  is  endeavoured  to  get  all  the  heat  possible 
from  the  gases  before  they  are  allowed  to  pass  away  up  the  chimney.  The 
principal  fittings  or  mountings  of  the  boiler  are  indicated  in  the  figures  and 
are  as  follows  :  G  is  a  dome  on  which  stands  the  stop-valve  N  through  which 
the  steam  is  carried  to  the  engine.  The  object  of  the  dome  is  to  take  the 

steam  from  a  point  as  far  away  from  the 
water  line  as  possible,  so  as  to  dry  it.  P  is 
a  safety  valve,  held  down  on  its  seat  by  the 
action  of  a  weighted  lever,  and  so  adjusted 
that  as  soon  as  the  pressure  of  steam  reaches 
its  intended  maximum  and  tends  to  rise 
beyond  it,  the  valve  is  lifted  and  the  steam 
rushes  away  into  the  air.  Q  is  a  manhole 
door  by  which  access  is  had  to  interior  of  the 
boiler,  when  it  is  empty  and  out  of  use,  for 
cleaning  and  repair.  R  is  a  pressure  gauge 
or  indicator,  standing  in  front  of  the  shell, 
showing,  by  a  hand  working  in  front  of  a  dial 
plate,  the  'boiler  pressure'  or  amount  which 
the  pressure  of  steam  inside  the  boiler  ex- 
ceeds that  of  the  atmosphere  surrounding  it.  S  is  a  water  gauge,  a  glass 
tube  connected  at  top  and  bottom  to  the  boiler,  its  upper  end  to  the  steam 
space,  and  the  lower  end  to  the  water  space.  The  water  stands  in  the  glass 
tube  at  the  same  level  as  in  the  boiler,  and  the  fireman  can  see  at  a  glance 
whether  it  is  at  the  right  height.  This  matter  is  of  great  importance, 
because  an  accidental  fall  of  water-level  is  a  frequent  cause  of  boiler  explo- 
sions. If,  for  instance,  the  water  fell  so  low  as  to  leave  the  top  of  the  furnace 
B  uncovered,  the  plates  would  get  red-hot  and  soften  so  much  as  to  collapse 


—467]  CornisJi  Engine.  427 

under  the  action  of  the  steam  pressure,  with  consequences  that  might  be 
most  serious. 

In  marine  boilers,  when  it  is  of  the  greatest  importance  to  get  as  much 
heating  surface  as  possible  into  a  small  space,  and  similarly  in  the  locomotive 
boiler  to  be  presently  described,  the  hot  gases  after  leaving  the  furnace  are 
made  to  pass  through  a  number  of  small  tubes  instead  of  one  large  one  as  in 
fig.  387.  Such  boilers  are  called  multitubular  boilers. 

Of  late  years  the  shells  of  large  boilers  have  frequently  been  made  of 
•*  mild  steel,'  produced  by  the  Bessemer  or  Siemens-Martin  processes,  rather 
than  of  wrought  iron.  In  locomotive  boilers,  where  the  combustion  is  very 
rapid  and  intense,  the  fire-boxes  are  frequently  made  of  copper,  a  much 
better  conductor  of  heat  than  either  iron  or  steel. 

467.  Cornish  engine. — Fig.  389  shows  the  oldest  of  all  the  types  of 
engines  still  in  use,  the  Cornish  pumping  engine,  which  is  worth  examina- 
tion both  for  its  historical  interest  and  on  account  of  the  special  way  in 
which  it  works.  (In  the  figure  all  details  except  those  absolutely  necessary 
to  illustrate  the  action  of  the  engine  are  omitted.)  The  engine  has  a  vertical 


Fig.  389- 

cylinder  A  (often  of  very  great  size,  and  with  as  much  as  10  or  n  ft.  stroke), 
in  which  works  a  piston  P,  whose  rod  is  connected  by  a  chain  to  a  sector  on 
the  end  of  a  beam  B.  Beside  the  cylinder  is  a  chamber  C  containing  the 
valves  for  admitting  and  discharging  steam,  whose  mode  of  working  will  be 
presently  described.  At  the  further  end  of  the  beam  a  second  sector  is 


428  On  Heat.  [467- 

connected  with  the  pump-rod,  at  the  upper  end  of  which  is  placed  a  heavy 
counterweight  Q.  Below  the  cylinder  a  pipe  M  leads  to  a  chamber  N  called 
the  condenser,  into  which  a  jet  of  water  from  the  tank  in  which  it  stands 
continually  plays.  The  condenser  in  its  turn  is  connected  with  a  pump 
called  an  air-pump,  worked  from  the  beam  by  the  rod  E,  and  fitted  with 
suction  and  discharge  valves,  and  valves  in  its  piston  in  the  usual  way. 

We  can  follow  the  working  of  the  engine  easily  by  supposing  the  piston 
to  start  at  the  top  of  its  stroke.  The  valves  are  then  in  the  position  shown, 
m  open,  n  and  o  closed.  Steam  passes  from  the  boiler  through  the  pipe  T 
to  the  top  of  the  piston,  and  forces  it  down  against  the  small  pressure  of  the 
steam  below  it,  this  steam  escaping  into  the  condenser  through  the  valve  o 
and  the  pipe  M.  The  pump-rods  or  pit  work,  and  the  weight  Q,  are  thus 
lifted  to  the  top  of  their  stroke.  When  the  piston  arrives  at  the  bottom  of 
its  stroke  the  valves  m  and  o  are  shut  and  n  is  opened.  This  allows  free 
communication  between  the  two  sides  of  the  piston,  and  so  puts  it  inta 
equilibrium.  The  counter-weight  Q,  together  with  the  pump-rods,  is  made 
somewhat  heavier  than  the  piston  and  rod  plus  the  whole  weight  of  the 
column  of  water  to  be  lifted.  It  therefore  falls  slowly  (the  whole  affair  thus 
becoming  an  Attwood's  machine  (77)  on  an  enormous  scale),  and  forces 
up  the  water  through  the  pumps.  As  soon  as  the  piston  has  once  more- 
got  to  the  top  of  its  stroke,  by  which  time  of  course  all  the  steam  has  been 
transferred  to  its  under  side,  the  position  of  the  valves  is  again  reversed, 
and  the  piston  once  more  begins  to  fall.  The  steam  below  the  piston  is 
suddenly  put  into  communication  with  the  condenser  N,  into  which  a  jet  of 
cold  water  is  always  playing.  It  is  therefore  reduced  in  temperature  almost 
instantaneously,  much  of  it  is  condensed  into  water,  and  the  rest,  which  still 
fills  the  space  below  the  piston,  is  necessarily  reduced  to  a  pressure  of  only 
about  3  pounds  per  square  inch  or  about  \  of  an  atmosphere.  As  the  pres- 
sure of  the  steam  coming  direct  from  the  boiler  in  such  engines  is  often  50 
pounds  per  sq.  inch  above  that  of  the  atmosphere,  it  follows  that  the  differ- 
ence of  pressure  on  the  two  sides  of  the  piston  in  such  a  case,  is  50  +  1 5  —  3 
=  62  pounds  per  square  inch,  and  it  is  this  difference  of  pressure  which 
compels  the  piston  to  move  downwards  and  lift  all  the  weight  at  the  other 
end  of  the  beam.  The  condensed  steam  and  the  condensing  water  fall 
together  at  the  bottom  of  the  condenser,  and  are  continually  removed  (along 
with  the  uncondensed  steam  and  any  air  that  may  be  present)  by  the  air 
pump,  which  is  a  simple  lift  pump  with  a  valve  in  its  piston  (216). 

In  all  modern  Cornish  engines  the  beams  are  of  iron  and  the  sector  and 
chains  are  replaced  by  an  arrangement  of  iron  links  forming  a  parallel  motion 
which  it  is  not  necessary  here  to  describe.  The  simple  arrangement  for 
working  the  valves,  shown  in  outline  in  the  figure,  is  also  replaced  by  a  much 
more  complicated  apparatus  in  which,  by  means  of  cataracts,  any  required 
length  of  pause  can  be  made  between  the  strokes  of  the  engine,  a  matter 
which  is  sometimes  of  importance  in  heavy  pumping  work.  It  will  be 
noticed  that  by  the  peculiar  single-acting  method  of  working  adopted  in 
the  Cornish  engine,  the  velocity  of  the  down  stroke  (also  called  the  steam 
stroke,  or  the  indoor  stroke]  depends — other  things  being  equal — upon  the 
steam  pressure,  but  the  velocity  of  the  up  stroke  (equilibrium  or  outdoor 
stroke]  depends  solely  on  the  overplus  weight  put  on  the  outer  end  of  the 


-469] 


Distribution  of  the  Steam.     Slide  Valves. 


429 


beam.     In  this  way  a  slow  and  quiet  upward  motion  can  be  given  to  the 
water,  no  matter  how  quickly  the  steam  may  move  the  piston. 

468.  Ordinary  Horizontal  engine. — The  engines  now  most  largely  used 
in  factories  for  driving  machinery  differ  altogether  in  their  action  from  the 
Cornish  engine.  In  them  the  cylinder  is  generally  horizontal,  and  the  crank 
is  driven  through  a  connecting  rod  only,  without  the  intervention  of  any 
beam.  Such  an  engine  is  shown  in  fig.  390.  Here  A  is  the  steam  cylinder,  B 


Fig.  390. 

the  valve  chest,  or  chamber  in  which  works  the  valve  whose  mode  of  action 
is  described  in  the  next  article.  D  is  the  main  shaft,  on  the  inner  end  of 
which  is  the  crank  driven  by  the  connecting  rod  E.  C  is  an  eccentric  (fig. 
392),  which  works  the  valve  by  the  rod  N.  F  is  a  governor  controlling  the 
admission  of  steam  to  the  cylinder  by  the  valve  H.  M  is  the  bedplate  or 
frame  of  the  engine,  and  L  the  flywheel. 

A  few  words  are  necessary  about  the  governor.  This  apparatus,  an 
invention  of  James  Watt's,  consists  of  two  weighted  arms  hinged  at  the  top, 
which  fly  outward  when  the  speed  of  rotation  is  increased  and  drop  together 
when  it  is  reduced.  The  outward  or  inward  motion  of  the  arms  is  caused 
by  a  simple  arrangement  to  turn  the  spindle  G  and  so  to  close  or  open  the 
valve  H,  which  admits  steam  through  K  to  the  cylinder.  In  this  way  the 
engine  automatically  controls  its  own  speed  (471). 

469.  Distribution  of  the  steam.  Slide  valves. — Figs.  391  and  392 
show  details  as  to  the  working  of  the  valve  and  the  distribution  of  the  steam 
in  the  engine  just  described.  The  former  is  a  longitudinal  section  of  the 
cylinder  shown  in  fig.  390.  A  is  the  cylinder  itself,  B  the  piston,  C  the 
piston-rod,  D  the  stuffing-box  through  which  the  piston  passes  steam- 
tight.  It  will  be  seen  that  uport  or  passage  L  communicates  between  each 
end  of  the  cylinder  and  the  surface  on  which  the  valve  works,  or  valve  face. 
On  this  face,  and  between  the  two  steam-ports,  comes  a  third  port  M, 
communicating  directly  with  the  atmosphere  or  with  a  condenser  as  the 
case  may  be.  The  valve  G  is  shaped  in  section  something  like  an  irregular 


430  On  Heat.  [469- 

D,  and  is  often  called  a  '  D 3  valve  in  consequence.  It  is  moved  continu- 
ously backwards  and  forwards  upon  the  valve  face  by  the  valve  rod  H 
working  in  the  stuffing-box  K.  When  in  the  position  shown  in  the  figure 
the  steam  enters  by  F,  and  passes  into  the  left-hand  end  of  the  cylinder 
(past  the  edge  of  the  valve)  and  pushes  the  piston  from  left  to  right.  The 
steam  at  present  in  the  cylinder  (as  shown  by  the  arrows)  passes  out  at 
L,  and  through  the  under  part  of  the  valve  G  to  the  exhaust  port  M.  As 
the  piston  moves  on,  the  valve  at  first  moves  in  the  same  direction,  opening 
the  port  a  little  wider,  then  gradually  moves  back  again  and  closes  the 


Fig.  391- 


Fig.  392- 


admission  port  altogether.  The  point  at  which  this  occurs  is  called  the 
point  of  cut  off.  No  more  steam  is  allowed  to  enter  the  cylinder  for  that 
stroke,  the  piston  being  pushed  forward  by  the  pressure  of  the  elastic 
steam  expanding  behind  it.  By  the  time  the  piston  has  got  to  the  end  of 
its  stroke,  the  position  of  the  valve  is  just  reversed  from  that  in  which  it  is 
shown,  and  steam  passes  into  the  cylinder  through  the  right-hand  port, 
driving  the  piston  from  right  to  left,  while  the  steam  which  has  already  done 
duty  in  the  left-hand  end  of  the  cylinder  passes  away,  in  its  turn,  through  the 
exhaust. 

The  eccentric  from  which  the  valve  receives  its  motion  (lettered  C  in 
fig.  390)  is  shown  in  detail  in  fig.  392.  Here  D  is  the  crank-shaft  and  A  a 
disc  (solid  or  ribbed)  fixed  eccentrically  on  it  so  as  to  revolve  with  it.  En- 
circling this  disc  (which  is  the  eccentric]  is  a  strap  or  ring  B  (made  in  two 
pieces  for  the  sake  of  getting  on  and  off),  rigidly  connected  with  a  rod  C, 
which  is  coupled  by  a  pin  to  the  valve-rod  E.  In  each  revolution  of  the 
eccentric  the  valve-rod  is  moved  backwards  and  forwards  through  a  space 
equal  to  twice  the-  eccentricity  of  the  eccentric,  or  distance  between  the 
centres  of  D  and  of  A.  The  eccentric  is  thus  equivalent  exactly  to  a  crank 
having  a  radius  equal  to  its  eccentricity.  It  is  used  instead  of  a  crank 
because  it  does  not  require  any  gap  to  be  left  in  the  shaft,  as  a  crank  would 
do,  but  allows  it  to  be  carried  continuously  on. 

In  locomotive  or  marine  engines  two  eccentrics  are  commonly  used,  one 
so  placed  as  to  give  the  valve  the  right  motion  when  the  shaft  rotates  in 
one  direction,  and  one  rightly  placed  for  the  other.  By  apparatus  called 
reversing  gear  either  one  or  the  other  can  be  caused  to  move  the  valve,  so 
that  the  engine  can  be  made,  at  pleasure,  to  turn  the  shaft  in  one  or  the 
other  direction. 


-470] 


Locomotives. 


431 


470.  locomotives. — Locomotive  engines,  or  simply  ^locomotives,  are 
steam  engines  which,  mounted  on  a  carriage,  propel  themselves  by  trans- 
mitting their  motion  to  wheels.  The  whole  machine,  fig.  393,  boiler  and 
engine,  is  fixed  to  a  wrought-iron  frame,  which,  therefore,  is  made  strong 


enough  to  carry  the  whole  weight,  and  which  in  turn  transmits  that  weight 
to  the  axle-boxes  (or  bearings  in  which  the  axles  turn),  by  means  of  springs, 
and  thence  through  the  wheels  to  the  rails.  The  boiler  is  of  a  special  type, 
adopted  in  order  to  get  the  greatest  possible  heating  surface  in  a  very  limited 


432  On  Heat.  [470- 

space.  It  consists  of  three  parts — the  fire-box,  barrel,  and  smoke-box.  The 
fire-box,  in  the  left  of  the  engraving,  is  generally  a  more  or  less  rectangular 
box,  with  a  flat  top,  placed  inside  a  second  box  of  somewhat  similar  shape, 
but  with  a  semi-cylindrical,  or,  as  in  the  figure,  domed  top.  In  the  inner 
fire-box  are  the  fire-bars,  on  which  the  fuel  is  placed  through  a  door  in  front. 
The  space  between  the  inner  and  outer  boxes  is  filled  with  water  to  a  height 
considerably  over  the  top  of  the  inner  one,  and  communicates  freely  with  a 
long  cylindrical  barrel,  closed  at  the  other  end  by  the  smoke-box.  This 
barrel,  which  forms  the  main  bulk  of  the  boiler,  is  filled  with  water  to  within 
nine  or  ten  inches  of  its  upper  side.  It  is  traversed  from  end  to  end  by  a 
great  number  of  small  tubes  (about  i^  inch  in  diameter)  which  communicate 
with  the  inner  fire-box  at  the  one  end,  and  with  the  smoke-box  at  the  other. 
They,  therefore,  are  entirely  immersed  in  the  water  from  end  to  end.  The 
gases  of  combustion,  formed  in  the  inner  fire-box,  pass  through  these  tubes 
to  the  smoke-box,  and  thence  up  the  chimney,  and  impart  most  of  their  heat 
to  the  water  as  they  pass  along.  There  are  two  steam  cylinders,  one  on  each 
side  of  the  frame,  each  one  with  its  piston  and  connecting  rod,  etc.,  being 
simply  an  ordinary  high-pressure  horizontal  engine.  Their  exhaust  steam 
is  discharged  through  a  blast  pipe  into  a  nozzle  inside  the  chimney  near  its 
base,  and  this  serves  to  excite  the  fierce  draught  which  is  required  in  order 
that  the  necessary  heat  may  be  developed  by  the  very  small  furnace.  The 
two  cylinders  work  cranks  at  right  angles  to  each  other,  so  that  one  may  be 
in  full  action  when  the  other  is  at  its  dead  point. 

A  locomotive  such  as  that  shown  in  the  figure  is  called  an  outside 
cylinder  engine,  on  account  of  the  position  of  its  cylinders.  In  England 
many  engines  have  cylinders  placed  inside  the  frames,  which  are  then  called 
inside  cylinder  locomotives.  In  express  engines  the  cylinders  frequently 
drive  only  one  very  large  pair  of  wheels,  as  is  shown  in  the  figure.  These 
are  called  driving  wheels,  those  on  the  front  axle  being  leading  wheels  and 
on  the  rear  axle  trailing  wheels.  In  the  case  of  goods  engines,  however  (as 
well  as  in  many  other  instances),  when  less  speed  but  a  greater  pull  is  re- 
quired, two  or  more  pairs  of  wheels  of  the  same  diameter  are  connected 
together  by  coupling  rods,  so  that  two  or  more  axles  may  be  directly  or 
indirectly  actually  driven  by  the  engine.  Such  engines  are  called  coupled 
engines. 

The  action  of  the  engine  upon  the  wheels  may  cause  them  either  to  slip 
round  on  the  rails  (in  which  case  the  engine,  of  course,  does  not  move 
onwards)  or  to  roll  on  them  in  the  usual  way.  To  prevent  slipping  occurring 
it  is  necessary  to  make  the  friction  between  the  wheels  and  the  rails  as 
great  as  possible.  This  is  done  by  making  as  large  a  proportion  of  the 
whole  weight  as  possible  rest  on  the  driving  or  the  coupled  wheels,  and  also 
— when  bad  weather  causes  the  rails  to  be  greasy  or  otherwise  unusually 
slippery — by  increasing  the  coefficient  of  friction  (47)  between  the  wheels 
and  the  rails  by  pouring  sand  on  the  latter.  All  locomotives  are  furnished 
with  a  sand-box  for  this  purpose. 

The  steam  pressure  in  locomotives  is  greater  than  that  commonly  used 
in  any  other  engines,  being  often  120  to  130  Ibs.  per  square  inch  above  the 
atmosphere.  In  marine  engines  70  to  80  Ibs.  is  e-ften  used,  in  stationary 
engines  seldom  quite  so  much. 


-471]  Various  kinds  of  Steam  Engine.     .  433 

The  following  is  an  explanation  of  the  reference  letters  in  fig.  393  : — A, 
the  main  steam-pipe,  conveying  steam  to  the  cylinder  F,  in  which  works  a 
piston  P,  driving  the  crank  M  through  the  connecting  rod  K,  rr  are  the 
piston-rod  guides,  V  the  stuffing-box.  The  exhaust  steam  is  discharged 
through  the  pipe  E.  (It  will  be  remembered  that  the  cylinder  and  all  this 
gear  are  duplicated  on  the  other  side  of  the  engine.)  D  Z  is  the  outer  fire- 
box and  X  the  barrel  of  the  boiler,  both  covered  with  felt  and  wood  or  sheet 
iron  to  prevent  loss  of  heat  by  radiation.  The  small  tubes  are  seen  at  a, 
Y  is  the  smoke-box,  and  Q  the  chimney  or  funnel.  TT  are  the  springs 
which  transmit  the  weight  of  the  frame  to  the  axle-boxes.  Of  the  smaller 
details,  G  I  is  the  arrangement  for  closing  or  opening  the  steam-admission 
valve,  B£C  the  reversing  gear,  RR  feed-water  pipes,  N  coupling  rod  for 
attaching  tender  and  rest  of  train,  e  i  safety  valves,  g  whistle,  m  steps,  n 
water  gauge,  t  cocks  for  blowing  water  out  'of  cylinders,  H  cock  for  blowing 
out  boiler  when  necessary. 

It  is  perhaps  hardly  necessary  to  explain  that  the  breaking  away  of  part 
of  the  fire-box,  cylinder,  etc.,  is  done  in  the  drawing  only  for  the  sake  of 
showing  clearly  the  internal  construction. 

471.  Various  kinds  of  steam  engine. — Three  types  of  steam  engine 
have  been  described  ;  the  Cornish  engine,  the  ordinary  horizontal  engine, 
and  the  locomotive  engine.  Others  ought  to  be  mentioned,  although  they 
cannot  be  here  described  in  detail.  Compound  engines  are  those  in  which 
the  steam  is  first  used  in  the  ordinary  way  in  one  cylinder  and  then  trans- 
ferred— of  course  at  a  comparatively  low  pressure — to  another  cylinder  and 
used  in  it  before  being  sent  away  to  the  condenser.  This  type  is  practically 
universal  for  marine  purposes,  and  is  very  common  for  stationary  engines. 
Its  main  advantage  is  a  thermodynamic  one.  In  an  ordinary  engine  the 
cylinder  walls  are  exposed  alternately  to  the  hot  steam  from  the  boiler 
and  the  cool  vapour  passing  to  the  condenser.  The  latter  so  reduces  the 
temperature  of  the  iron,  that  when  the  first  rush  of  fresh  steam  comes  into 
the  cylinder,  much  of  it  is  immediately  condensed  on  the  cool  metal,  and  an 
enormous  quantity  of  heat  is  thereby  lost.  By  passing  the  steam  through 
an  intermediate,  or  low-pressure,  cylinder  on  its  way  to  the  condenser,  the 
sides  of  the  first  or  high-pressure  cylinder  are  never  exposed  to  condenser 
temperature,  but  only  to  that  of  the  steam  as  it  passes  to  the  low-pressure 
cylinder  ;  they  therefore  are  not  so  much  cooled,  and  the  loss  of  steam  by 
condensation  on  them  is  very  much  reduced.  There  is  no  mechanical  gain, 
as  has  sometimes  been  stated,  in  the  use  of  two  cylinders  instead  of  one. 

Sometimes  the  cylinder  of  an  engine  is  inclosed  in  a  second,  slightly 
larger,  cylinder,  and  fresh  steam  at  boiler  pressure  admitted  to  the  annular 
space  so  formed  outside  the  working  cylinder.  The  object  of  this  is  to  re- 
duce still  further  the  condensation  in  the  cylinder  just  alluded  to.  Such  an 
engine  is  said  to  be  steam-jacketed. 

A  surface-condensing  engine  is  one  in  which  the  steam  is  condensed  by 
contact  with  the  surface  of  a  number  of  small  tubes  through  which  cold 
water  is  kept  continually  circulating  without  being  itself  actually  mixed  with 
the  condensing  water.  By  this  arrangement  the  condensed  steam  is  kept 
by  itself,  and  being  distilled  water  it  can  be  used  very  advantageously  to  feed 
the  boiler  again.  Compound  marine  engines  are  almost  invariably  surface- 

F  F 


434  On  Heat.  [471- 

condensing.  In  this  case  the  air  pump  only  takes  away  the  condensed 
steam,  a  separate  pump,  called  a  circulating  pump,  being  used  to  force  the 
condensing  water  through  the  tubes. 

Engines  without  any  condenser,  like  that  shown  in  fig.  390,  in  which  the 
steam  is  exhausted  directly  into  the  atmosphere  after  it  has  done  its  work, 
are  often  called  high-pressure  engines,  but  high  pressures  (of  So  to  90  pounds 
per  square  inch)  are  now  frequently  used  in  condensing  engines,  so  that  the 
name  may  be  somewhat  misleading. 

In  such  an  engine  as  is  shown  in  fig.  390  we  have  seen  that  the  governor 
keeps  the  speed  constant,  by  closing  or  opening  an  exterior  valve  through 
which  the  steam  passes  on  its  way  to  the  main  valve.  An  artificial  resist- 
ance is  in  this  way  opposed  to  the  passage  of  the  steam,  by  increasing 
which  the  pressure  can  be  reduced,  and  therefore  the  work  done  by  the 
steam,  so  that  the  engine  will  not  run  too  fast  if  the  resistance  to  its  motion 
be  diminished  (as  by  the  disconnecting  of  some  of  the  machines  it  is  driving, 
etc.).  The  actual  weight  of  steam  passing  into  the  cylinder  at  each  stroke 
remains  unchanged,  but  the  amount  of  tiseful  work  the  steam  can  do  is 
diminished  artificially  by  giving  it  some  useless  work  to  do  in  addition,  in 
forcing  its  way  through  a  constricted  passage.  This  is  now  known  to  be  a 
wasteful  way  of  controlling  speed.  In  modern  engines,  therefore,  the 
governor  is  frequently  made  to  act  by  regulating  the  quantity  of  steam  ad- 
mitted by  each  stroke,  and  thus  making  the  consumption  of  steam  as  nearly 
as  possible  proportional  to  the  work  done.  Engines  so  arranged,  of  which 
the  Corliss  engine  is  one  of  the  best-known  examples,  are  said  to  be  fitted 
with  automatic  cut-off  gear. 

There  is  a  popular  misconception,  that  somehow  or  other  work  is  lost  in 
an  engine  of  the  ordinary  type  between  the  piston  and  the  crank,  the  latter 
receiving  less  work  than  is  done  on  the  former  in  consequence  of  the  nature 
of  the  mechanism  connecting  them.  It  is  probably  unnecessary  to  point 
out  here  the  fallacy  of  this  notion,  but  it  has  received  sufficient  acceptance 
to  lead  to  the  invention  of  a  host  of  rotary  engines,  in  which  it  is  endeavoured 
to  obtain  the  desired  rotary  motion  in  a  somewhat  more  direct  fashion. 
Reuleaux  has  shown  that  in  almost  every  case  the  mechanisms  used  in  the 
rotary  engines  are  the  same  as  those  of  ordinary  engines,  although  disguised 
in  form,  so  that  the  idea  of  mechanical  advantage  is  doubly  a  mistake,  while 
in  almost  every  case  the  rotary  engines  possess  such  grave  mechanical 
defects  that  none  of  them  have  practically  come  into  use. 

472.  Work  of  an  engine.  Horse-power. — The  unit  of  work  by  which 
the  performance  of  an  engine  is  measured  is  in  this  country  always  the  foot- 
pound. The  number  of  foot-pounds  of  work  done  by  the  engine  in  any 
given  time  is  equal  to  the  average  effective  pressure  upon  its  piston  during 
that  time,  multiplied  by  th,e  total  distance  through  which  the  piston  has 
moved  under  that  pressure.  By  average  effective  pressure  is  meant  the 
average  value  of  the  difference  between  the  pressures  on  its  two  sides. 
Taking  the  time  as  one  minute,  this  quantity  of  work  in  foot-pounds  is 
equal  to : — 

Area  of  piston  x  mean  intensity  of  pressure  on  piston  x  length  of  stroke 
x  number  of  strokes  per  minute. 

The  stroke  must  be  taken  in  feet.     If  the  area  is  in  square  feet,  the 


-473]  Indicator.     Brake.  435 

pressure  must  be  in  pounds  per  square  foot ;  if  the  area  is  in  square  inches, 
the  pressure  must  be  in  pounds  per  square  inch.  If  the  strokes  are  double 
strokes,  each  corresponding,  that  is,  to  one  whole  revolution  of  the  shaft,  the 
length  of  stroke  must  be  multiplied  by  2.  To  find,  for  example,  the  work 
done  in  one  minute  by  an  engine  with  cylinder  16  inches  diameter  and  24 
inches  stroke,  making  50  (double)  strokes  per  minute  with  a  mean  pressure 
of  52  pounds  per  square  inch,  we  have 

(82  x  3-1416)  x  52  x  f  2A^L\  x  50  =  2,091,000 ft.-lbs. 

The  rate  at  which  an  engine  does  work  is  often  measured  in  horse-power  of 
33,000  ft.-lbs.  per  minute,  an  arbitrary  unit  supposed  to  represent  the  maxi- 
mum rate  at  which  work  could  actually  be  done  by  a  horse.  In  the  case 

supposed  the  horse-power  would  be  -Jz2_!___  =  63-4. 

33,000 

On  the  Continent  the  unit  of  work  is  a  kilogrammetre,  which  is  very 
closely  equal  to  7|  ft.-lbs.  The  horse-power  used  abroad,  of  75  kilo- 
grammetres  per  second,  is  nearly  2  per  cent,  smaller  than  that  in  use  in  this 
country. 

473.  Indicator.  Brake. — By  the  expression  work  done  by  an  engine  we 
may  mean  either  of  two  things,  viz. — the  total  work  done  by  the  engine,  or 
what  is  called  its  useful,  or  effective,  work.  The  total  work  is  the  actual  work 
done  by  the  steam  on  the  piston  and  obtained  by  calculation,  as  described 
in  the  last  paragraph.  The  useful  work  is  what  remains  of  this  total  after 
deduction  has  been  made  of  the  work  necessary  to  drive  the  engine  itself 
against  its  own  frictional  resistances.  The  total  work  of  an  engine  is  mea- 
sured by  means  of  an  apparatus  called  an  indicator,  invented  by  Watt,  of 
which  fig.  394  shows  one  of  the  most  recent  forms  (Richard's),  omitting  a 
number  of  constructional  details.  The  steam-engine  indicator  consists  of  a 
small  cylinder  A,  half  a  square  inch  in  area,  in  which  works  a  piston  B,  the 
under  side  of  which  can  be  put  into  full  communication  with  the  cylinder 
of  the  engine  by  opening  the  cock  C.  Between  the  top  side  of  the  piston 
and  the  under  side  of  the  cylinder-cover  is  a  spiral  spring.  The  motion 
of  the  piston-rod  is  transferred  to  a  parallel  motion  DD,  and  so  causes  a 
point  E  to  move  in  a  straight  line  up  and  down,  its  stroke  being  about 
four  times  as  great  as  that  of  the  small  piston.  The  indicator  is  fixed  on  to 
the  cylinder  of  the  steam  engine  near  one  end,  so  that  when  the  cock  C  is 
opened,  there  is  the  same  pressure  of  steam  on  the  indicator  piston  as  on  the 
engine  piston.  This  pressure  forces  up  the  piston,  and  the  amount  of  com- 
pression of  the  spring  so  caused  is  proportionate  to  the  pressure  causing  it. 
The  upward  motion  of  E,  therefore,  is  proportional  to  the  steam  pressure. 
In  front  of  E  is  a  vertical  drum  F  on  which  a  strip  of  paper  can  be  fixed, 
and  this  drum  is  caused  to  rotate  about  its  axis  by  attaching  the  cord  G 
to  any  suitable  part  of  the  engine.  The  paper  thus  moves  horizontally 
under  the  pencil,  with  a  motion  proportional  to  the  stroke  of  the  engine, 
while  the  pencil  moves  up  and  down  on  the  paper  with  a  motion  proportional 
to  the  steam  pressure  on  the  piston.  The  two  motions  occurring  simul- 
taneously, the  pencil  traces  on  the  paper  a  curve  whose  horizontal  and 
vertical  ordinates  are  proportional  to  the  two  quantities  just  named,  and 

F  F2 


On  Heat.  [473- 

whpse  area  is  therefore  proportional  to  the  product  of  these  quantities  or 
which  is  the  same  thing,  to  the  work  done  by  the  piston  as  defined  in  'the 
last  paragraph.  The  curve  is  called  an  indicator  card,  or  indicator  diagram 


Fig.  39.S- 


Fig.  394- 


Fig.  396. 


and  while  its  whole  area  shows  the  whole  work  done  by  the  steam,  its  form 
shows  the  engineer  what  is  happening  within  the  cylinder  at  each  point  of 
the  stroke,  which  he  may  often  require  to  know. 

Figs.  395  and  396  show  two  forms  of  indicator  diagram.  The  curves 
themselves,  as  drawn  by  the  indicators,  are  lettered  ABCD.  Beside  them 
a  scale  of  pressure  in  atmospheres  is  placed.  In  fig.  395  the  steam  is  ex- 
panded about  seven  times,  and  the  back  pressure  is  about  f  of  an  atmo- 
sphere, the  pressure  during  admission  being  five  atmospheres.  The  engine 
is  a  condensing  one,  and  the  diagram  is  fairly  good.  Fig.  396  is  for  a  non- 
condensing  engine,  the  back  pressure  being  above  that  of  the  atmosphere. 
The  steam  is  cut  off  (at  B)  only  at  about  f  of  the  stroke,  so  that  it  is  not 
working  economically,  and  from  the  roundness  of  its  corners  the  diagram 
would  be  considered  a  poor  one. 

The  useful  work  of  an  engine  is  measured  by  an  entirely  different  piece 
of  apparatus,  called  a  dynamometer.  This  is  used  in  many  forms,  but  fig. 
397  shows  the  principle  upon  which  the  majority  act.  The  apparatus 
shown  in  the  figure  is  known  as  a  Fronts  friction  brake.  A  is  the  shaft, 
the  usual  work  transmitted  by  which  we  require  to  find.  Upon  the  shaft  is 
a  fixed  pulley  B,  embraced  by  two  blocks  Bx  and  B2,  which  can  be  tightened 
up  by  the  screws  at  Cx  and  C2.  To  the  lower  block  is  fixed  a  lever  D,  from 
which  hangs  a  weight,  and  which  has  at  its  extremity  a  small  pointer  work- 
ing against  a  short  scale  F.  If  such  an  apparatus  be  set  in  motion  by 
turning  the  shaft  A,  one  of  two  things  must  happen  ;  either  the  pulley  must 


-474] 


Efficiency  of  Heat  Engines. 


437 


slip  round  in  the  blocks,  or  it  must  so  grip  them  as  to  carry  both  them  and 
the  lever  D  round  its  own  axis.  The  moment  of  resistance  to  the  former  is 
r  F,  if  r  be  the  radius  of  the  pulley  and  F  the  frictional  resistance  at  its 


Fig.  397- 

periphery;  that  of  the  latter  is  RW,  where  R  is  the  radius  of  the  weight 
and  W  the  weight  itself.  In  practice  the  screw  C2  is  loosened  just  suffi- 
ciently to  keep  the  weight  just  lifted  from  the  ground,  while  the  pulley  is 
always  turning  round  in  the  blocks,  so  that,  therefore, 


The  work  done  at  the  brake  per  minute  is  equal  to  the  frictional  resistance 
multiplied  by  the  distance  through  which  it  is  overcome  in  the  same  time, 
or,  if  n  be  the  number  of  revolutions  per  minute, 


It  is  therefore  just  the  same  as  if  a  resistance  =  W  were  continually  being 
overcome  at  the  periphery  of  a  wheel  of  radius  R,  making  n  turns  per  minute. 
As  the  values  of  all  the  quantities  in  the  expression  2?rRW/2  are  very  readily 
determined,  it  will  be  seen  that  this  brake  affords  a  very  simple  way  of 
measuring  the  net  work  transmitted  through  the  shaft  of  an  engine. 

™,         ,.    useful  work  work  shown  by  brake     .        n    ,  ,,       ^  . 

The  ratio  -  -  -  —  .  or  -  -  -  -  —  £-—  -  is  called  the  efficiency 
total  work          work  shown  by  indicator 

of  the  engine  as  a  machine,  or  its  mechanical  efficiency.  It  is  often  as  much 
as  O'85,  and  sometimes  even  higher  than  0*9  or  90  per  cent.,  being  generally 
greatest  in  large  engines. 

474.  Efficiency  of  heat  engines.  —  There  is  another  ratio  of  efficiency 
connected  with  the  steam  engine,  namely  the  ratio 

Total  work  done  by  engine 
Total  heat  expended 

which  is  called  the  efficiency  of  the  engine  as  a  heat  engine  or  its  thermo- 
dynamic  efficiency.  If  T,  and  T2  be  respectively  the  absolute  temperatures 
(496^  of  the  steam  and  the  feed  water  in  any  engine,  then  it  can  be  shown 


On  Heat.  [474- 

that  such  an  engine,  if  working  quite  perfectly,  could  transform  no  more 

(•"P  T  \ 
— !— — ? )  of  the  heat  which  it  receives  into  work.    This  fraction  in  the 
ii     ' 

case  of  a  steam  engine  is  seldom  more  than  about  0*25.  The  value  of  the 
actual  efficiency  of  the  engine  is  often  from  crio  to  0-14  ;  while,  therefore, 
an  ordinary  steam  engine,  with  such  an  efficiency,  turns  into  work  only  from 
Y1^  to  \  of  the  whole  heat  it  receives,  yet  it  may  be  turning  into  work  £  or 
more  of  the  whole  heat  which  it  could  possibly  transform  into  work  if  it 
were  perfect. 

To  increase  the  economy  of  steam  engines  we  require  to  make  the  value 

of  ( — LZ — ?J  larger.     This  is  done  either  by  raising  Tx  or  by  lowering  T2,  or 
V      Ll     / 

both.  The  chief  difficulty  is  that  we  cannot  raise  Tl  without  increasing  the 
steam  pressure,  which  it  is  often  not  convenient  to  do,  while  we  cannot  lower 
T2  below  such  a  temperature,  50°  to  60°  F.,  as  can  readily  be  obtained 
naturally,  at  all  seasons  of  the  year. 

475.  Hot-air  engines. — The  difficulty  as  to  T1  just  mentioned  is  got  over 
by  the  use  of  some  fluid  whose  pressure  is  not  a  function  of  its  tempe- 
rature, and   naturally  air  is   the   most   convenient  fluid   for  the  purpose. 
Many  *  hot-air '  engines  have  been  designed,  and  some  have  found  a  con- 
siderable measure  of  success  commercially,  as  Rider's,  Hock's,  and  Leh- 
mann's.    In  all  cases  the  engines  consist  essentially  of  one  (or  two)  chambers 
placed  so  that  one  end  can  be  heated  by  a  furnace  and  the  other  cooled  by 
a  refrigerator.     The  air  is  compelled  to  move  from  the  cold  space  to  the  hot 
and  back  again  continually.     When  hot  it  is  allowed  to  expand  and  push 
forward  a  piston,  when  cold  it  is  compressed  by  pushing  back  the  piston 
again  to  its  original  position.     The  difference  between  these  two  quantities 
of  work  is  the  whole  work  done  by  the  engine.     By  making  TT  a  very  high 

temperature,  the  theoretical  efficiency  f— lZ — ?j  of  an  air  engine  maybe 

\     Ll     / 

made  much  higher  than  that  of  a  steam  engine.  But  it  is  so  much  more 
difficult  to  attain  the  theoretical  efficiency  in  the  air  than  in  the  steam 
engine,  that  its  actual  efficiency  is  generally  much  lower  than  that  of  a 
steam  engine.  There  are  constructive  difficulties  connected  with  the  hot- 
air  chambers,  and  with  the  regulation  of  the  speed,  and  these,  as  well  as  with 
the  large  bulk  of  most  air  engines  in  proportion  to  their  power,  have  stood 
greatly  in  the  way  of  their  development.  No  doubt,  however,  much  more 
improvement  would  have  taken  place  in  these  engines  had  not  gas  engines 
come  into  prominence  of  late  years  and  proved  much  more  convenient. 

476.  Gas  engines. — Gas  engines,  like  steam  engines  and  air  engines,  are 
heat  engines,  but  in  them  the  working  fluid  is  ordinary  coal  gas  mixed  with 
air,  in  the  proportion  of  about  I  to  1 1  by  volume.     The  principle  of  action 
is  very  simple  : — The  explosive  mixture  after  being  drawn  into  the  cylinder 
is  set  light  to,  the  heat  generated  by  the  very  rapid  combustion  which 
we  call  an  explosion  causes  the  mixed  gases  to  expand  and  drive  forward 
the  piston.     The  great  difficulty  for  many  years  was  that  the  explosion  was 
so  rapid  that  the  comparatively  slow-going  piston  could  not  keep  up  with  it, 
and  the  greater  part  of  the  energy  of  the  explosion  was  lost  by  radiation  and 
conduction.     In  the  more  modern  gas  engines,  however  (Otto's  and  Clerk's 


_476]  Gas  Engines.  439 

and  others),  this  difficulty  is  got  over  by  compressing  the  charge  before 
igniting  it,  a  treatment  which  is  found  to  decrease  very  much  the  rapidity 
of  the  explosion  and  so  greatly  increase  the  actual  efficiency  of  the  engine. 
Fig.  398  shows  the  principal  parts  of  an  Otto  'Silent'  gas  engine,  as  now  made. 
A  is  the  cylinder,  open  at  front  and  single-acting,  in  which  works  a  deep 
piston  F,  driving  a  crank  in  the  usual  manner.  The  cylinder  is  surrounded 
by  a  water  jacket,  to  prevent  it  from  getting  too  hot.  At  the  back  of  the 
cylinder  is  a  slide  valve  B,  worked  by  a  cam,  not  shown  in  drawing,  on  the 


Fig.  398. 

lay  shaft  G.  The  valve  B  is  kept  up  against  its  face  by  spiral  springs  E. 
D  is  a  chamber  in  which  a  small  jet  of  gas  for  igniting  the  mixture  is  con- 
tinually burning.  Cl  is  the  cock  for  admission  of  gas,  and  C.2  an  india- 
rubber  bag  to  equalise  the  gas  pressure.  The  working  of  the  engine  is  as 
follows  : — the  piston  moves  from  left  to  right  and  draws  into  the  cylinder  the 
explosive  mixture.  On  the  return  stroke  it  compresses  the  mixture  to  about 
3  atmospheres.  The  igniting  flame  is  then  allowed  to  come  for  an  instant 
into  contact  with  the  compressed  mixture,  which  burns  very  rapidly  (or 
explodes  slowly,  whichever  expression  be  preferred)  and  pushes  the  piston 
forward  again,  the  pressure  rising  to  10  or  12  atmospheres.  On  the  next 
return  stroke  the  burnt  gases  are  pushed  out  through  the  opening  shown  in 
the  drawing,  and  the  process  begins  again  once  more.  There  are  many 
ingenious  arrangements  about  this  type  of  engine  which  our  space  will  not 
allow  us  to  mention  in  detail.  It  must  suffice  to  say  that  the  engine  has 
proved  distinctly  economical,  and  has  such  very  great  conveniences  as  may 
fairly  account  for  the  rapid  way  in  which  its  use  (and  that  of  other  gas 
engines)  has  extended. 

In  conclusion,  it  is  as  well  to  point  out  that,  as  long  as  they  work  between 
the  same  temperatures,  there  is  no  difference  between  steam,  air,  and  gas 
engines  as  to  theoretical  economy.  The  last  two  gain  by  the  possibility  of 
using  higher  limits  of  temperature  than  can  be  employed  in  a  steam  engine, 
but,  so  far,  have  lost  by  constructive  and  mechanical  difficulties  which  pre- 
vent their  theoretical  efficiency  from  being  attained. 


440  On  Heat.  [477- 


CHAPTER  XI. 

SOURCES  OF  HEAT  AND  COLD. 

477.  Different  sources    of  beat. — The   following  different  sources   of 
heat  may  be  distinguished  :  i.  the  mechanical  sources,  comprising  friction, 
percussion,  and  pressure  ;  ii.  the  physical  sources — that  is,  solar  radiation, 
terrestrial  heat,  molecular  actions,  change   of  condition,  and   electricity ; 
iii.  the  chemical  sources^  or  molecular  combinations,  and  more  especially 
combustion. 

In  what  follows  it  will  be  seen  that  heat  may  be  produced  by  reversing 
its  effects  ;  as,  for  instance,  when  a  liquid  is  solidified  or  a  gas  compressed 
'(479)  j  though  it  does  not  necessarily  follow  that  in  all  cases  the  reversal  of 
its  effects  causes  heat  to  be  produced — instead  of  it,  an  equivalent  of  some 
other  form  of  energy  may  be  generated. 

In  like  manner  heat  may  be  forced  to  disappear,  or  cold  be  produced 
when  a  change  such  as  heat  can  produce  is  brought  about  by  other  means, 
as  when  a  liquid  is  vaporised  or  a  solid  liquefied  by  solution  •  though  here 
also  the  disappearance  of  heat  is  not  always  a  necessary  consequence  of 
the  production,  by  other  means,  of  changes  such  as  might  be  effected  by 
heat. 

MECHANICAL  SOURCES. 

478.  Heat  due  to  friction. — The  friction  of  two  bodies,  one  against  the 
other,  produces  heat,  which  is  greater  the  greater  the  pressure  and  the  more 
rapid  the  motion.     For  example,  the  axles  of  carriage  wheels,  by  their  fric- 
tion against  the  boxes,  often  become  so  strongly  heated  as  to  take  fire.     By 
rubbing  together  two  pieces  of  ice  in  a  vacuum  below  zero,  Sir  H.  Davy 
partially  melted  them.     In  boring  a  brass  cannon  Rumford  found  that  the 
heat  developed  in  the  course  of  2^-  hours  was  sufficient  to  raise  263  pounds 
of  water  from  zero  to  100°,  which  represents  2,650  thermal  units  (447).    Mayer 
raised  water  from  12°  to  13°  by  shaking  it.    At  the  Paris  Exhibition,  in  1855, 
Beaumont  and  Mayer  exhibited  an  apparatus,  which  consisted  of  a  wooden 
cone  covered  with  hemp,  and  moving  with  a  velocity  of  400  revolutions  in  a 
minute,  in  a  hollow  copper  cone,  which  was  fixed  and  immersed  in  the  water 
of  an  hermetically-closed  boiler.     The  surfaces  were  kept  covered  with  oil. 
By  means  of  this  apparatus  88  gallons  of  water  were  raised  from  10  to  130 
degrees  in  the  course  of  a  few  hours. 

In  the  case  of  flint  and  steel,  the  friction  of  the  flint  against  the  steel 
raises  the  temperature  of  the  metallic  particles,  which  fly  off,  heated  to  such 
an  extent  that  they  take  fire  in  the  air. 

The  luminosity  of  aerolites  is  considered  to  be  due  to  their  friction 
against  the  air,  and  to  their  condensation  of  the  air  in  front  of  them  (479), 
their  velocity  attaining  as  much  as  1 50  miles  in  a  second. 


-479]  Heat  due  to  Pressure  and  Percussion.  441 

Tyndall  has  devised  an  experiment  by  which  the  great  heat  developed  by 
friction  is  illustrated  in  a  striking  manner.  A  brass  tube  (fig.  399),  about 
7  inches  in  length  and  f  of  an  inch  in  diameter,  is  fixed  on  a  small  wheel. 
By  means  of  a  cord  passing  round  a  much  larger  wheel,  this  tube  can  be 
rotated  with  any  desired  velocity.  The  tube  is  three  parts  full  of  water,  and 
is  closed  by  a  cork.  In  making  the  experiment,  the  tube  is  pressed  between 
a  wooden  clamp,  while  the  wheel  is  rotated  with  some  rapidity.  The  water 
rapidly  becomes  heated  by  the  friction,  and  its  temperature  soon  exceeding 
the  boiling-point,  the  cork  is  projected  to  a  height  of  several  yards  by  the 
•elastic  force  of  the  steam. 

479.  Heat  due  to  pressure  and  percussion. — If  a  body  be  so  com- 
pressed that  its  density  is  increased,  its  temperature  rises  according  as  the 


Fig.  399- 

volume  diminishes.  Joule  has  verified  this  in  the  case  of  water  and  of  oil, 
which  were  exposed  to  pressures  of  15  to  25  atmospheres.  In  the  case  of 
water  at  i'2°C,  increase  of  pressure  caused  lowering  of  temperature — a  result 
which  agrees  with  the  fact  that  water  contracts  by  heat  at  this  temperature. 
Similarly,  when  weights  are  laid  on  metallic  pillars,  heat  is  evolved,  and 
absorbed  when  they  are  removed.  So  in  like  manner  the  stretching  of  a 
metallic  wire  is  attended  with  a  diminution  of  temperature. 

The  production  of  heat  by  the  compression  of  gases  is  easily  shown  by 
means  of  the  pneumatic  syringe  (fig.  400).  This  consists  of  a  glass  tube 
with  thick  sides,  closed  hermetically  by  a  leather  piston.  At  the  bottom  of 
this  there  is  a  cavity  in  which  a  small  piece  of  cotton,  moistened  with 
•ether  or  bisulphide  of  carbon,  is  placed.  The  tube  being  full  of  air,  the 
piston  is  suddenly  plunged  downwards ;  the  air  thus  compressed  disengages 
so  much  heat  as  to  ignite  the  cotton,  which  is  seen  to  burn  when  the  piston 
is  rapidly  withdrawn.  The  ignition  of  the  cotton  in  this  experiment  indicates 
a  temperature  of  at  least  300°. 

The  elevation  of  temperature  produced  by  the  compression  in  the  above 
experiment  is  sufficient  to  effect  the  combination,  and  therefore  the  detona- 
tion, of  a  mixture  of  hydrogen  and  oxygen. 

A  curious  application  of  the  principle  of  the  pneumatic  syringe  is  met 


442  On  Heat.  [479- 

with  in  the  American  powder  ram  for  pile-driving.  On  the  pile  to  be  driven 
is  fixed  a  powder  mortar,  above  which  is  suspended  at  a  suitable  distance  an 
iron  rammer,  shaped  like  a  gigantic  stopper,  which  just  fits  in  the  mortar. 
Gunpowder  is  placed  in  the  mortar,  and  when  the  rammer  is  detached  it 
falls  into  the  mortar,  compresses  the  air,  producing  so  much  heat  that  the 


Fig.  400. 

powder  is  exploded.  The  force  of  the  gases  projects  the  rammer  into  its 
original  position,  where  it  is  caught  by  a  suitable  arrangement ;  at  the  same 
time  the  reaction  of  the  mortar  on  the  pile  drives  this  in  with  far  greater 
force  than  the  fall  of  the  rammer.  After  adding  a  fresh  charge  of  powder, 
the  rammer  is  again  allowed  to  fall,  again  produces  heat,  explosion,  and  so 
forth,  so  that  the  driving  is  effected  in  a  surprisingly  short  time. 

Percussion  is  also  a  source  of  heat.  In  firing  shot  at  an  iron  target,  a 
sheet  of  flame  is  frequently  seen  at  the  moment  of  impact ;  and  Sir  J.  Whit- 
worth  has  used  iron  shells  which  are  exploded  by  the  concussion  on  striking 
an  iron  target.  A  small  piece  of  iron  hammered  on  the  anvil  becomes  very 
hot.  The  heat  is  not  simply  due  to  an  approximation  of  the  molecules — 
that  is,  to  an  increase  in  density — but  arises  from  a  vibratory  motion  im- 
parted to  them ;  for  lead,  which  does  not  increase  in  density  by  hammering, 
nevertheless  becomes  heated. 

The  heat  due  to  the  impact  of  bodies  is  not  difficult  to  calculate.  When- 
ever a  body  moving  with  a  velocity  v  is  suddenly  arrested  in  its  motion, 
its  vis  viva  is  converted  into  heat.  This  holds  equally  whatever  be  the 
cause  to  which  the  motion  is  due  :  whether  it  be  that  acquired  by  a  stone 
falling  from  a  height,  by  a  bullet  fired  from  a  gun,  or  the  rotation  of  a 
copper  disc  by  means  of  a  turning-table.  The  vis  viva  of  any  moving  body 

is  expressed  by  1J^-  or  in  foot-pounds  by  ^— -,  where  p  is  the  weight  in 

O 

pounds,  v  the  velocity  in  feet  per  second,  and  g  is  about  32  (29) ;  and  if  the 
whole  of  this  be  converted  into  heat,  its  equivalent  in  thermal  units  will  be 

—     Suppose,  for  instance,  a  lead  ball  weighing  a  pound  be  fired 

«?>          *3V 

from  a  gun,  and  strike  against  a  target,  what  amount  of  heat  will  it  produce  ? 
We  may  assume  that  its  velocity  will  be  about  1,600  feet  per  second  ;  then 

its  vis  viva  will  be  — =  40,000  foot-pounds.     Some  of  this  will  have 

2  x  32 

been  consumed  in  producing  the  vibrations  which  represent  the  sound  of  the 
shock,  some  of  it  also  in  its  change  of  shape  ;  but  neglecting  these  two,  as 
being  small,  and  assuming  that  the  heat  is  equally  divided  between  the  ball 


-480]  Solar  Radiation.  443 

and  the  target,  then,  since  40,000  foot-pounds  is  the  equivalent  of  287 
thermal  units,  the  share  of  the  ball  will  be  14*3  thermal  units  ;  and  if,  for 
simplicity's  sake,  we  assume  that  its  initial  temperature  is  zero,  then,  taking 
its  specific  heat  at  0*0314,  we  shall  have 

i  x  0-0314  x  /  =  14-3  or  ^  =  457°, 

which  is  a  temperature  considerably  above  that  of  the  melting  point  of 
lead  (338). 

By  allowing  a  lead  ball  to  fall  from  various  heights  on  an  iron  plate,  both 
experience  an  increase  of  temperature  which  may  be  measured  by  the 
thermopile  ;  and  from  these  increases  it  may  be  easily  shown  that  the  heat 
is  directly  proportional  to  the  height  of  fall,  and  therefore  to  the  square  of 
the  velocity. 

By  similar  methods  Mayer  has  calculated  that  if  the  motion  of  the  earth 
were  suddenly  arrested  the  temperature  produced  would  be  sufficient  to  melt 
and  even  volatilise  it ;  while,  if  it  fell  into  the  sun,  as  much  heat  would  be 
produced  as  results  from  the  combustion  of  5,000  spheres  of  carbon  the  size 
of  our  globe. 

PHYSICAL   SOURCES. 

480.  Solar  radiation. — The  most  intense  of  all  sources  of  heat  is  wthe 
sun.  Different  attempts  have  been  made  to  determine  the  quantity  of  heat 
which  it  emits.  Pouillet  made  the  first 
accurate  measurements  of  the  heat  of 
the  sun  by  means  of  an  instrument 
called  the  pyroheliometer.  The  form 
represented  in  fig.  401  consists  of  a 
flat  cylindrical  metal  box  3  inches  in 
diameter  and  £  an  inch  deep,  contain- 
ing a  known  weight  of  water.  To  it  is 
fitted  a  metal  tube  which  contains  the 
stem  of  a  delicate  thermometer,  the 
bulb  of  which  dips  in  the  liquid  of  the 
box,  being  fitted  by  means  of  a  cork. 
The  tube  works  in  two  collars,  so  that 
by  means  of  a  milled  head  it  can  be 
turned,  and  with  it  the  vessel,  and  the 
liquid  thus  be  uniformly  mixed.  The 
face  of  the  vessel  is  coated  with  lamp- 
black, and  is  so  adjusted  that  the 
sun's  rays  fall  perpendicularly  upon  it. 
This  can  be  ascertained  by  observing 
when  the  shadow  exactly  covers  the 
lower  disc  which  is  fitted  to  the  same 
axis. 

The   instrument  was   exposed  for 
five   minutes   at  a  time  to  the   sun's  Fig.  4oi. 

rays ;  knowing  the  weight  of  the  water,  its  rise  in  temperature  could  be  easily 
calculated  (449).  Corrections  were  necessary  for  the  heat  reflected  by  the 
lampblack,  and  also  for  the  heat  absorbed  by  the  air. 


444  On  Heat.  [480- 

Pouillet  calculated  from  the  results  of  experiments  with  this  apparatus 
that  if  the  total  quantity  of  heat  which  the  earth  receives  from  the  sun  in  the 
course  of  a  year  were  employed  to  melt  ice,  it  would  be  capable  of  melting  a 
layer  of  ice  all  round  the  earth  of  35  yards  in  thickness.  The  heat  emitted 
by  the  sun  is  equal  to  that  produced  by  the  combustion  of  1,500  pounds  of 
coal  in  an  hour  on  each  square  foot  of  its  surface.  But  from  the  surface 
which  the  earth  exposes  to  the  solar  radiation,  and  from  the  distance  which 
separates  the  earth  from  the  sun,  the  quantity  of  heat  which  the  earth 
receives  can  only  be  2i881ii00ifl00  of  the  heat  emitted  by  the  sun. 

Faraday  calculated  that  the  average  amount  of  heat  radiated  in  a  day  on 
each  acre  of  ground  in  the  latitude  of  London  is  equal  to  that  which  would 
be  produced  by  the  combustion  of  sixty  sacks  of  coal. 

The  heat  of  the  sun  cannot  be  due  to  combustion,  for  even  if  the  sun 
consisted  of  hydrogen,  which  of  all  substances  gives  the  most  heat  in  com- 
bining with  oxygen,  it  can  be  calculated  that  the  heat  thus  produced  would 
not  last  more  than  3,000  years.  Another  supposition  is  that  originally  put 
forth  by  Mayer,  according  to  which  the  heat  which  the  sun  loses  by  radiation 
is  replaced  by  the  fall  of  aerolites  against  its  surface.  One  class  of  these  is 
what  we  know  as  shooting  stars,  which  often  appear  in  the  heavens  with 
great  brilliancy,  especially  on  August  14  and  November  15  ;  the  term  meteoric 
stone  or  aerolite  being  properly  restricted  to  the  bodies  which  fall  on  the 
earth.  They  are  often  of  considerable  size,  and  are  even  met  with  in  the 
form  of  dust.  Although  some  of  the  sun's  heat  may  be  restored  by  the 
impact  of  such  bodies  against  the  sun,  the  amount  must  be  very  small,  for 
Sir  W.  Thomson  has  proved  that  a  fall  of  0-3  gramme  of  matter  in  a  second 
on  each  square  metre  of  surface  would  be  necessary  for  this  purpose.  The 
effect  of  this  would  be  that  the  mass  of  the  sun  would  increase,  and  the 
velocity  of  the  earth's  rotation  about  the  sun  would  be  accelerated  to  an 
extent  which  would  be  detected  by  astronomical  observations. 

Helmholtz  considers  that  the  heat  of  the  sun  was  produced  originally  by 
the  condensation  of  a  nebulous  mass,  and  is  kept  up  by  a  continuance  of 
this  contraction.  A  sudden  contraction  of  the  primitive  nebular  mass  of  the 
sun  to  its  present  volume  would  produce  a  temperature  of  28  millions  of 
degrees  Centigrade ;  and  a  contraction  of  jofoo  °f  ^ts  mass  would  be 
sufficient  to  supply  the  heat  radiated  by  the  sun  in  2,000  years.  This  amount 
of  contraction  could  not  be  detected  even  by  the  most  refined  astronomical 
methods. 

481.  Terrestrial  heat. — Our  globe  possesses  a  heat  peculiar  to  it,  which 
is  called  the  terrestrial  heat.  The  variations  of  temperature  which  occur  at 
the  surface  gradually  penetrate  to  a  certain  depth,  at  which  their  influence 
becomes  too  slight  to  be  sensible.  It  is  hence  concluded  that  the  solar  heat 
does  not  penetrate  below  a  certain  internal  layer,  which  is  called  the  layer  of 
constant  annual  temperature ;  its  depth  below  the  earth's  external  surface 
varies,  of  course,  in  different  parts  of  the  globe  ;  at  Paris  it  is  about  30  yards, 
and  the  temperature  is  constant  at  11*8°  C. 

Below  the  layer  of  constant  temperature,  the  temperature  is  observed  to 
increase,  on  the  average,  i°  C.  for  every  90  feet.  The  most  rapid  increase 
is  at  Irkutsk  in  Siberia,  where  it  is  i°  for  20  feet,  and  the  slowest  in  the  mines 
at  Mansfield,  where  it  is  about  i°  C.  for  330  feet.  This  increase  has  been 


—482]          Heat  produced  by  Absorption  and  Imbibition.  445 

verified  in  mines  and  artesian  wells.  According  to  this  at  a  depth  of  3,000 
yards,  the  temperature  of  a  corresponding  layer  would  be  100°,  and  at  a 
depth  of  20  to  30  miles  there  would  be  a  temperature  sufficient  to  melt  all 
substances  which  exist  on  the  surface.  Hot  springs  and  volcanoes  confirm 
the  existence  of  this  central  heat. 

Various  hypotheses  have  been  proposed  to  account  for  the  existence  of 
this  central  heat.  The  one  usually  admitted  by  physicists  is  that  the  earth 
was  originally  in  a  liquid  state  in  consequence  of  the  high  temperature,  and 
that  by  radiation  the  surface  has  gradually  solidified,  so  as  to  form  a  solid 
crust.  The  thickness  of  this  crust  is  not  believed  to  be  more  than  40  to  50 
miles,  and  the  interior  is  probably  still  in  a  liquid  state.  The  cooling  must 
be  very  slow,  in  consequence  of  the  imperfect  conductivity  of  the  crust.  For 
the  same  reason  the  central  heat  does  not  appear  to  raise  the  temperature 
of  the  surface  more  than  i-  of  a  degree. 

482.  Beat  produced  by  absorption  and  Imbibition.—  Molecular  phe- 
nomena, such  as  imbibition,  absorption,  capillary  actions,  are  usually  accom- 
panied by  disengagement  of  heat.  Pouillet  found  that  whenever  a  liquid  is 
poured  on  a  finely-divided  solid,  an  increase  of  temperature  is  produced 
which  varies  with  the  nature  of  the  substances.  With  inorganic  substances, 
such  as  metal,  the  oxides,  the  earths,  the  increase  is  ~  of  a  degree ;  but 
with  organic  substances,  such  as  sponge,  flour,  starch,  roots,  dried  mem- 
branes, the  increase  varies  from  I  to  10  degrees. 

The  absorption  of  gases  by  solid  bodies  presents  the  same  phenomena. 
Dobereiner  found  that  when  platinum,  in  the  fine  state  of  division  known  as 
platinum  black,  is  placed  in  oxygen,  it  absorbs 
many  hundred  times  its  volume,  and  that  the  gas 
is  then  in  such  a  state  of  density,  and  the  tempera- 
ture so  high,  as  to  give  rise  to  intense  combustions. 
Spongy  platinum  produces  the  same  effect.  A  jet 
of  hydrogen  directed  on  it  takes  fire. 

The  apparatus  known  as  Dobereiner 's  Lamp 
depends  on  this  property  of  finely-divided  platinum. 
It  consists  of  two  glass  vessels  (fig.  402).  The 
first,  A,  fits  in  the  lower  vessel  by  means  of  a 
tubulure  which  closes  it  hermetically.  At  the  end 
of  the  tubulure  is  a  lump  of  zinc,  Z,  immersed  in 
dilute  sulphuric  acid.  By  the  chemical  action  of 
the  zinc  on  the  dilute  acid  hydrogen  gas  is  gene- 
rated, which,  finding  no  issue,  forces  the  liquid  out 
of  the  vessel  B  into  the  vessel  A,  so  that  the  zinc 
is  not  in  contact  with  the  liquid.  The  stopper  of 
the  upper  vessel  is  raised  to  give  exit  to  the  air  in 
proportion  as  the  water  rises.  On  a  copper  tube, 
H,  fixed  in  the  side  of  the  vessel  B,  there  is  a  small 
cone,  a,  perforated  by  an  orifice  ;  above  this  there  is  some  spongy  platinum 
in  the  capsule,  c.  As  soon  now  as  the  cock,  which  closes  the  tube,  H,  is 
opened,  the  hydrogen  escapes,  and,  coming  in  contact  with  the  spongy 
platinum,  is  ignited. 

The  condensation  of  vapours  by  solids  often  produces  an  appreciable 


Fig.  402. 


446  On  Heat.  [482- 

increase  of  temperature.  This  is  particularly  the  case  with  humus,  which,  to 
the  benefit  of  plants,  is  warmer  in  moist  air  than  the  air  itself. 

Favre  has  found  that  when  a  gas  is  absorbed  by  charcoal  the  amount  of 
heat  produced  by  the  absorption  of  a  given  weight  of  sulphurous  acid,  or  of 
protoxide  of  nitrogen,  greatly  exceeds  that  which  is  disengaged  in  the  lique- 
faction of  the  same  weight  of  gas  ;  for  carbonic  acid,  the  heat  produced  by 
absorption  exceeds  even  the  heat  which  would  be  disengaged  by  the  solidi- 
fication of  the  gas.  The  heat  produced  by  the  absorption  of  these  gases 
connot,  therefore,  be  explained  by  assuming  that  the  gas  is  liquefied,  or  even 
solidified  in  the  pores  of  the  charcoal.  It  is  probable  that  it  is  in  part  due  to 
that  produced  by  the  liquefaction  of  the  gas,  and  in  part  to  the  heat  due  to 
the  imbibition  in  the  charcoal  of  the  liquid  so  produced. 

The  heat  produced  by  the  changes  of  condition  has  been  already  treated 
of  in  the  articles  Solidification  and  Liquefaction  ;  the  heat  produced  by  elec- 
trical action  will  be  discussed  under  the  head  of  Electricity. 


CHEMICAL   SOURCES. 

483.  Chemical  combination.  Combustion — Chemical  combinations 
are  usually  accompanied  by  a  certain  elevation  of  temperature.  When  these 
combinations  take  place  slowly,  as  when  iron  oxidises  in  the  air,  the  heat 
produced  is  imperceptible  ;  but  if  they  take  place  rapidly,  the  disengagement 
of  heat  is  very  intense.  The  same  quantity  of  heat  is  produced  in  both  cases, 
but  when  evolved  slowly  it  is  dissipated  as  fast  as  formed. 

Combustion  is  chemical  combination  attended  with  the  evolution  of  light 
and  heat.  In  ordinary  combustion  in  lamps,  fires,  candles,  the  carbon  and 
hydrogen  of  the  coal,  or  of  the  oil,  etc.,  combine  with  the  oxygen  of  the  air. 
But  combustion  does  not  necessarily  involve  the  presence  of  oxygen.  If 
either  powdered  antimony  or  a  fragment  of  phosphorus  be  placed  in  a  vessel 
of  chlorine,  it  unites  with  chlorine,  producing  thereby  heat  and  flame. 

Many  combustibles  burn  with  flame.  A  Jlame  is  a  gas  or  vapour  raised 
to  a  high  temperature  by  combustion.  Its  illuminating  power  varies  with 
the  nature  of  the  product  formed.  The  presence  of  a  solid  body  in  the  flame 
increases  the  illuminating  power.  The  flames  of  hydrogen,  Carbonic  oxide, 
and  alcohol  are  pale,  because  they  only  contain  gaseous  products  of  com- 
bustion. But  the  flames  of  candles,  lamps,  coal  gas,  have  a  high  illuminating 
power.  They  owe  this  to  the  fact  that  the  high  temperature  produced  de- 
composes certain  of  the  gases,  with  the  production  of  carbon,  which,  not, 
being  perfectly  burnt,  becomes  incandescent  in  the  flame.  Coal  gas,  when 
burnt  in  an  arrangement  by  which  it  obtains  an  adequate  supply  of  air,  such 
as  a  Bunsen's  burner,  is  almost  entirely  devoid  of  luminosity.  A  non-lumi- 
nous flame  may  be  made  luminous  by  placing  in  it  platinum  wire  or  asbestos. 
The  temperature  of  a  flame  does  not  depend  on  its  illuminating  power. 
A  hydrogen  flame,  which  is  the  palest  of  all  flames,  gives  the  greatest 
heat. 

Chemical  decomposition,  in  which  the  attraction  of  heterogeneous  mole- 
cules for  each  other  is  overcome,  and  they  are  moved  further  apart,  is  an 
operation  requiring  an  expenditure  of  work  or  an  equivalent  consumption  of 


-484]  Heat  disengaged  during  Combustion.  447 

heat ;  and  conversely,  in  chemical  combination,  motion  is  transformed  into 
heat.  When  bodies  attract  each  other  chemically  their  molecules  move 
towards  each  other  with  gradually  increasing  velocity,  and  when  impact  has 
taken  place  the  progressive  motion  of  the  molecules  ceases,  and  is  converted 
into  a  rotating,  vibrating,  or  progressive  motion  of  the  molecules  of  the  new 
body. 

The  heat  produced  by  chemical  combination  of  two  elements  may  be 
compared  to  that  due  to  the  impact  of  bodies  against  each  other.  Thus  the 
action  of  the  atoms  of  oxygen,  which  in  virtue  of  their  progressive  motion, 
and  of  chemical  attraction,  rush  against  ignited  carbon,  has  been  likened  by 
Tyndall  to  the  action  of  meteorites  which  fall  into  the  sun. 

The  heat  of  combustion  of  allotropic  forms  of  the  same  substance  is  not 
identical,  as  is  seen  from  the  case  of  charcoal,  graphite,  and  diamond;  and  is 
also  found  in  different  varieties  of  sulphur. 

As  regards  compounds,  it  differs  in  such  as  are  metameric  with  each  other, 
those,  that  is  to  say,  which  have  the  same  empirical  formula.  Thus,  that  of 
acetic  acid  is  3505  and  of  methyl  formate  4157.  With  polymeric  compounds, 
or  those  which  have  the  same  percentage  composition,  and  only  differ  by  the 
number  of  atoms  in  the  molecule,  the  heat  of  combustion  diminishes  with  the 
complexity  of  the  molecule.  Thus,  that  of  amylene  C5H10  is  11491,  and  that 
ofmetamylene  C20H40  is  10928. 

484.  Heat  disengaged  during  combustion. — Many  physicists,  more 
especially  Lavoisier,  Rumford,  Dulong,  Despretz,  Hess,  Favre  and  Silber- 
mann,  and  Andrews,  have  investigated  the  quantity  of  heat  disengaged  by 
various  bodies  in  chemical  combinations. 

In  these  experiments  Lavoisier  used  the  ice  calorimeter  already  described. 
Rumford  used  a  calorimeter  known  by  his  name,  which  consists  of  a  rect- 
angular copper  canister  filled  with  water.  In  this  canister  there  is  a  worm 
which  passes  through  the  bottom  of  the  box,  and  terminates  below  in  an 
inverted  funnel.  Under  this  funnel  is  burnt  the  substance  experimented 
upon.  The  products  of  combustion,  in  passing  through  the  worm,  heat  the 
water  of  the  canister,  and  from  the  increase  of  its  temperature  the  quantity 
of  heat  evolved  is  calculated.  Despretz  and  Dulong  successively  modified 
Rumford's  calorimeter  by  allowing  the  combustion  to  take  place,  not 
outside  the  canister,  but  in  a  chamber  placed  in  the  liquid  itself;  the 
oxygen  necessary  for  the  combustion  entered  by  a  tube  in  the  lower  part  of 
the  chamber,  and  the  products  of  combustion  escaped  by  another  tube 
placed  at  the  upper  part  and  twisted  in  a  serpentine  form  in  the  mass  of  the 
liquid  to  be  heated.  Favre  and  Silbermann  have  improved  this  calorimeter 
very  greatly  (463),  not  only  by  avoiding  or  taking  account  of  all  possible 
sources  of  error,  but  by  arranging  it  for  the  determination  of  the  heat  evolved 
in  other  chemical  actions  than  those  of  ordinary  combustion. 

The  experiments  of  Favre  and  Silbermann  are  the  most  trustworthy,  as 
having  been  executed  with  the  greatest  care.  They  agree  very  closely  with 
those  of  Dulong.  Taking  as  thermal  unit  the  heat  necessary  to  raise  the 
temperature  of  a  pound  of  water  through  one  degree  Centigrade,  the  follow- 
ing table  gives  the  thermal  units  in  round  numbers  disengaged  by  a  pound 
of  each  of  the  substances  while  burning  in  oxygen  : — 


448  On  Heat.  [484- 

Hydrogen      .         .         .  34462  Diamond         .         .         .  7770 

Marsh  gas     .         .         .  13063  Absolute  alcohol     .         .  7180 

Olefiant  gas  .         .         .  11858  Coke       ....  7000 

Oil  of  turpentine  .         .  10852  Phosphorus     .         .         .  5750 

Olive  oil        ...  9860  Wood,  dry      .         .         .  4025 

Ether    .         .       ...       .  9030  Bisulphide  of  carbon       .  3401 

Anthracite     .         .         .  8460  Wood,  moist  .         .         .3100 

Charcoal        .     ...  8080  Carbonic  oxide       -J     %  2400 

Coal      .         .         .  •      .  8000  Sulphur  .        .         .         .  2220 

Graphite        .         .         .  7797  Zinc        ,       >;:;;..:.,  } ;.,  1300 

Tallow.         .         .         .  8000  Iron         .        i.  .. I:  .;,-.,  1181 

Bunsen's  calorimeter  (451)  has  been  used  with  advantage  for  studying 
the  heat  produced  in  chemical  reactions  for  cases  in  which  only  very  small 
quantities  are  available. 

The  experiments  of  Dulong,  of  Despretz,  and  of  Hess  proved  that  a  body 
in  burning  always  produces  the  same  quantity  of  heat  in  reaching  the  same 
degree  of  oxidation,  whether  it  attains  this  at  once,  or  only  reaches  it  after 
passing  through  intermediate  stages.  Thus  a  given  weight  of  carbon  gives 
out  the  same  amount  of  heat  in  burning  directly  to  carbonic  acid,  as  if  it 
were  first  changed  into  carbonic  oxide,  and  then  this  were  burnt  into  carbonic 
acid. 

The  temperature  of  combustion,  or,  in  the  case  of  gases,  the  temperature 
of  the  flame,  is  the  upper  limit  of  the  temperature  which  can  be  attained  by 
the  combustion  of  a  body.  This  can  be  deduced  from  the  heat  of  combus- 
tion, and  from  the  specific  heats  of  the  bodies  produced.  The  theoretical 
temperature  of  combustion  of  hydrogen  in  oxygen  is  calculated  at  6,715°; 
this,  however,  is  never  even  approximately  reached,  for  at  the  lower  tem- 
peratures aqueous  vapour  is  dissociated  (389),  and  the  combustion  cannot 
exceed  a  certain  limit. 

485.  Animal  beat. —  In  all  the  organs  of  the  human  body,  as  well  as 
those  of  all  animals,  processes  of  oxidation  are  continually  going  on.  Oxygen 
passes  through  the  lungs  into  the  blood,  and  so  into  all  parts  of  the  body.  In 
like  manner  the  oxidisible  bodies,  which  are  principally  hydrocarbons,  pass 
by  the  process  of  digestion  into  the  blood,  and  likewise  into  all  parts  of  the 
body,  while  the  products  of  oxidation,  carbonic  acid  and  water,  are  eliminated 
by  the  skin,  the  lungs,  etc.  Oxidation  in  the  muscle  produces  motions  of  the 
molecules,  which  are  changed  into  contraction  of  the  muscular  fibres  ;  all 
other  oxidations  produce  heat  directly.  When  the  body  is  at  rest,  all  its 
functions,  even  involuntary  motions,  are  transformed  into  heat.  When  the 
body  is  at  work,  the  more  vigorous  oxidations  of  the  working  parts  are 
transferred  to  the  others.  Moreover,  a  great  part  of  the  muscular  work  is 
changed  into  heat,  by  friction  of  the  muscle  and  of  the  sinews  in  their  sheaths, 
and  of  the  bones  in  their  sockets.  Hence  the  heat  produced  by  the  body 
when  at  work  is  greater  than  when  at  rest.  The  blood  distributes  heat 
uniformly  through  the  body,  which  in  the  normal  condition  has  a  temperature 
of  37°  C  =  98*6  F.  The  blood  of  mammalia  has  the  same  temperature,  that  of 
birds  is  somewhat  higher.  In  fever  the  temperature  rises  to  42° -43°,  and  in 
cholera,  or  when  near  death,  sinks  to  35°. 


-488]  Draught  of  Fireplaces.  449 

The  function  of  producing  work  in  the  animal  organism  was  formerly  con- 
sidered as  separate  from  that  of  the  production  of  heat.  The  latter  was 
held  to  be  specially  due  to  the  oxidation  of  the  hydrocarbons  of  the  fat,  while 
the  work  was  ascribed  to  the  chemical  activity  of  the  nitrogenous  matter. 
This  view  has  now  been  generally  abandoned  ;  for  it  has  been  found  that 
during  work  there  is  no  increase  in  the  secretion  of  urea,  which  is  the  result 
of  the  oxidation  of  nitrogenous  matter  ;  moreover,  the  organism  while  at 
rest  produces  less  carbonic  acid,  and  requires  less  oxygen  than  when  it  is  at 
work  ;  and  the  muscle  itself,  both  in  the  living  organism  and  also  when 
removed  from  it  and  artificially  stimulated,  requires  more  oxygen  in  a  state 
of  activity  than  when  at'  rest.  For  these  reasons  the  production  of  work  is 
ascribed  to  the  Oxidation  of  the  organic  matter  generally. 

The  process  of  vegetation  in  the  living  plant  is  not  in  general  connected 
with  any  oxidation.  On  the  contrary,  under  the  influence  of  the  sun's  rays, 
the  green  parts  of  plants  decompose  the  carbonic  acid  of  the  atmosphere 
into  free  oxygen  gas  and  into  carbon/which,  uniting  with  the  elements  of 
water,  form  cellulose,  starch,  sugar,  and  so  forth.  In  order  to  effect  this,  an 
expenditure  of  heat  is  required  which  is  stored  up  in  the  plant,  and  which 
reappears  during  the  combustion  of  the  wood,  or  of  the  coal  arising  from  its 
decomposition. 

At  the  time  of  blossoming  a  process  of  oxidation  goes  on,  which,  as  in 
the  case  of  the  blossoming  of  the  Victoria  regia,  is  attended  with  an  appreci- 
able rise  of  temperature. 

HEATING. 

486.  Different  kinds  of  beating:. —  Heating  is  the  art  of  utilising  for 
domestic  and  industrial  purposes  the  sources  of  heat  which  nature  offers  to 
us.     Our  principal  source  of  artificial  heat  is  the  combustion  of  coal,  coke, 
turf,  wood,  and  charcoal. 

We  may  distinguish  five  kinds  of  heating,  according  to  the  apparatus 
used:  ist,  heating  with  an  open  fire  ;  2nd,  heating  with  an  enclosed  fire,  as 
with  a  stove  ;  3rd,  heating  by  hot  air  ;  4th,  heating  by  steam  ;  5th,  heating 
by  the  circulation  of  hot  water. 

487.  Fireplaces. — Fireplaces  are  open  hearths  built  against  a  wall  under 
a  chimney,  through  which  the  products  of  combustion  escape. 

However  much  they  may  be  improved,  fireplaces  will  always  remain  the 
most  imperfect  and  costly  mode  of  heating,  for  they  only  render  available 
13  per  cent,  of  the  total  heat  yielded  by  coal  or  coke,  and  6  per  cent,  of  that 
by  wood.  This  enormous  loss  of  temperature  arises  from  the  fact  that  the 
current  of  air  necessary  for  combustion  always  carries  with  it  a  large  quan- 
tity of  the  heat  produced,  which  is  dissipated  in  the  atmosphere.  Hence 
Franklin  said  '  fireplaces  should  be  adopted  in  cases  where  the  smallest 
quantity  of  heat  was  to  be  obtained  from  a  given  quantity  of  fuel.'  Not- 
withstanding their  want  of  economy,  however,  they  will  always  be  preferred 
as  the  healthiest  and  pleasantest  mode  of  heating,  on  account  of  the  cheerful 
light  which  they  emit,  and  the  ventilation  which  they  ensure. 

488.  Draught  of  fireplaces. — The  draught  of  a  fir-e  is  the  upward  cur- 
rent in  the  chimney  caused  by  the  ascent  of  the  products  of  combustion  ; 
when  the  current  is  rapid  and  continuous,  the  chimney  is  said  to  draw  well. 

G  G 


450 


On  Heat. 


[488- 


The  draught  is  caused  by  the  difference  between  the  temperature  of  the 
inside  and  that  on  the  outside  of  the  chimney ;  for,  in  consequence  of  this 

difference,  the  gaseous  bodies  which  fill  the 
chimney  are  lighter  than  the  air  of  the  room, 
and  consequently  equilibrium  is  impossible. 
The  weight  of  the  column  of  gas  CD,  fig. 
403,  in  the  chimney  being  less  than  that  of 
the  external  column  of  air  AB  of  the  same 
height,  there  is  a  pressure  from  the  outside 
to  the  inside  which  causes  the  products  of 
combustion  to  ascend  the  more  rapidly  in 
proportion  as  the  difference  in  weight  of  the 
two  gaseous  masses  is  greater. 

The  velocity  of  the  draught  of  a  chimney 
may  be  determined  theoretically  by  the 
formula 


in  which  g  is  the  acceleration  of  gravity,  a 
the  coefficient  of  the  expansion  of  air,  h  the 

height  of  the  chimney,  /'  the  mean  temperature  of  the  air  inside  the  chimney, 
and  /  the  temperature  of  the  surrounding  air. 

The  currents  caused  by  the  difference  in  temperature  of  two  communi- 
cating gaseous  masses  may  be  demonstrated  by  placing  a  candle  near  the 
top  and  near  the  bottom  of  the  partially-opened  door  of  a  warm  room.  At 
the  top,  the  flame  will  be  turned  from  the  room  .towards  the  outside,  while 
the  contrary  effect  will  be  produced  when  the  candle  is  placed  on  the 
ground.  The  two  effects  are  caused  by  the  current  of  heated  air  which 
issues  by  the  top  of  the  door,  while  the  cold  air  which  replaces  it  enters  at 
the  bottom. 

In  order  to  have  a  good  draught,  a  chimney  ought  to  satisfy  the  following 
conditions  : — 

i.  The  section  of  the  chimney  ought  not  to  be  larger  than  is  necessary  to 
allow  an  exit  for  the  products  of  combustion  ;  otherwise  ascending  and  de- 
scending currents  are  produced  in  the  chimney,  which  cause  it  to  smoke.  It 
is  advantageous  to  place  on  the  top  of  the  chimney  a  conical  pot'  narrower 
than  the  chimney,  so  that  the  smoke  may  escape  with  sufficient  velocity  to 
resist  the  action  of  the  wind. 

ii.  The  chimney  ought  to  be  sufficiently  high,  for,  as  the  draught  is 
caused  by  the  excess  of  the  external  over  the  internal  pressure,  this  excess  is 
greater  in  proportion  as  the  column  of  heated  air  is  longer. 

iii.  The  external  air  ought  to  pass  into  the  chamber  with  sufficient 
rapidity  to.  supply  the  wants  of  the  fire.  In  an  hermetically-closed  room 
combustibles  would  not  burn,  or  descending  currents  would  be  formed  which 
would  drive  the  smoke  into  the  room.  Usually  air  enters  in  sufficient 
quantity  by  the  crevices  of  the  doors  and  windows. 

iv.  Two  chimneys  should  not  communicate,  for  if  one  draws  better  than 
the  other,  a  descending  current  of  air  is  produced  in  the  latter,  which  carries 
smoke  with  it. 


491] 


Heating  by  Hot  A  ir. 


For  the  strong  fires  required  by  steam  boilers  and  the  like,  very  high 
chimneys  are  needed  :  .of  course  the  increase  in  height  would  lose  its  effect 
if  the  hot  column  above  became  cooled  down.  Hence  chimneys  are  often 
made  with  hollow  walls — that  is,  of  separate  concentric  layers  of  masonry 
or  brickwork — the  space  between  them  containing  air. 

489.  Stoves. — Stoves  are  apparatus  for  heating  with  a  detached  fire, 
placed  in  the  room  to  be  heated,  so  that  the  heat  radiates  in  all  directions 
round  the  stove.     At  the  lower  part  is  the  draught-hole  by  which  the  air 
necessary  for  combustion  enters.     The  products  of  combustion  escape  by 
means  of  iron  chimney-pipes.     This  mode  of  heating  is  one  of  the  most 
economical,  but  it  is  by  no  means  so  healthy  as  that  by  open  fireplaces,  for 
the  ventilation  is  very  bad,  more  especially  where,  as  in   Sweden  and  in 
Germany,  the  stoves  are  fed  from  the  outside  of  the  room.     These  stoves 
also  emit  a  bad  smell,  arising  in  part  from  the  decomposition  of  organic  sub- 
stances which  are  always  present  in  the  air  by  their  contact  with  the  heated 
sides  of  the  chimney-pipes  ;  or  possibly,  as  Deville  and  Troost's  researches 
seem  to  show,  from  the  diffusion  of  gases  through  the  heated  sides  of  the 
stove. 

The  heating  is  very  rapid  with  blackened  metal  stoves,  but  they  also 
cool  very  rapidly.  Stoves  constructed  of  polished  earthenware,  which  are 
common  on  the  Continent,  heat  more  slowly,  but  more  pleasantly,  and  they 
retain  the  heat  longer. 

490.  Heating:  by  steam. — Steam,  in  condensing,  gives  up  its  latent  heat 
of  vaporisation,  and  this  property  has  been  used  in  heating  baths,  workshops, 
public  buildings,  hothouses,  &c.     For  this  purpose  steam  is  generated  in 
boilers  similar  to  those  used  for  steam-engines,  and  is  then  made  to  circulate 
in  pipes  placed  in  the  room 

to  be  heated.  The  steam 
condenses,  and  in  doing  so 
imparts  to  the  pipes  its  latent 
heat,  which  becomes  free, 
and  thus  heats  the  surround- 
ing air. 

491.  Beating:     by     not 
air. —  Heating     by    hot    air 
consists  in  heating  the  air  in 
the  lower  part  of  a  building, 
from  whence  it  rises  to  the 
higher  parts  in  virtue  of  its 
lessened  density.    The  appa- 
ratus is   arranged  as  repre- 
sented in  fig.  404. 

A  series  of  tubes,  AB, 
only  one  of  which  is  shown 
in  the  figure,  is  placed  in  a 
furnace,  F,  in  the  cellar.  The 
air  passes  into  the  tubes 


Fig.  404. 


through  the  lower  end,  A,  where  it  becomes  heated,  and,  rising  in  the  direc- 
tion of  the  arrows,  reaches  the   room  M  by  a  higher  aperture,  B.      The 

G  G  2 


452 


On  Heat. 


[491- 


various  rooms  to  be  heated  are  provided  with  one  or  more  of  these  aper- 
tures, which  are  placed  as  low  in  the  room  as  possible.  The  conduit  O  is 
an  ordinary  chimney.  These  apparatus  are  more  economical  than  open  fire- 
places, but  they  are  less  healthy,  unless  special  provision  is  made  for  venti- 
lation. 

492.  Beating:  by  fcot  water. — This  consists  of  a  continuous  circulation 
of  water,  which,  having  been  heated  in  a  boiler,  rises  through  a  series  of  tubes, 
and  then,  after  becoming  cool,  passes  into  the  boiler  again  by  a  similar  series. 
Fig.  405  represents  an  apparatus  for  heating  a  building  of  several 
storeys.  The  heating  apparatus,  which  is  in  the  basement,  consists  of  a 
bell-shaped  boiler,  o  o,  with  an  internal  flue,  F.  A  long  pipe,  M,  fits  in 
the  upper  part  of  the  boiler,  and  also  in  the  reservoir  O,  placed  in  the 
upper  part  of  the  building  to  be  heated.  At  the  top  of  this  reservoir  there 
is  a  safety  valve,  .r,  by  which  the  pressure  of  the  vapour  in  the  interior  can 

be  regulated. 

The  boiler,  the 
pipe  M,  and  a  por- 
tion of  the  reservoir 
Q,  being  filled  with 
water,  as  it  becomes 
heated  in  the  boiler 
an  ascending  current 
of  hot  water  rises  to 
the  reservoir  Q,  while 
at  the  same  time  de- 
scending currents  of 
colder  and  denser 
water  pass  from  the 
lower  part  of  the  re- 
servoir Q  into  re- 
ceivers, b,  d,  /,  filled 
with  water.  The 
water  from  these 
passes  again  through 
pipes  into  other  re- 
ceivers, a,  c,  e,  and 
ultimately  reaches 
the  lower  part  of  the 
boiler. 

Fig>4°5-  During  this  circu- 

lation the  hot  water  heats  the  pipes  and  the  receivers,  which  thus  become 
true  water-stoves.  The  number  and  the  dimensions  of  these  parts  are 
determined  from  the  fact  that  a  cubic  foot  of  water  in  falling  through  a 
temperature  of  one  degree  can  theoretically  impart  the  same  increase  of 
temperature  to  3,200  cubic  feet  of  air  (460).  In  the  interior  of  the  receivers, 
#,  £,  c,  d,  <?,/,  there  are  cast-iron  tubes  which  communicate  with  the  out- 
side by  pipes,  P,  placed  underneath  the  flooring.  The  air  becomes  heated 
in  these  tubes,  and  issues  at  the  upper  part  of  the  receiver. 

The  principal  advantage  of  this  mode  of  heating  is  that  of  giving  a  tern- 


-494] 


Cold  produced  by  the  Expansion  of  Gases. 


453 


perature  which  is  constant  for  a  long  time,  for  the  mass  of  water  only  cools 
slowly.  It  is  much  used  in  hothouses,  baths,  artificial  incubation,  drying 
rooms,  and  generally  wherever  a  uniform  temperature  is  desired. 


SOURCES   OF   COLD. 

493.  Various  sources  of  cold.— Besides  the  cold  caused  by  the  passage 
of  a  body  from  a  solid  to  the  liquid  state,  of  which  we  have  already  spoken, 
cold  is  produced  by  the  expansion  of  gases,  by  radiation  in  general,  and  more 
especially  by  radiation  at  night. 

494.  Cold  produced  by  the  expansion  of  gases.     Zee  machines. — We 
have  seen   that  when  a  gas  is  compressed,  the  temperature   rises.     The 
reverse  of  this  is  also  the  case :   when  a  gas  is  rarefied,  a  reduction   of 
temperature  ensues,  because  a  quantity  of  sensible  heat  disappears  when  the 
gas  becomes  increased  to  a  larger  volume.     This  may  be  shown  by  placing 
a  delicate  Breguet's  thermometer  under  the  receiver  of  an  air-pump,  and 
exhausting  ;  at  each  stroke  of  the  piston  the  needle  moves  in  the  direction 
of  zero,  and  regains  its  original  temperature  when  air  is  admitted. 

The  production  of  cold  when  a  gas  is  expanded  has  been  extensively 
applied  in  machines  for  artificial  refrigeration  on  a  large  scale.  By  Wind- 
hausen's  ice  machine,  from  1 5,000  to  1 50,000  feet  of  air  can  be  cooled  in  an 
hour,  through  40  to  100  degrees  in  temperature,  by  means  of  a  steam-engine 
of  from  6  to  20  horse-power.  The  essential  parts  of  this  machine  are  repre- 
sented in  fig.  406.  The  piston  B  in  the  cylinder  A  is  worked  to  the  right  by 
.a  steam-engine  and  to  the  left  by  a  steam-engine  and  by  the  compressed  air. 


a 


Fig.  406. 

As  it  moves  towards  the  right  the  valve  a  opens,  and  air  under  the  ordinary 
atmospheric  pressure  enters  the  space  Ax.  When  this  is  full  the  piston  moves 
towards  the  left,  the  air  in  A  is  compressed  to  about  2  atmospheres,  the 
valve  a  is  closed,  the  valve  b  opens,  and  air  passes  in  the  direction  of  the 
arrows  into  the  cooler,  C.  By  its  compression  it  has  become  strongly 
heated,  and  the  necessary  cooling  is  effected  by  means  of  pipes  through 
which  cold  water  circulates,  entering  at  5  and  emerging  at  6.  The  air,  thus 
compressed  and  cooled,  passes  out  through  the  valve  c,  which  is  automatically 
worked  by  the  machine,  into  the  space  Aa,  where,  in  conjunction  with  the 


454  On  Heat.  [494- 

steam-engine,  it  moves  the  piston  to  the  left,  and  compresses  the  air  in  Al  ; 
for  at  a  certain  position  of  the  piston  the  valve  c  is  closed,  the  compressed 
air  in  the  cylinder  A.,  expands,  and  thereby  is  cooled  far  below  the  freezing 
point.  As  the  piston  moves  again  to  the  right,  the  valve  d  is  opened  by  the 
working  of  the  machine,  and  the  cooled  air  emerges  through  the  tube  4  to 
its  destination.  If  it  passes  into  an  ordinary  room  it  fills  it  with  snowflakes. 
Machines  of  this  kind  are  extensively  employed  in  the  arts  ;  in  breweries, 
oil  refineries,  in  the  artificial  production  of  ice,  and  in  cooling  rooms  for 
the  transport  of  dead  meat,  &c.  on  board  ship. 

495.  Cold   produced    by   radiation    at    night. — During   the    day,    the 
ground  receives  from  the  sun  more  heat  than  radiates  into  space,  and  the 
temperature  rises.     The  reverse  is  the  case  during  night.     The  heat  which 
the  earth  loses  by  radiation  is  no  longer  compensated  for,  and  consequently 
a  fall  of  temperature  takes  place,  which  is  greater  according  as  the  sky  is 
clearer,  for  clouds  send  towards  the  earth  rays  of  greater  intensity  than 
those  which  come  from  the  celestial  spaces.     In  some  winters  it  has  been 
found  that  rivers  have  not  frozen,  the  sky  having  been  cloudy,  although  the 
thermometer  had  been  for  several  days  below   —  4°  ;  while  in  other  less 
severe  winters  the  rivers  freeze  when  the  sky  is  clear.     The  emissive  power 
exercises  a  great  influence  on  the  cold  produced  by  radiation  ;  the  greater  it 
is,  the  greater  is  the  cold. 

In  Bengal,  the  nocturnal  cooling  is  used  in  manufacturing  ice.  Large 
flat  vessels  containing  water  are  placed  on  non-conducting  substances,  such 
as  straw  or  dry  leaves.  In  consequence  of  the  radiation  the  water  freezes, 
even  when  the  temperature  of  the  air  is  10°  C.  The  same  method  can  be 
applied  in  all  cases  with  a  clear  sky. 

It  is  said  that  the  Peruvians,  in  order  to  preserve  the  shoots  of  young 
plants  from  freezing,  light  great  fires  in  their  neighbourhood,  the  smoke  of 
which,  producing  an  artificial  cloud,  hinders  the  cooling  produced  by 
radiation. 

496.  Absolute  zero  of  temperature. — As  a  gas  is  increased  273  of  its 
volume  for  each  degree  Centigrade,  it  follows  that  at  a  temperatuae  of  273° 
C.  the  volume  of  any  gas  measured  at  zero  is  doubled.     In  like  manner,  if 
the  temperature  of  a  given  volume  at  zero  were  lowered  through  -273°,  the 
contraction  would  be  equal  to  the  volume  :  that  is,  the  volume  would  not 
exist.     At  this  temperature  the  motion  of  the  molecules  of  the  gas  would 
completely  cease,  and  the  pressure  thereby  occasioned.     In  all  probability, 
before  reaching  this  temperature,  gases  would  undergo  some  change. 

This  point  on  the  Centigrade  scale  is  called  the  absolute  zero  of  tempera- 
ttire  ;  the  temperatures  reckoned  from  this  point  are  called  absolute  tem- 
peratures. They  are  clearly  obtained  by  adding  273  to  the  temperature  on 
the  Centigrade  scale.  Thus  -  35°  C.  is  238°  on  the  absolute  scale  of  tem- 
perature, and  +  15°  C.  is  288°. 


-497]  Mechanical  Equivalent  of  Heat.  455 


CHAPTER   XII. 
\ 

MECHANICAL   EQUIVALENT   OF   HEAT. 

497.  Mechanical  equivalent  of  beat. — If  the  various  instances  of  the 
production  of  heat  by  motion  be  examined,  it  will  be  found  that  in  all  cases 
mechanical  force  is  consumed.  Thus  in  rubbing  two  bodies  against  each 
other,  motion  is  apparently  destroyed  by  friction  ;  it  is  not,  however,  lost, 
but  appears  in  the  form  of  a  motion  of  the  particles  of  the  body  ;  the  motion 
of  the  mass  is  transformed  into  a  motion  of  the  molecules. 

Again,  if  a  body  be  allowed  to  fall  from  a  height,  it  strikes  against  the 
ground  with  a  certain  velocity.  According  to  older  views,  its  motion  is  de- 
stroyed, vis  viva  is  lost.  This,  however,  is  not  the  case  ;  the  vis  viva  of 
the  body  appears  as  vis  viva  of  its  molecules. 

In  the  case,  too,  of  chemical  action,  the  most  productive  artificial  source 
of  heat,  it  is  not  difficult  to  conceive  that  there  is,  in  the  act  of  combining, 
an  impact  of  the  dissimilar  molecules  against  each  other,  an  effect  analogous 
to  the  production  of  heat  by  the  impact  of  masses  of  matter  against  each 
other  (483). 

In  like  manner,  heat  may  be  made  to  produce  motion,  as  in  the  case  of 
the  steam-engine,  and  the  propulsion  of  shot  from  a  gun. 

Traces  of  a  view  that  there  is  a  connection  between  heat  and  motion  are 
to  be  met  with  in  the  older  writers,  Bacon  for  example  ;  and  Locke  says, 
'  Heat  is  a  very  brisk  agitation  of  the  insensible  parts  of  the  object,  which 
produces  in  us  that  sensation  from  whence  we  denominate  the  object  hot ; 
so  that  what  in  our  sensation  is  heat,  in  the  object  is  nothing  but  motion.' 
Rumford,  in  explaining  his  great  experiment  of  the  production  of  heat  by 
friction,  was  unable  to  assign  any  other  cause  for  the  heat  produced  than 
motion  ;  and  Davy,  in  the  explanation  of  his  experiment  of  melting  ice  by 
friction  in  vacuo,  expressed  similar  views.  Carnot,  in  a  work  on  the  steam- 
engine,  published  in  1824,  also  indicated  a  connection  between  heat  and 
work. 

The  views,  however,  which  had  been  stated  by  isolated  writers  had  little 
or  no  influence  on  the  progress  of  scientific  investigation,  and  it  is  in  the 
year  1842  that  the  modern  theories  may  be  said  to  have  had  their  origin. 
In  that  year  Dr.  Mayer,  a  physician  in  Heilbronn,  formally  stated  that  there 
exists  a  connection  between  heat  and  work  ;  and  he  it  was  who  first  intro- 
duced into  science  the  expression  '  mechanical  equivalent  of  heat?  Mayer 
also  gave  a  method  by  which  this  equivalent  -could  be  calculated  ;  the  par- 
ticular results,  however,  are  of  no  value,  as  the  method,  though  correct  in 
principle,  is  founded  on  incorrect  data. 

In  the  same  year  too,  Colding  of  Copenhagen  published  experiments  on 


456 


On  Heat. 


[497 


the  production  of  heat  by  friction,  from  which  he  concluded  that  the  evolu- 
tion of  heat  was  proportional  to  the  mechanical  energy  expended. 

About  the  same  time  as  Mayer,  but  quite  independently  of  him,  Joule 
commenced  a  series  of  experimental  investigations  on  the  relation  between 
heat  and  work.  These  first  drew  the  attention  of  scientific  men  to  the 
subject,  and  were  admitted  as  a  proof  that  the  transformation  of  heat  into 
mechanical  energy,  or  of  mechanical  energy  into  heat,  always  takes  place  in 
a  definite  numerical  ratio. 

Subsequently  to  Mayer  and  Joule,  several  physicists,  by  their  theoretical 
and  experimental  investigations,  have  contributed  to  establish  the  mechanical 
theory  of  heat :  namely,  in  this  country,  Sir  W.  Thomson  and  Rankine  ;  in 
Germany,  Helmholtz,  Clausius,  and  Holtzmann  ;  and  in  France,  Clapeyron, 
and  Regnault.  The  following  are  some  of  the  most  important  and  satis- 
factory of  Joule's  experiments. 

A  copper  vessel,  B  (fig.  407),  was  provided  with  a  brass  paddle-wheel 
indicated  by  the  dotted  lines),  which  could  be  made  to  rotate  about  a 


Fig.  407. 

vertical  axis.  Two  weights,  E  and  F,  were  attached  to  cords  which  passed 
over  the  pulleys  C  and  D,  and  were  connected  with  the  axis  A.  These 
weights  in  falling  cause  the  wheel  to  rotate.  The  height  of  the  fall,  which  in 
Joule's  experiments  was  about  63  feet,  was  indicated  on  the  scales  G  and  H. 

The  roller  A  was  so  constructed  that  by  detaching  a  pin  the  weights  could 
be  raised  without  moving  the  wheel.  The  vessel  B  was  filled  with  water 
and  placed  on  a  stand,  and  the  weights  allowed  to  sink.  When  they  had 
reached  the  ground,  the  roller  was  detached  from  the  axis,  and  the  weights 
again  raised,  the  same  operations  being  repeated  twenty  times.  The  heat 
produced  was  measured  by  ordinary  calorimetric  methods  (447). 

The  work  expended  is  measured  by  the  product  of  the  weight  into  the 
height  through  which  it  falls,  or//j,  less  the  work  lost  by  the  friction  of  the 
various  parts  of  the  apparatus.  This  is  diminished  as  far  as  possible  by  the 
use  of  friction  wheels  (77),  and  its  amount  is  determined  by  connecting  C 


497]  Mechanical  Equivalent  of  Heat.  457 

and  D  without  causing  them  to  pass  over  A,  and  then  determining  the 
weight  necessary  to  communicate  to  them  a  uniform  motion. 

In  this  way  it  has  been  found  that  a  thermal  unit — that  is,  the  quantity  of 
heat  by  which  a  pound  of  water  is  raised  through  i°  C. — is  generated  by  the 
expenditure  of  the  same  amount  of  work  as  would  be  required  to  raise  1,392 
pounds  through  I  foot,  or  I  pound  through  1,392  feet.  This  is  expressed  by 
saying  that  the  mechanical  equivalent  of  the  thermal  unit  is  1,392  foot- 
pounds. 

The  friction  of  an  iron  paddle-wheel  in  mercury  gave  1,397  foot-pounds, 
and  that  of  the  friction  of  two  iron  plates  gave  1,395  foot-pounds,  as  the 
mechanical  equivalent  of  one  thermal  unit. 

In  another  series  of  experiments,  the  air  in  a  receiver  was  compressed  by 
means  of  a  force-pump,  both  being  immersed  in  a  known  weight  of  water  at 
a  known  temperature.  After  300  strokes  of  the  piston  the  heat,  C,  was 
measured  which  the  water  had  gained.  This  heat  was  due  to  the  compres- 
sion of  the  air  and  to  the  friction  of  the  piston.  To  eliminate  the  latter  in- 
fluence, the  experiment  was  made  under  the  same  conditions,  but  leaving  the 
receiver  open.  The  air  was  not  compressed,  and  300  strokes  of  the  piston 
developed  C'  thermal  units.  Hence  C-  C'is  the  heat  produced  by  the  com- 
pression of  the  gas.  Representing  the  foot-pounds  expended  in  producing 

this  heat  by  W,  we  have  _ — _ *  for  the  value  of  the  mechanical  equivalent. 

\^  —  \^ 

By  this  method  Joule  obtained  the  number  1,442. 

The  mean  number  which  Joule  adopted  for  the  mechanical  equivalent  of 
one  thermal  unit  on  the  Centigrade  scale  is  1,390  foot-pounds  ;  on  the 
Fahrenheit  scale  it  is  772  foot-pounds.  The  number  is  called  Joules  equi- 
valent^ and  is  usually  designated  by  the  symbol  J. 

On  the  metrical  system  424  metres  usually  are  taken  as  the  height  through 
which  a  kilogramme  of  water  must  fall  to  raise  its  temperature  i  degree 
Centigrade.  This  is  equal  to  42,400,00x3  ergs  or  42-4  x  io6  grammes  raised 
through  a  height  of  a  centimetre. 

Professor  Rowland  of  Baltimore  has  recently  made  a  very  careful  and 
complete  determination  of  the  mechanical  equivalent  of  heat,  by  Joule's 
method,  in  which  he  has  examined  and  allowed  for  all  possible  sources  of 
error.  His  results  give  426-9  kilogramme-metres  as  the  mean  value  of  this 
constant  for  the  latitude  of  Baltimore. 

Hirn  made  the  following  determination  of  the  mechanical  equivalent  by 
means  of  the  heat  produced  by  the  compression  of  lead.  A  large  block  of 
sandstone,  CD  (fig.  408),  is  suspended  vertically  by  cords  ;  its  weight  is  P. 
E  is  a  piece  of  lead,  fashioned  so  that  its  temperature  may  be  determined  by 
the  introduction  of  a  thermometer.  The  weight  of  this  is  II,  and  its  specific 
heat  c.  AB  is  a  cylinder  of  cast  iron,  whose  weight  is/.  If  this  be  raised  to 
A'B',  a  height  of  7z,  and  allowed  to  fall  again,  it  compresses  the  lead,  E, 
against  the  anvil,  CD.  It  remains  to  measure  on  the  one  hand  the  work 
lost,  and  on  the  other  the  heat  gained. 

The  hammer  AB  being  raised  to  a  height  7z,  the  work  of  its  fall  is  ph  ; 
but  as,  by  its  elasticity,  it  rises  again  to  a  height  hl9  the  work  is/  (h-h^. 
The  anvil  CD,  on  the  other  hand,  has  been  raised  through  a  height  H 
to  CD'  and  has  required  in  so  doing  PH  units  of  work.  The  work,  W, 


458 


On  Peat, 


[497 


definitely  absorbed  by  the  lead  is  p  (h—  1i^)  —  PH.     On  the  other  hand,  the 
lead  has  been  heated  by  #,  it  has  gained  Ucd  thermal   units,  c  being  the 


Fig.  408.  .   ^  t 

specific  heat  of  lead,  and  the  mechanical  equivalent  J  is  equal  to  the  quotient 
A  series  of  six  experiments  gave  1,394  for  the  mechanical  equivalent 

as  thus  obtained. 

The  following  is  the  method  which  Mayer  employed  in  calculating  the 
mechanical  equivalent  of  heat.  It  is  taken,  with  slight  modifications,  from 
Prof.  Tyndall's  work  on  Heat,  who,  while  strictly  following  Mayer's  reason- 
ing, has  corrected  his  data. 

Let  us  suppose  that  a  rectangular  vessel  with  a  section  of  a  square  foot 
contains  at  o°  a  cubic  foot  of  air  under  the  ordinary  atmospheric  pressure  ; 
and  let  us  suppose  that  it  is  enclosed  by  a  piston  without  weight. 

Suppose  now  that  the  cubic  foot  of  air  is  heated  until  its  volume  is 
doubled  ;  from  the  coefficient  of  expansion  of  air  we  know  that  this  is  the 
case  at  273°  C.  The  gas  in  doubling  its  volume  will  have  raised  the  piston 
through  a  foot  in  height ;  it  will  have  lifted  the  atmospheric  pressure  through 
this  distance.  But  the  atmospheric  pressure  on  a  square  foot  is  in  round 
numbers  15  x  144  =  2,160  pounds.  Hence  a  cubic  foot  of  air  in  doubling  its 
volume,  has  lifted  a  weight  of  2,160  pounds  through  a  height  of  a  foot. 

Now,  a  cubic  foot  of  air  at  zero  weighs  1*29  ounce,  and  the  specific  heat 
of  air  under  constant  pressure — that  is,  when  it  can  expand  freely — as  com- 
pared with  that  of  an  equal  weight  of  water,  is  0*24  ;  so  that  the  quantity  of 
heat  which  will  raise  1-29  ounce  of  air  through  273°  will  only  raise  0*24  x  1*29 
=  0-31  oz.  of  water  through  the  same  temperature  ;  but  0-31  oz.  of  water  raised 
through  273°  is  equal  to  5*29  pounds  of  water  raised  through  i°  C. 

That  is,  the  quantity  of  heat  which  will  double  the  volume  of  a  cubic  foot 
of  air,  and  in  so  doing  will  lift  2,160  pounds  through  a  height  of  a  foot,  is 
5*29  thermal  units. 

Now,  in  the  above  case  the  gas  has  been  heated  under  constant  pressure, 
that  is,  when  it  could  expand  freely.  If,  however,  it  had  been  heated  under 
constant  volume,  its  specific  heat  would  have  been  less  in  the  ratio  I  :  1*414 
(460),  so  that  the  quantity  of  heat  required  under  these  circumstances  to 


raise  the  temperature  of  a  cubic  foot  of  air   would   be   5-29  x 


1-41 


374- 


497] 


Mechanical  Equivalent  of  Heat. 


459 


Deducting  this  from  5  -29,  the  difference  1-55  represents  the  weight  of  water 
which  would  have  been  raised  i°  C.  by  the  excess  of  heat  imparted  to  the 
air  when  it  could  expand  freely.  But  this  excess  has  been  consumed  in  the 
work  of  raising  2,160  pounds  through  a  foot.  Dividing  this  by  1-55  we  have 
1,393.  Hence  the  heat  which  will  raise  a  pound  of  water  through  i°  C.  will 
raise  a  weight  of  1,393  pounds  through  a  height  of  a  foot  ;  a  numerical  value 
of  the  mechanical  equivalent  of  heat  agreeing  as  closely  as  can  be  expected 
with  that  which  Joule  adopted  as  the  most  certain  of  his  experimental 
results. 

The  law  of  the  relation  of  heat  to  mechanical  energy  may  be  thus  stated  : — 
Heat  and  mechanical  energy  are  mutually  convertible  ;  and  heat  requires  f 01 
its  production,  and  produces  by  its  disappearance,  mechanical  energy  in  the 
ratio  of  1,^0  foot-pounds  for  every  thermal  unit. 

A  variety  of  experiments  may  in  like  manner  be  adduced  to  show  that 
whenever  heat  disappears  work  is  produced.  For  example,  if  in  a  reservoir 
immersed  in  water  the  air  be  compressed  to  the  extent  of  10  atmospheres  : 
supposing  that  now,  when  the  compressed  air  has  acquired  the  temperature 
of  the  water,  it  be  allowed  to  act  upon  a  piston  loaded  by  a  weight,  the 
weight  is  raised.  At  the  same  time  the  water  becomes  cooler,  showing  that 
a  certain  quantity  of  heat  had  disappeared  in  producing  the  mechanical 
effort  of  raising  the  weight.  This  may  also  be  illustrated  by  the  following 
experiment,  due  to  Prof.  Tyndall  : — 

A  strong  metal  box  is  taken,  provided  with  a  stopcock,  on  which  can  be 
screwed  a  small  condensing  pump.  Having  compressed  the  air  by  its  means 
as  it  becomes  heated  by  this  process,  the  box  is  allowed  to  stand  for  some 


Fig.  409. 

time,  until  it  has  acquired  the  temperature  of  the  surrounding  medium.  On 
opening  the  stopcock,  the  air  rushes  out  :  it  is  expelled  by  the  expansive 
force  of  the  internal  air  ;  in  short,  the  air  drives  itself  out.  Work  is  there- 
fore performed  by  the  air,  and  there  should  be  a  disappearance  of  heat ;  and 
if  the  jet  of  air  be  allowed  to  strike  against  the  thermopile,  the  galvano- 


460  On  Heat.  [497- 

meter  is  deflected,  and  the  direction  of  its  deflection  indicates  a  cooling 
(fig.  409).  The  same  effect  is  observed  when,  on  opening  a  bottle  of  soda 
water,  the  carbonic  gas  which  escapes  is  allowed  to  impinge  against  the 
thermopile. 

If,  on  the  contrary,  the  experiment  is  made  with  an  ordinary  pair  of 
bellows,  and  the  current  of  air  is  allowed  to  strike  against  the  pile,  the 
deflection  of  the  galvanometer  is  in  the  opposite  direction,  indicating  an 
increase  of  temperature  (fig.  410).  In  this  case  the  hand  of  the  experimenter 
performs  the  work,  which  is  converted  into  heat. 

Joule  placed  in  a  calorimeter  two  equal  copper  reservoirs,  which  could 
be  connected  by  a  tube.  One  of  these  contained  air  at  22  atmospheres,  the 
other  was  exhausted.  When  they  were  connected,  they  came  into  equi- 
librium under  a  pressure  of  1 1  atmospheres  ;  but  as  the  gas  in  expanding 
had  done  no  work,  there  was  no  alteration  in  temperature.  When,  however, 


Fig.  410. 

the  second  reservoir  was  full  of  water,  the  air  in  entering  was  obliged  to 
expel  it  and  thus  perform  work,  and  the  temperature  sank,  owing  to  an 
absorption  of  heat. 

For  further  information  the  student  of  this  subject  is  referred  to  the 
following  works  :— Tyndall  on  Heat  as  a  Mode  of  Motion,  Maxwell  on  Heat, 
WormelPs  Thermodynamics  (Longmans),  and  Tait  on  Thermodynamics 
(Edmonston  and  Douglas).  A  condensed,  though  complete  and  systematic 
account  of  the  dynamical  theory  of  heat  is  met  with  in  Professor  Foster's 
articles  on  «  Heat,'  in  Watt's  Dictionary  of  Chemistry. 

498.  Dissipation  of  energy. — Rankine  has  the  following  interesting 
observations  on  a  remarkable  consequence  of  the  mutual  convertibility  which 
has  been  shown  to  exist  between  heat  and  other  forms  of  energy  : — Sir  W. 
Thomson  has  pointed  out  the  fact  that  there  exists,  at  least  in  the  present 
state  of  the  known  world,  a  predominating  tendency  to  the  conversion  of  all 
the  other  forms  of  physical  energy  into  heat,  and  to  the  uniform  diffusion  of 
heat  throughout  all  matter.  The  form  in  which  we  generally  find  energy 
originally  collected  is  that  of  a  store  of  chemical  power  consisting  of  uncom- 


-498]  Dissipation  of  Energy.  461 

bined  elements.  The  combination  of  these  elements  produces  energy  in  the 
form  known  by  the  name  of  electrical  currents,  part  only  of  which  can  be 
employed  in  analysing  chemical  compounds,  and  thus  reconverted  into  a 
store  of  chemical  power  ;  the  remainder  is  necessarily  converted  into  heat ; 
a  part  only  of  this  heat  can  be  employed  in  analysing  compounds  or  in  re- 
producing electric  currents.  If  the  remainder  of  the  heat  be  employed  in 
expanding  an  elastic  substance,  it  may  be  converted  entirely  into  visible 
motion,  or  into  a  store  of  visible  mechanical  power  (by  raising  weights,  for 
example),  provided  the  elastic  substance  is  enabled  to  expand  until  its 
temperature  falls  to  the  point  which  corresponds  to  the  absolute  privation 
of  heat  ;  but  unless  this  condition  is  fulfilled,  a  certain  proportion  only  of 
the  heat,  depending  on  the  range  of  temperature  through  which  the  elastic 
body  works,  can  be  converted,  the  rest  remaining  in  the  state  of  heat.  On 
the  other  hand,  all  visible  motion  is  of  necessity  ultimately  converted  into- 
heat  by  the  agency  of  friction.  There  is,  then,  in  the  present  state  of  the 
known  world,  a  tendency  towards  the  conversion  of  all  physical  energy  into 
the  sole  form  of  heat. 

Heat,  moreover,  tends  to  diffuse  itself  uniformly  by  conduction  and  radia- 
tion, until  all  matter  shall  have  acquired  the  same  temperature.  There  is, 
consequently,  so  far  as  we  understand  the  present  condition  of  the  universe, 
a  tendency  towards  a  state  in  which  all  physical  energy  will  be  in  the  state  of 
heat,  and  that  heat  so  diffused  that  all  matter  will  be  at  the  same  temperature  ; 
so  that  there  will  be  an  end  of  all  physical  phenomena. 

Vast  as  this  speculation  may  seem,  it  appears  to  be  soundly  based  on 
experimental  data,  and  to  truly  represent  the  present  condition  of  the  uni- 
verse as  far  as  we  know  it. 


462  On  Light.  [499- 


BOOK   VII. 

ON    LIGHT. 

CHAPTER    I. 
TRANSMISSION,  VELOCITY,   AND   INTENSITY   OF   LIGHT. 

/  499.  Theories  of  light. — Light  is  the  agent  which,  by  its  action  on  the 
retina,  excites  in  us  the  sensation  of  vision.  That  part  of  physics  which  deals 
with  the  properties  of  light  is  known  as  optics. 

In  order  to  explain  the  origin  of  light,  various  hypotheses  have  been  made, 
the  most  important  of  which  are  the  emission  or  corpuscular  theory,  and  the 
xmdulatory  theory. 

On  the  emission  theory  it  is  assumed  that  luminous  bodies  emit,  in  all 
directions,  an  imponderable  substance,  which  consists  of  molecules  of  an 
extreme  degree  of  tenuity  :  these  are  propagated  in  right  lines  with  an  almost 
infinite  velocity.  Penetrating  into  the  eye  they  act  on  the  retina,  and  deter- 
mine the  sensation  which  constitutes  vision. 

On  the  undulatory  theory,  all  bodies,  as  well  as  the  celestial  spaces,  are 
filled  by  an  extremely  subtle  elastic  medium,  which  is  called  the  luminiferous 
.ether.  The  luminosity  of  a  body  is  due  to  an  infinitely  rapid  vibratory  motion 
of  its  molecules,  which,  when  communicated  to  the  ether,  is  propagated  in  all 
directions  in  the  form  of  spherical  waves,  and  Jhis  vibratory  motion,  being 
thus  transmitted  to  the  retina,  calls  forth  the  sensation  of  vision.  The 
vibrations  of  the  ether  take  place  not  in  the  direction  of  the  wave,  but  in  a 
plane  at  right  angles  to  it.  The  latter  are  called  the  transversal  vibrations. 
An  idea  of  these  may  be  formed  by  shaking  a  rope  at  one  end.  The  vibra- 
tions, or  to  and  fro  movements,  of  the  particles  of  the  rope,  are  at  right 
angles  to  the  length  of  the  rope,  but  the  onward  motion  of  the  wave's  form 
is  in  the  direction  of  the  length. 

On  the  emission  theory  the  propagation  of  light  is  effected  by  a  motion 
or  translation  of  particles  of  light  thrown  out  from  the  luminous  body,  as  a 
"bullet  is  discharged  from  a  gun  ;  on  the  undulatory  theory  there  is  no  pro- 
gressive motion  of  the  particles  themselves,  but  only  of  the  state  of  disturb- 
ance which  was  communicated  by  the  luminous  body  ;  it  is  a  motion  of 
oscillation,  and,  like  the  propagation  of  waves  in  water,  takes  place  by  a  series 
of  vibrations. 

The  luminiferous  ether  penetrates  all  bodies,  but  on  account  of  its 
-extreme  tenuity  it  is  uninfluenced  by  gravitation  ;  it  occupies  space,  and 
although  it  presents  no  appreciable  resistance  to  the  motion  of  the  denser 
bodies,  it  is  possible  that  it  hinders  the  motion  of  the  smaller  comets.  It  has 


-502]       Propagation  of  Light  in  a  Homogeneous  Medium.       463 

been  found,  for  example,  that  Encke;s  comet,  whose  period  of  revolution  is 
about  3^  years,  has  its  period  diminished  by  about  o-ii  of  a  day  at  each 
successive  rotation,  and  this  diminution  is  ascribed  by  some  to  the  resistance 
of  the  ether. 

The  fundamental  principles  of  the  undulatory  theory  were  enunciated  by 
Huyghens,  and  subsequently  by  Euler.  The  emission  theory,  principally 
owing  to  Newton's  powerful  support,  was  for  long  the  prevalent  scientific 
creed.  The  undulatory  theory  was  adopted  and  advocated  by  Young,  who 
showed  how  a  large  number  of  optical  phenomena,  particularly  those  of 
diffraction,  were  to  be  explained  by  that  theory.  Subsequently  too,  though 
independently  of  Young,  Fresnel  showed  that  the  phenomena  of  diffraction, 
and  also  that  of  polarisation,  are  explicable  on  the  same  theory,  which,  since 
his  time,  has  been  generally  accepted. 

The  undulatory  theory  not  only  explains  the  phenomena  of  light,  but  it 
reveals  an  intimate  connection  between  these  phenomena  and  those  of  heat 
(429)  ;  it  shows,  also,  how  completely  analogous  the  phenomena  of  light  are 
to  those  of  sound,  regard  being  had  to  the  differences  of  the  media  in  which 
these  two  classes  of  phenomena  take  place. 

500.  Luminous,  transparent,  translucent,  and  opaque  bodies.— Lumi- 
nous bodies  are  those  which  emit  light,  such  as  the  sun,  and  ignited  bodies. 
Transparent  or  diaphanous  bodies  are  those  which  readily  transmit  light, 
and  through  which  objects  can  be  distinguished  :  water,  gases,  polished  glass 
are  of  this  kind.     Translucent  bodies  transmit  light,  but  objects  cannot  be 
distinguished  through  them  :  ground  glass,  oiled  paper,  &c.  belong  to  this 
class.     Opaque  bodies  do  not  transmit  light  ;  for  example,  wood,  metals,  &c. 
No  bodies  are  quite  opaque  ;  they  are  all  more  or  less  translucent  when  cut 
in  sufficiently  thin  leaves. 

Foucault  showed  that  when  the  object-glass  of  a  telescope  is  thinly 
silvered,  the  layer  is  so  transparent  that  the  sun  can  be  viewed  through  it 
without  danger  to  the  eyes,  since  the  metallic  surface  reflects  the  greater 
part  of  the  heat  and  light. 

501.  Luminous  ray  and  pencil. — A  luminous  ray  is  the  direction  of  the 
line  in  which  light  is  propagated  ;  a  luminous  pencil  is  a  collection  of  rays 
from  the  same  source  ;  it  is   said  to  be  parallel  when  it  is  composed  of 
parallel  rays,  divergent  when  the  rays  separate  from  each  other,  and  con- 
vergent when  they  tend  towards  the  same  point.    Every  luminous  body  emits  ' 
divergent  rectilinear  rays  from  all  its  points,  and  in  all  directions. 

502.  Propagation  of  light  in  a  homogeneous  medium. — A  medium  is 
any  space  or  substance  which  light  can  traverse,  such  as  a  vacuum,  air,  water, 
glass,  &c.     A  medium  is  said  to  be  homogeneous  when  its  chemical  compo- 
sition and  density  are  the  same  in  all  parts. 

/;/  every  homogeneous  medium  light  is  propagated  in  a  right  line.  For, 
if  an  opaque  body  is  placed  in  the  right  line  which  joins  the  eye  and  the 
luminous  body,  the  light  is  intercepted.  The  light  which  passes  into  a  dark 
room  by  a  small  aperture  leaves  a  luminous  trace,  which  is  visible  from  the 
light  falling  on  the  particles  of  dust  suspended  in  the  atmosphere. 

Light  changes  its  direction  on  meeting  an  object  which  it  cannot  pene- 
trate, or  when  it  passes  from  one  medium  to  another.  These  phenomena 
will  be  described  under  the  heads  reflection  and  refraction. 


464  On  Light,  [503- 

503.  Shadow,  penumbra, — When  light  falls  upon  an  opaque  body  it 
cannot  penetrate  into  the  space  immediately  behind  it,  and  this  space  is 
called  the  shadow. 

In  determining  the  extent  and  the  shape  of  a  shadow  projected  by  a  body, 
two  cases  are  to  be  distinguished  ;  that  in  which  the  source  of  light  is  a 
single  point,  and  that  in  which  it  is  a  body  of  any  given  extent. 

In  the  first  case,  let  S  (fig.  411)  be-  the  luminous  point,  and  M  a  spherical 
body,  which  causes  the  shadow.  If  an  infinitely  long  straight  line,  SG, 


Fig-  4". 

move  round  the  sphere  M  tangentially,  always  passing  through  the  point  S, 
this  line  will  produce  a  conical  surface,  which,  beyond  the  sphere,  separates 
that  portion  of  space  which  is  in  shadow  from  that  which  is  illuminated.  In 
the  present  case,  on  placing  a  screen,  PQ,  behind  the  opaque  body  the  limit 
of  the  shadow  HG  will  be  sharply  defined.  This  is  not,  however,  usually 
the  case,  for  luminous  bodies  have  always  a  certain  magnitude,  and  are  not 
merely  luminous  points. 

Suppose  that  the  luminous  and  illuminated  bodies  are  two  spheres,  SL 
and  MN  (fig.  412).     If  an  infinite  straight  line,  AG,  moves  tangentially  to 


Fig.  412. 

both  spheres,  always  cutting  the  line  of  the  centre  in  the  point  A,  it  will  pro- 
duce a  conical  surface  with  this  point  for  a  summit,  and  which  traces  behind 
the  sphere  MN  a  perfectly  dark  space  MGHN.  If  a  second  right  line,  LD, 
which  cuts  the  line  of  centre  in  B,  moves  tangentially  to  the  two  spheres,  so 
as  to  produce  a  new  conical  surface,  BUG,  it  will  be  seen  that  all  the  space 
outside  this  surface  is  illuminated,  but  that  the  part  between  the  two  conical 
surfaces  is  neither  quite  dark  nor  quite  light.  So  that  if  a  screen,  PQ,  is 
placed  behind  the  opaque  body,  the  portion  cGdH  of  the  screen  is  quite  in 
the  shadow,  while  the  space  ab  receives  light  from  certain  parts  of  the  lumi- 
nous body,  and  not  from  others.  It  is  brighter  than  the  true  shadow,  and 


-504]  Images  produced  by  Small  Apertures.  465 

not  so  bright  as  the  rest  of  the  screen,  and  it  is  accordingly  called  the 
penumbra. 

Shadows  such  as  these  are  geometrical  shadows;  physical  shadows,  or 
those  which  are  really  seen,  are  by  no  means  so  sharply  defined.  A  certain 
quantity  of  light  passes  into  the  shadow,  even  when  the  source  of  light  is  a 
mere  point,  and  conversely  the  shadow  influences  the  illuminated  part.  This 
phenomenon,  which  will  be  afterwards  described,  is  known  by  the  name  of 
diffraction  (646). 

504.  Images  produced  by  small  apertures. — When  luminous  rays, 
which  pass  into  a  dark  chamber  through  a  small  aperture,  are  received  upon 
a  screen,  they  form  images  of  external  objects.  These  images  are  inverted, 
their  shape  is  always  that  of  the  external  objects,  and  is  independent  of  the 
shape  of  the  aperture. 

The  inversion  of  the  images  arises  from  the  fact  that  the  luminous  rays 
proceeding  from  external  objects,  and  penetrating  into  the  chamber,  cross 
one  another  in  passing  the  aperture,  as  shown  in  fig.  413.  Continuing  in  a 


Fig.  413- 

straight  line,  the  rays  from  the  higher  parts  meet  the  screen  at  the  lower 
parts ;  and  conversely,  those  which  come  from  the  lower  parts  meet  the 
higher  parts  of  the  screen.  Hence  the  inversion  of  the  image.  In  the 
article  Camera  Obscura  it  will  be  seen  how  the  brightness  and  precision  of 
these  images  are  increased  by  means  of  lenses. 

In  order  to  show  that  the  shape  of  the  image  is  independent  of  that  of 
the  aperture,  when  the  latter  is  sufficiently  small  and  the  screen  at  an  ade- 
quate distance,  imagine  a  triangular  aperture,  O  (fig.  414),  made  in  the  door 


Fig.  414. 

of  a  dark  chamber,  and  let  ab  be  a  screen  on  which  is  received  the  image  of 
a  flame,  AB.  A  divergent  pencil  from  each  point  of  the  flame  passes  through 
the  aperture,  and  forms  on  the  screen  a  triangular  image  resembling  the 

H  H 


466  On  Light.  [504- 

aperture.  But  the  union  of  all  these  partial  images  produces  a  total  image 
of  the  same  form  as  the  luminous  object.  For  if  we  conceive  that  an  infinite 
straight  line  moves  round  the  aperture,  with  the  condition  that  it  is  always 
tangential  to  the  luminous  object  AB,  and  that  the  aperture  is  very  small,  the 
straight  line  describes  two  cones,  the  apex  of  which  is  the  aperture,  while  one 
of  the  bases  is  the  luminous  object  and  the  other  the  luminous  object  on 
the  screen — that  is,  the  image.  Hence,  if  the  screen  is  perpendicular  to  the 
right  line  joining  the  centre  of  the  aperture  and  the  centre  of  the  luminous 
body,  the  image  is  similar  to  the  body ;  but  if  the  screen  is  oblique,  the 
image  is  elongated  in  the  direction  of  its  obliquity.  This  is  what  is  seen  in 
the  shadow  produced  by  foliage  ;  the  luminous  rays  passing  through  the  leaves 
produce  images  of  the  sun,  which  are  either  round  or  elliptical,  according  as 
the  ground  is  perpendicular  or  oblique  to  the  solar  rays  ;  and  this  is  the 
case  whatever  be  the  shape  of  the  aperture  through  which  the  light  passes. 

505.  Velocity  of  ligrbt. — Light  moves  with  such  a  velocity  that  at  the 
surface  of  the  earth  there  is,  to  ordinary  observation,  no  appreciable  interval 
between  the  occurrence  of  any  luminous  phenomenon  and  its  perception  by 
the  eye.  And,  accordingly,  this  velocity  was  first  determined  by  means  of 
astronomical  observations.  Romer,  a  Danish  astronomer,  in  1675,  first 
deduced  the  velocity  of  light  from  an  observation  of  the  eclipses  of  Jupiter's 
first  satellite. 

Jupiter  is  a  planet,  round  which  four  satellites  revolve,  as  the  moon 
does  round  the. earth.  This  first  satellite,  E  (fig.  415),  suffers  occultation— 


Fig.  415- 

that  is,  passes  into  Jupiter's  shadow — at  equal  intervals  of  time,  which  are 
42h.  28m.  365.  While  the  earth  moves  in  that  part  of  its  orbit,  ab^  nearest 
Jupiter,  its  distance  from  that  planet  does  not  materially  alter,  and  the 
intervals  between  two  successive  occultations  of  the  satellite  are  approximately 
the  same  ;  but,  in  proportion  as  the  earth  moves  away  in  its  revolution 
round  the  sun,  S,  the  interval  between  two  occultations  increases,  and  when, 
at  the  end  of  six  months,  the  earth  has  passed  from  the  position  T  to  the 
position  T7,  a  total  retardation  of  i6m.  363.  is  observed  between  the  time  at 
which  the  phenomenon  is  seen  and  that  at  which  it  is  calculated  to  take 
place.  But  when  the  earth  was  in  the  position  T,  the  sun's  light  reflected 
from  the  satellite  E  had  to  traverse  the  distance  ET,  while  in  the  second 
position  the  light  had  to  traverse  the  distance  ET'.  This  distance  exceeds 
the  first  by  the  quantity  XT',  for,  from  the  great  distance  of  the  satellite  E, 
the  rays  ET  and  ET7  may  be  considered  parallel.  Consequently,  light 
requires  i6m.  365.  to  travel  the  diameter  TT'of  the  terrestrial  orbit,  or  twice 


—506]       Apparatus  for  determining'  tJie  Velocity  of  Light.        467 

the  distance  of  the  earth  from  the  sun,  which  gives  for  its  velocity  190,000 
miles  in  a  second. 

The  stars  nearest  the  earth  are  separated  from  it  by  at  least  206,265 
times  the  distance  of  the  sun.  Consequently,  the  light  which  they  send 
requires  more  than  3  years  to  reach  us.  Those  stars,  which  are  only  visible 
by  means  of  the  telescope,  are  possibly  at  such  a  distance  that  thousands 
of  years  would  be  required  for  their  light  to  reach  our  planetary  system. 
They  might  have  been  extinguished  for  ages  without  our  knowing  it. 

506.  Foucault's  apparatus  for  determining:  the  velocity  of  light. — 
Notwithstanding  the  prodigious  velocity  of  light,  Foucault  has  succeeded  in 
determining  it  experimentally  by  the  aid  of  an  ingenious  apparatus,  based 
on  the  use  of  the  rotating  mirror,  which  was  adopted  by  Wheatstone  in 
measuring  the  velocity  of  electricity. 

In  the  description  of  this  apparatus,  a  knowledge  of  the  principal  pro- 
perties of  mirrors  and  of  lenses  is  presupposed.  Fig.  416  represents  the 
chief  parts  of  Foucault's  arrangement.  The  window  shutter,  K,  of  a  dark 
chamber  is  perforated  by  a  square  aperture,  behind  which  the  platinum 
wire  o  is  stretched  vertically.  A  beam  of  sunlight  reflected  from  the  out- 
side upon  a  mirror  enters  the  dark  room  by  the  square  aperture,  meets  the 
platinum  wire,  and  then  traverses  an  achromatic  lens,  L,  with  a  long  focus, 
placed  at  a  distance  from  the  platinum  wire  less  than  double  the  principal 
focal  distance.  The  image  of  the  platinum  wire,  more  or  less  magnified, 
would  thus  be  formed  on  the  axis  of  the  lens  ;  but  the  luminous  pencil, 
having  traversed  the  lens,  impinges  on  a  plane  mirror,  ;;z,  rotating  with  great 
velocity ;  it  is  reflected  from  this,  and  forms  in  space  an  image  of  the 
platinum  wire,  which  is  displaced  with  an  angular  velocity  double  that  of  the 
mirror  (520).  This  image  is  reflected  by  a  concave  mirror,  M,  whose  centre 


Fig.  416.  Fig.  417. 

of  curvature  coincides  with  the  axis  of  rotation  of  the  mirror  »z,  and  with  its 
centre  of  figure.  The  pencil  reflected  from  the  mirror  M  returns  upon  itself, 
is  again  reflected  from  the. mirror  m,  traverses  the  lens  a  second  time,  and 

H  H  2 


468  On  Light.  [506- 

forms  an  image  of  the  platinum  wire,  which  appears  on  the  wire  itself  so 
long  as  the  mirror  in  turns  slowly. 

In  order  to  see  this  image  without  hiding  the  pencil  of  light  which  enters 
by  the  aperture  in  K,  a  mirror  of  unsilvered  glass,  V,  with  parallel  faces,  is 
placed  between  the  lens  and  the  wire,  and  is  inclined  so  that  the  reflected 
rays  fall  upon  a  powerful  eyepiece,  P. 

The  apparatus  being  arranged,  if  the  mirror  m  is  at  rest,  the  ray  after 
meeting  M  is  reflected  to  m,  and  from  thence  returns  along  its  former  path, 
till  it  meets  the  glass  plate  V  in  <z,  and  being  partially  reflected,  forms  at  d  — 
the  distance  ad  being  equal  to  ao  —  an  image  of  the  wire,  which  the  eye  is 
enabled  to  observe  by  means  of  the  eyepiece,  P.  If  the  mirror,  instead  of 
being  fixed,  is  moving  slowly  round  —  its  axis  being  at  right  angles  to  the 
plane  of  the  paper  —  there  will  be  no  sensible  change  in  the  position  of  the 
mirror  m  during  the  brief  interval  elapsing  while  light  travels  from  m  to  M 
and  back  again,  but  the  image  will  alternately  disappear  and  reappear.  If 
now  the  velocity  of  M  is  increased  to  upwards  of  30  turns  per  second,  the 
interval  between  the  disappearance  and  reappearance  is  so  short  that  the 
impression  on  the  eye  is  persistent,  and  the  image  appears  perfectly  steady. 

Lastly,  if  the  mirror  turns  with  sufficient  velocity,  there  is  no  appreciable 
change  in  its  position  during  the  time  which  the  light  takes  in  making  the 
double  journey  from  m  to  M,  and  from  M  to  m  ;  the  return  ray,  after  its 
reflection  from  the  mirror  ;/z,  takes  the  direction  mb,  and  forms  its  image 
at  i  }  that  is,  the  image  has  undergone  a  total  deviation  dt.  Speaking  pire"- 
cisely,  there  is  a  deviation  as  soon  as  the  mirror  turns,  even  slowly  ;  but  it  is 
only  appreciable  when  it  has  acquired  a  certain  magnitude,  which  is  the  case 
when  the  velocity  of  rotation  is  sufficiently  rapid,  or  the  distance  Mm  suffi- 
ciently great,  for  the  deviation  necessarily  increases  with  the  time  which  the 
light  takes  in  returning  on  its  own  path. 

In  Foucault's  experiment  the  distance  Mm  was  only  13^  feet  ;  when  the 
mirror  rotated  with  a  velocity  of  600  to  800  turns  in  a  second,  deviations  of 
_2_  to  T3o  of  a  millimetre  were  obtained. 

Taking  M;;z  =  /,  Lm  =  I',  oL  =  r,  and  representing  by  n  the  number  of 
turns  in  a  second,  by  8  the  absolute  deviation  di,  and  by  V  the  velocity  of 
light,  Foucault  arrived  at  the  formula 


from  which  the  velocity  of  light  is  calculated  at  185,157  miles  in  a  second  ; 
this  number,  which  is  less  than  that  ordinarily  assumed,  agrees  remarkably 
well  with  the  value  deduced  from  the  new  determinations  of  the  value  of  the 
solar  parallax. 

The  mechanism  by  which  the  mirror  was  turned  consisted  of  a  small 
steam  turbine,  bearing  a  sort  of  resemblance  to  the  syren,  and,  like  that 
instrument,  giving  a  higher  sound  as  the  rotation  is  more  rapid  :  in  fact,  it 
is  by  the  pitch  of  the  note  that  the  velocity  of  the  rotation  is  determined. 

In  this  apparatus  liquids  can  be  experimented  upon.  For  that  purpose 
a  tube,  AB,  10  feet  long,  and  filled  with  distilled  water,  is  placed  between  the 
turning  mirror  m,  and  a  concave  mirror  Mx,  identical  with  the  mirror  M. 
The  luminous  rays  reflected  by  the  rotating  mirror,  in  the  direction  mM', 
traverse  the  column  of  water  AB  twice  before  returning  to  V.  But  the  return 


-508]  Laws  of  llie  Intensity  of  Light.  469 

ray  then  becomes  reflected  at  c,  and  forms  its  image  at  h  :  the  deviation  is 
consequently  greater  for  rays  which  have  traversed  water  than  for  those 
which  have  passed  through  air  alone  ;  hence  the  velocity  of  light  is  less  in 
water  than  in  air. 

This  is  the  most  important  part  of  these  experiments.  For  it  had  been 
shown  theoretically  that  on  the  undulatory  theory  the  velocity  of  light  must 
be  less  in  the  more  highly  refracting  medium  (638),  while  the  opposite  is  a 
necessary  consequence  of  the  emission  theory.  Hence  Foucault's  result  may 
be  regarded  as  a  crucial  test  of  the  validity  of  the  undulatory  theory. 

507.  Experiments  of  Fizeau. — In   1849  Fizeau  measured  directly  the 
velocity  of  light,  by  ascertaining  the  time  it  took  to  travel  from  Suresnes  to 
Montmartre  and  back  again.     The  apparatus  employed  was  a  toothed  wheel, 
capable  of  being  turned  more  or  less  quickly,  and  with  a  velocity  that  could 
be  exactly  ascertained.     The  teeth  were  made  of  precisely  the  same  width 
as  the  intervals  between  them.     The  apparatus  being  placed  at  Suresnes,  a 
pencil  of  parallel  rays   was  transmitted  through  an  interval  between  two 
teeth  to  a  mirror  placed  at  Montmartre.     The  pencil,  directed  by  a  properly 
arranged  system  of  tubes  and  lenses,  returned  to  the  wheel.     As  long  as  the 
apparatus  was  at  rest  the  pencil  returned  exactly  through  the  same  interval 
as  that   through  which  it  first  set  out.     But  when  the  wheel  was  turned 
sufficiently  fast,  a  tooth  was  made  to  take  the  place  of  an  interval,  and  the 
ray  was  intercepted.     By  causing  the  wheel  to  turn  more  rapidly,  it  re- 
appeared when  the  interval  between  the  next  two  teeth  had  taken  the  place 
of  the  former  tooth  at  the  instant  of  the  return  of  the  pencil. 

The  distance  between  the  two  stations  was  28,334  feet.  By  means  of  the 
data  furnished  by  this  distance,  by  the  dimensions  of  the  wheel,  its  velocity 
of  rotation,  &c.,  Fizeau  found  the  velocity  of  light  to  be  196,000  miles  per 
second — a  result  agreeing  with  that  given  by  astronomical  observation  as 
closely  as  can  be  expected  in  a  determination  of  this  kind. 

Cornu  recently  investigated  the  velocity  of  light  by  Fizeau's  method, 
but  with  improvements  so  that  the  probable  error  did  not  exceed  ¥^  of  the  total 
amount  j  the  two  stations,  which  were  6'4  miles  apart,  were  a  pavilion  of 
the  Ecole  Polytechnique  and  a  room  in  the  barracks  of  Mont  Vale'rien.  By 
means  of  electromagnetic  arrangements  the  rotation  of  the  toothed  disc, 
and  the  times  of  obscuration  and  illumination,  were  registered  on  a  blackened 
cylinder,  on  the  principle  of  the  method  described  in  (245).  Cornu  thus 
obtained  the  number  185,420  miles — a  result  closely  agreeing  with  that 
of  Foucault,  and  which  is  supported  by  calculations  based  on  the  results  of 
astronomical  observations  of  the  transit  of  Venus  in  1874.  Michelson  made 
a  determination  of  the  velocity  of  light  by  Foucault's  method,  by  which  he 
obtained  the  result  186,380,  with  a  possible  error  of  33  miles. 

508.  Laws  of  the  intensity  of  light. — The  intensity  of  illumination  is 
the  quantity  of  light  received  on  the  unit  of  surface  ;  it  is  subject  to  the 
following  laws  : — 

I.  The  intensity  of  illumination    on  a  given  surface  is  inversely  as  the 
square  of  its  distance  from  the  source  of  light. 

II.  The  intensity  of  illumination  which  is  received  obliquely  is  propor- 
tional to  the  cosine  of  the  angle  which  the  luminous  rays  make  with  the 
normal  to  the  illuminated  surface. 


470  On  Light.  [508- 

In  order  to  demonstrate  the  first  law,  let  there  be  two  circular  screens, 
CD  and  AB  (fig.  418),  one  placed  at  a  certain  distance  from  a  source  of 

light,  L,  and  the  other  at 
double  this  distance,  and 
let  s  and  S  be  the  areas 
of  the  two  screens.  If 
a  be  the  total  quantity  of 
light  which  is  emitted  by 
the  source  in  the  direc- 
tion of  the  cone  ALB, 
the  intensity  of  the  light 


Fig.  4ii 


on  the  screen  CD—  that 
is,    the    quantity   which 


falls  on  the  unit  of  surface — is  -,  and  the  intensity  on  the  screen  AB  is  -• 

•S  o 

Now  as  the  triangles  ALB  and  CLD  are  similar,  the  diameter  of  AB  is 
double  that  of  CD  ;  and  as  the  surfaces  of  circles  are  as  the  squares  of  their 

diameters,  the  surface  S  is  four  times  s,  consequently  the  intensity  g-  is  one- 
fourth  that  of  -. 
s 

The  same  law  may  also  be  demonstrated  by  an  experiment  with  the 
apparatus  represented  in  fig.  420.  It  is  made  by  comparing  the  shadows  of  an 
opaque  rod  cast  upon  a  glass  plate,  in  one  case  by  the  light  of  a  single  candle, 
and  in  another  by  that  of  a  lamp  equalling  four  candles,  placed  at  double  the 
distance  of  the  first.  In  both  cases  the  shadows  have  the  same  intensity. 

Fig.  418  shows  that  it  is  owing  to  the  divergence  of  the  luminous  rays 
emitted  from  the  same  source  that  the  intensity  of  light  is  inversely  as  the 
square  of  the  distance.  The  illumination  of  a  surface  placed  in  a  beam  of 
parallel  luminous  rays  is  the  same  at  all  distances  in  a  vacuum  ;  in  air  and 
in  other  transparent  media  the  intensity  of  light  decreases,  in  consequence 
of  absorption,  more  rapidly  than  the  square  of  the  distance. 

The  second  law  of  intensity  corresponds  to  the  law  which  we  have  found 
to  prevail  for  heat :  it  may  be  theoretically  deduced  as  follows  : — Let  DA, 
EB  (fig.  419)  be  a  pencil  of  parallel  rays  falling  obliquely  on  a  surface,  AB, 

and  let  out  be  the  normal  to  this 
surface.  If  S  is  the  section  of  the 
pencil,  a  the  total  quantity  of  light 
which  falls  on  the  surface  AB,  and 
I  that  which  falls  on  the  unit  of 
surface — that  is,  the  intensity  of 

illumination — we  have  I =  — .  But 
AB 

g<  4I9'  as  S  is  only  the  projection  of  AB 

on  a  plane  perpendicular  to  the  pencil,  we  know  from  trigonometry  that 

c 

S  =  AB  cos  a,  from  which  AB  = This  value  substituted  in  the  above 

cos  a 

equation,  gives  I  =  ^  cos  a  ;  a  formula  which  demonstrates  the  law  of  the 

O 


-509] 


Photometers. 


471 


cosine,  for  as  a  and  S  are  constant  quantities,  I  is  proportional  to 
cos  a. 

The  law  of  the  cosine  applies  also  to  rays  emitted  obliquely  by  a  luminous 
surface  ;  that  is,  the  rays  are  less  intense  in  proportion  as  they  are  more 
inclined  to  the  surface  which  emits  them.  In  this  respect  they  correspond 
to  the  third  law  of  the  intensity  of  radiant  heat. 

509.  Photometers. — A  photometer  is  an  apparatus  for  measuring  the 
relative  intensities  of  different  sources  of  light. 

Rumfortfs  photometer. — This  consists  of  a  ground  glass  screen,  in  front 
of  which  is  fixed  an  opaque  rod  (fig.  420) ;  the  lights  to  be  compared — for 
instance,  a  lamp  and  a  candle — are  placed  at  a  certain  distance  in  such  a 
manner  that  each  projects  on  the  screen  a  shadow  of  the  rod.  The  shadows 
thus  projected  are  at  first  of  unequal  intensity,  but  by  altering  the  position 
of  the  lamp,  it  may  be  so  placed  that  the  intensity  of  the  two  shadows  is  the 
same.  Then,  since  the  shadow  thrown  by  the  lamp  is  illuminated  by  the 
candle,  and  that  thrown  by  the  candle  is  illuminated  by  the  lamp,  the  illu- 
mination of  the  screen  due  to  each  light  is  the  same.  The  intensities  of  the 


Fig.  420. 

two  lights  —  that  is,  the  illuminations  which  they  would  give  at  equal  dis- 
tances—are then  directly  proportional  to  the  squares  of  their  distances  from 
the  shadows  ;  that  is  to  say,  if  the  lamp  is  three  times  the  distance  of  the 
candle,  its  illuminating  power  is  nine  times  as  great. 

For  if  /  and  /'  are  the  intensities  of  the  lamp  and  the  candle  at  the  unit 
of  distance,  and  d  and  d'  their  distances  from  the  shadows,  it  follows,  from 
the  first  law  of  the  intensity  of  light,  that  the  intensity  of  the  lamp  at  the 

distance  d  is   *   and  that  of  the  candle  —-  at  the  distance  d'.     On  the  screen 


t 

these  two  intensities  are  equal  ;  hence  -4  =  -L  or  4>  =  —^  which  was  to  be 

proved. 

Bunseris  photometer.—  When  a  grease-spot  is  made  on  a  piece  of  bibu- 
lous paper,  the  part  appears  translucent.  If  the  paper  be  illuminated  by  a 
light  placed  in  front,  the  spot  appears  darker  than  the  surrounding  space  ; 
if,  on  the  contrary,  it  be  illuminated  from  behind,  the  spot  appears  light  on 
a  dark  ground.  If  the  greased  part  and  the  rest  appear  unchanged,  the, 


4/2 


On  Light. 


[509- 


intensity  of  illumination  on  both  sides  is  the  same.     Bunsen's  photometer 
depends  on  an  application  of  this  principle.     Its  essential  features  are  repre- 


Fig.  421. 

sented  in  fig.  421.  A  circular  spot  is  made  on  a  paper  screen  by  means  of  a 
solution  of  spermaceti  in  naphtha  :  on  one  side  of  this  is  placed  a  light  of  a 
certain  intensity,  which  serves  as  a  standard ;  in  London  it  is  a  sperm 
candle  of  six  to  the  pound,  and  burning  120  grains  in  an  hour.  The  light  to 
be  tested,  a  petroleum  lamp  or  a  gas  burner  consuming  a  certain  volume  of 
gas  in  a  given  time,  is  then  moved  in  a  right  line  to  such  a  distance  on  the 
other  side  of  the  screen  that  there  is  no  difference  in  brightness  between  the 
greased  part  and  the  rest  of  the  screen.  By  measuring  the  distances  of 
the  lights  from  the  screen  by  means  of  the  scale,  their  relative  illuminating 
powers  are  respectively  as  the  squares  Of  their  distances  from  the  screen. 

The  difficulty  of  getting  more  carefully  constructed  candles  to  give  a 
light  sufficiently  uniform  for  standard  purposes,  has  led  Harcourt  to  adopt 
as  unit  the  light  formed  by  burning  a  mixture  of  7  volumes  pentane  gas  and 
20  volumes  of  air,  at  the  rate  of  half  a  cubic  foot  in  an  hour,  in  a  specially 
constructed  burner  so  as  to  produce  a  flame  of  a  definite  height.  This  has 
been  found  to  answer  well  in  practice. 

By  this  kind  of  determination  the  degree  of  accuracy  which  can  be 
attained  is  not  so  great  as  in  many  physical  determinations,  more  especially 
when  the  lights  to  be  compared  are  of  different  colours  ;  one,  for  instance, 
being  yellow,  and  the  other  of  a  bluish  tint.  It  gives,  however,  results  which 
are  sufficiently  accurate  for  practical  purposes,  and  is  almost  universally 
employed  for  determining  the  illuminating  power  of  coal  gas  and  of  other 
artificial  lights. 

Wheatstonds  photometer. — The   principal  part   of  this  instrument  is  a 

steel  bead,  P  (fig.  422),  fixed  on  the 
edge  of  a  disc,  which  rotates  on  a 
pinion,  o,  working  in  a  larger 
toothed  wheel.  The  wheel  fits  in  a 
cylindrical  brass  box  which  is  held 
in  one  hand,  while  the  other  works- 
a  handle,  A,  which  turns  a  central 
axis,  the  motion  of  which  is  trans- 
mitted by  a  spoke,  #,  to  the  pinion 
o.  In  this  way  the  latter  turns  on 
itself,  and  at  the  same  time  revolves  round  the  circumference  of  the  box ; 


Fig.  422. 


Fig-  423- 


-510]      Relative  Intensities  of  Various  Sources  of  Light.         473 

the  bead  shares  the  double  motion  and  consequently  describes  a  curve  in 
the  form  of  a  rose  (fig.  423). 

Now,  let  M  and  N  be  the  two  lights  whose  intensities  are  to  be  com- 
pared ;  the  photometer  is  placed  between  them  and  rapidly  rotated.  The 
brilliant  points  produced  by  the  reflection  of  the  light  on  the  two  opposite 
sides  of  the  bead  give  rise  to  two  luminous  bands,  arranged  as  represented 
in  fig.  423.  If  one  of  them  is  more  brilliant  than  the  other — that  which  pro- 
ceeds from  the  light  M,  for  instance — the  instrument  is  brought  nearer  the 
other  light  until  the  two  bands  exhibit  the  same  brightness.  The  distance 
of  the  photometer  from  each  of  the  two  lights  being  then  measured,  their 
intensities  are  proportional  to  the  squares  of  the  distances. 

510.  Relative  intensities  of  various  sources  of  lignt — The  light  of  the 
sun  is  600,000  times  as  powerful  as  that  of  the  moon  ;  and  16,000,000,000 
times  as  powerful  as  that  of  a  Centanri^  the  third  in  brightness  of  all  the 
stars.  The  moon  is  thus  27,000  times  as  bright  as  this  star  ;  the  sun  is  5,500 
million  times  as  bright  as  Jupiter,  and  80  billion  times  as  bright  as  Neptune. 
Its  light  is  estimated  to  be  670,000  times  that  of  a  wax  candle  at  a  distance 
of  I  foot.  According  to  Fizeau  and  Foucault  the  electric  light  produced  by  50 
Bunsen's  cells  is  about  \  as  strong  as  sunlight. 

The  relative  luminosities  of  the  following  stars  are  as  compared  with 
Vega=i;  Pole  Star  0-13,  Aldebaran  0-30,  Saturn  0-47,  Arcturus  079, 
Mars  2-93,  Sirius  4^291,  Jupiter  8*24,  Venus  38-9. 

A  difference  in  the  strength  of  light  or  shadow  is  perceived  when  the 
duller  light  is  ff  of  the  brightness  of  the  other,  and  both  are  near  together, 
especially  when  the  shadow  is  moved  about. 


474 


On  Light. 


[511- 


CHAPTER   II. 

REFLECTION    OF    LIGHT.      MIRRORS. 

511.  laws  of  the  reflection  of  ligrfct.—  When  a  ray  of  light  meets  a 
polished  surface,  it  is  reflected  according  to  the  two  following  laws,  which, 
as  we  have  seen,  also  hold  for  heat. 

I.  The  angle  of  reflection  is  equal  to  the  angle  of  incidence. 

II.  The  incident  and  the  reflected  ray  are  both  in  the  same  plane,  which 
is  perpendicular  to  the  reflecting  surface. 

The  words  are  here  used  in  the  same  sense  as  in  article  411,  and  need 

no  further  explanation. 

First  proof.— The  two   laws   may  be   demonstrated   by  the  apparatus 

represented  in  fig.  424.     It  consists  of  a  graduated  circle  in  a  vertical  plane. 

Two  brass  slides  move  round  the  cir- 
cumference ;  on  one  of  them  there  is 
a  piece  of  ground  glass,  P,  and  on  the 
other  an  opaque  screen,  N,  in  the 
centre  of  which  is  a  small  aperture. 
Fixed  to  the  latter  slide  there  is  also 
a  mirror,  M,  which  can  be  more  or  less 
inclined,  but  always  remains  in  a  plane 
perpendicular  to  the  plane  of  the  gra- 
duated circle.  Lastly,  there  is  a  small 
polished  metallic  mirror,  ;;/,  placed 
horizontally  in  the  centre  of  the  circle. 
In  making  the  experiment,  a  pencil 
of  solar  or  any  suitable  artificial  light, 
S,  is  caused  to  fall  on  the  mirror 
M,  which  is  so  inclined  that  the  re- 
flected light  passes  through  the  aper- 
ture in  N,  and  falls  on  the  centre  of 
the  mirror,  m.  The  luminous  pencil 
then  experiences  a  second  reflection 
in  a  direction  ;#P,  which  is  ascertained 

by  moving  P  until  an  image  of  the  aperture  is  found  in  its  centre.     The 

number  of  degrees  comprised  in  the  arc  AN  is  then  read  off,  and  likewise 

that  in  AP  ;  these  being  equal,  it  follows  that  the  angle  of  reflection  AmP 

is  equal  to  the  angle  of  incidence  AmM. 

The  second  law  follows  from  the  arrangement  of  the  apparatus,  the  plane 

of  the  rays  Mm  and  mP  being  parallel  to  the  plane  of  the  graduated  circle, 

and,  consequently,  perpendicular  to  the  mirror  m. 


Fig.  424. 


-513]  Formation  of  Images  by  Plane  Mirrors.  475 

Second  proof. — The  law  of  the  reflection  of  light  may  also  be  demon- 
strated by  the  following  experiment,  which  is  susceptible  of  greater  accuracy 
that  than  just  described  : — In  the  centre  of  a  graduated  circle,  M  (fig.  425), 
placed  in  a  vertical  position,  there  is  a  small  telescope  movable  in  a  plane 
parallel  to  the  limb  ;  at  a  suitable  distance  there  is  a  vessel  D  full  of  mercury, 
which'  forms  a  perfectly  horizontal  plane  mirror.  Some  particular  star  of 
the  first  or  second  magnitude  is  viewed  through  the  telescope  in  the  direction 
AE,  and  the  telescope  is  then  inclined  so  as  to  receive  the  ray  AD  coming 
from  the  star  after  being  reflected  from  the  brilliant  surface  of  the  mercury. 


Fig.  425- 

In  this  way  the  two  angles  formed  by  the  rays  EA  and  DA,  with  the  hori- 
zontal AH,  are  found  to  be  equal,  from  which  it  may  easily  be  shown  that 
the  angle  of  incidence  E'DE  is  equal  to  the  angle  of  reflection  EDA.  For 
if  DE  is  the  normal  to  the  surface  of  the  mercury,  it  is  perpendicular  to  AH, 
and  AED,  ADE  are  the  complements  of  the  equal  angles  EAH,  DAH  ; 
therefore  AED,  ADE  are  equal  ;  but  the  two  rays  AE  and  DE7  may  be 
considered  parallel,  in  consequence  of  the  great  distance  of  the  star,  and 
therefore  the  angles  EDE'  and  DEA  are  equal,  for  they  are  alternate  angles 
and,  consequently,  the  angle  E'DE  is  equal  to  the  angle  EDA. 

REFLECTION   OF   LIGHT   FROM   PLANE   SURFACES. 

512.  Mirrors.     Images. — Mirrors   are  bodies  with   polished   surfaces, 
which  show  by  reflection  objects  presented  to  them.     The  place  at  which 
objects  appear  is  their  image.     According  to  their  shape,  mirrors.are  divided 
into  plane,  concave,  convex,  spherical,  parabolic,  conical,  £c. 

513.  Formation  of  images  by  plane  mirrors. — The  determination  of 
the  position  and  size  of  images  resolves  itself  into  investigating  the  images 
of  a  series  of  points.   And  first,  the  case  of  a  single  point,  A,  placed  in  front 
of  a  plane  mirror,  MN  (fig.  426),  will  be  considered.     Any  ray,  AB,  incident 
from  this  point  on  the  mirror  is  reflected  in  the  direction  BO,  making  the 
angle  of  reflection  DBO  equal  to  the  angle  of  incidence  DBA. 

If,  now,  a  perpendicular,  AN,  be  let  fall  from  the  point  A  on  the  mirror, 


476  On  Light.  [513- 

and  if  the  ray  OB  be  prolonged  below  the  mirror  until  it  meets  this  perpen- 
dicular in  the  point  a,  two  triangles  are  formed,  ABN  and  BN#,  which  are 
equal,  for  they  have  the  side  BN  common  to  both,  and  the  angles  ANBr 
ABN,  equal  to  the  angles  «NB,  «BN  ;  for  the  angles  ANB  and  aNB  are 
right  angles,  and  the  angles  ABN  and  #BN  are  each  equal  to  the  angle 
OEM.  From  the  equality  of  these  triangles,  it  follows  that  «N  is  equal  to 
AN  ;  that  is,  that  any  ray,  AB,  takes  such  a  direction  after  being  reflected,, 
that  its  prolongation  below  the  mirror  cuts  the  perpendicular  Aa  in  the  point 
a,  which  is  at  the  same  distance  from  the  mirror  as  the  point  A.  This  ap- 
plies also  to  the  case  of  any  other  ray  from  the  point  A — AC,  for  example. 


Fig.  426.  Fig.  427. 

From  this  the  important  consequence  follows,  that  all  rays  from  the  point 
A,  reflected  from  the  rmryor,  follow,  after  reflection,  the  sajne  direction  as  if 
they  had  all  proceeded  from  the  point  a.  The  eye  is  deceived,  and  sees  the 
point  A  at  a,  as  if  it  were  really  situated  at  a.  Hence  in  plane  mirrors  the 
image  of  any  point  is  formed  behind  the  mirror  at  a  distance  equal  to  that  of 
the  given  point,  and  on  the  perpendicular  let  fall  from  this  point  on  the 
mirror. 

It  is  manifest  that  the  image  of  any  object  will  be  obtained  by  construct- 
ing, according  to  this  rule,  the  image  of  each  of  its  points,  or,  at  least,  of  those 
which  are  sufficient  to  determine  its  form.  Fig.  427  shows  how  the  image 
ab  of  any  object,  AB,  is  formed. 

It  follows  from  this  construction  that  in  plane  mirrors  the  image  is  of  the 
same  size  as  the  object ;  for  if  the  trapezium  ABCD  be  applied  to  the  trapezium 
DCfl£,  they  are  seen  to  coincide,  and  the  object  AB  agrees  with  its  image. 

A  further  consequence  from  the  above  construction  is,  that  in  plane 
mirrors  the  image  is  symmetrical  in  reference  to  the  object,  and  not  inverted. 

514.  Virtual  and  real  images. — There  are  two  cases  relative  to  the 
direction  of  rays  reflected  by  mirrors  according  as  the  rays  after  reflection 
are  convergent  or  divergent.  In  the  first  case  the  reflected  rays  do  not  meet, 
but  if  they  are  supposed  to  be  produced  on  the  other  side  of  the  mirror,  their 
prolongations  coincide  in  the  same  point,  as  shown  in  figs.  425  and  426. 
The  eye  is  then  affected  just  as  if  the  rays  proceeded  from  this  point,  and 
it  sees  an  image.  But  the  image  has  no  real  existence,  the  luminous  rays  do- 
not  come  from  the  other  side  of  the  mirror  :  this  appearance  is  called  the 
virtual  image.  The  images  of  real  objects  produced  by  plane  mirrors  are  of 
this  kind. 

In  the  second  case,  where  the  reflected  rays  converge,  of  which  we  shall 


-516]  Multiple  Images  from  Two  Plane  Mirrors.  477 

soon  have  an  example  in  concave  mirrors,  the  rays  coincide  at  a  point  in 
front  of  the  mirror,  and  on  the  same  side  as  the  object.  They  form  there  an 
image  called  the  real  image,  for  it  can  be  received  on  a  screen.  The  dis- 
tinction may  be  expressed  by  saying  that  real  images  are  those  formed  by  the 
reflected  rays  themselves,  and  'virtual  images  those  formed  by  their  prolonga- 
tions. 

515.  Multiple    images  formed   by  glass    mirrors. — Metallic   mirrors 
which  have  but  one  reflecting  surface  only  give  one  image ;  glass  mirrors 
give  rise  to  several  images,  which  are  readily  ob- 
served when  the  image  of  a  candle  is  looked  at 

obliquely  in  a  looking-glass.  A  very  feeble  image 
is  first  seen,  and  then  a  very  distinct  one  ;  behind 
this  there  are  several  others,  whose  intensities  gra- 
dually decrease  until  they  disappear. 

This  phenomenon  arises  from  the  looking-glass 
having  two  reflecting  surfaces.  When  the  rays 
from  the  point  A  meet  the  surface,  fig.  428,  a  part  is 
reflected  and  forms  an  image,  a,  of  the  point  A,  on 
the  prolongation  of  the  ray  <£E,  reflected  by  this  Flgt  428> 

surface  ;  the  other  part  passes  into  the  glass,  and  is  reflected  at  c,  from  the 
layer  of  metal  which  covers  the  hinder  surface  of  the  glass,  and  reaching  the 
eye  in  the  direction  d?H  gives  the  image  a'.  This  image  is  distant  from  the 
first  by  double  the  thickness  of  the  glass.  It  is  more  distinct,  because  metal 
reflects  better  than  glass. 

In  regard  to  other  images  it  will  be  remarked  that  whenever  light  is 
transmitted  from  one  medium  to  another — for  instance,  from  glass  to  air — 
only  some  of  the  rays  get  through  ;  the  remainder  are  reflected  at  the  surface 
which  bounds  the  two  media.  Consequently  when  the  pencil  cd,  reflected 
from  c,  attempts  to  leave  the  glass  at  d,  most  of  the  rays  composing  it  pass 
into  the  air,  but  some  are  reflected  at  d,  and  continue  within  the  glass. 
These  are  again  reflected  by  the  metallic  surface,  and  form  a  third  image  of 
A  ;  after  this  reflection  they  come  to  MN,  when  many  emerge  and  render 
the  third  image  visible  ;  but  some-are  again  reflected  within  the  glass,  and 
in  a  similar  manner  give  rise  to  a  fourth,  fifth, 
&c.,  image,  thereby  completing  the  series 
above  described.  It  is  manifest  from  the 
above  explanation  that  each  image  must  be 
much  feebler  than  the  one  preceding  it,  and 
consequently  not  more  than  a  small  number 
are  visible — ordinarily  not  more  than  eight 
or  ten  in  all. 

This  multiplicity  of  images  is  objection- 
able in  observations,  and,  accordingly,  me- 
tallic mirrors  are  to  be  preferred  in  optical 
instruments. 

516.  Multiple  images  from  two  plane  Fig  42p> 
mirrors. — When  an  object  Is   placed    be- 
tween two  plane  mirrors,  which  form  an  angle  with  each  other,  either  right 
or  acute,  images  of  the  object  are  formed,  the  number  of  which  increases 


478  On  Light  [516- 

with  the  inclination  of  the  mirrors.  If  they  are  at  right  angles  to  each 
other,  three  images  are  seen,  arranged  as  represented  in  fig.  429.  The  rays 
OC  and  OD  from  the  point  O,  after  a  single  reflection,  give  the  one  an 
image  O',  and  the  other  an  image  O",  while  the  ray  OA,  which  has  under- 
gone two  reflections  at  A  and  B,  gives  the  third  image  O'".  When  the 
angle  of  the  mirrors  is  60°,  five  images  are  produced,  and  seven  if  it  is  45°. 
The  number  of  images  continues  to  increase  in  proportion  as  the  angle 
diminishes,  and  when  it  is  zero — that  is,  when  the  mirrors  are  parallel — the 
number  of  images  is  theoretically  infinite.  This  multiplicity  arises  from  the 
fact  that  the  luminous  rays  undergo  an  increasing  number  of  reflections 
from  one  mirror  to  the  other. 

The  kaleidoscope,  invented  by  Sir  D.  Brewster,  depends  on  this  property 
of  inclined  mirrors.  It  consists  of  a  tube,  in  which  are  three  mirrors  inclined 
at  60°  ;  one  end  of  the  tube  is  closed  by  a  piece  of  ground  glass,  and  the  other 
by  a  cap  provided  with  an  aperture.  Small  irregular  pieces  of  coloured  glass 
are  placed  at  one  end  between  the  ground  glass  and  another  glass  disc,  and 
on  looking  through  the  aperture,  the  other  end  being  held  towards  the  light, 
the  objects  and  their  images  are  seen  arranged  in  beautiful  symmetrical  forms; 
by  turning  the  tube,  an  almost  endless  variety  of  these  shapes  is  obtained. 

517.  Multiple  images  in  two  plane  parallel  mirrors. — In  this  case 
the  number  of  images  of  an  object  placed  between  them  is  theoretically  in- 
finite. Physically  the  number  is  limited,  for  as  the  incident  light  is  never 
totally  reflected,  some  of  it  being  always  absorbed,  the  images  gradually 
become  fainter,  and  are  ultimately  quite  extinguished. 

Fig.  430  shows  how  the  pencil  L#  reflected  once  from  M  gives  at  I  the 
image  of  the  object  L  at  a  distance  MI  =  ML  ;  then  the  pencil  L<£  reflected 
once  from  the  mirror  M,  and  once  from  N,  furnishes 
the  image  F  at  a  distance  «I'«=»I;  in  like  manner 
the  pencil  L^,  after  two  reflections  on  M,  and  one 
on  N,  forms  the  image  I"  at  a  distance  m\"  =  m\', 
and  so  on  for  an  infinite  series.  The  images  /,  zv,  i'r 

are  formed 
in  the  same 
manner  by 
rays  of  light 
which  emit- 
ted by  the 
object  L  fall 
first  on  the 
mirror  N. 

518.  Irregular  reflection.      Diffused    ligrnt.— The 
reflection  from  the  surfaces  of  polished  bodies,  the  laws 
of  which  have  just  been  stated,  is  called  the  regular  or 
specular  reflection  ;  but  the  quantity  thus  reflected  is  less 
Fig.  43o.  than  that  of  the  mcident  light.     The  light  incident  on  an 

opaque  body  separates,  in  fact,  into  three  parts  :  one  is  reflected  regularly  : 
another  irregularly— that  is,  in  all  directions  ;  while  a  third  is  extinguished, 
or  absorbed  by  the  reflecting  body.  If  light  falls  on  a  transparent  body,  a 
considerable  portion  is  transmitted  with  regularity. 


-520]     Reflection  of  a  Ray  of  Light  in  a  Rotating  Mirror.      479 

The  irregularly  reflected  light  is  called  scattered  light :  it  is  that  which 
makes  bodies  visible  (502).  The  light  which  is  reflected  regularly  does  not 
give  us  the  image  of  the  reflecting  surface,  but  that  of  the  body  from 
which  the  light  proceeds.  If,  for  example,  a  beam  of  sunlight  be  incident  on 
a  well-polished  mirror  in  a  dark  room,  the  more  perfectly  the  light  is  reflected 
the  less  visible  is  the  mirror  in  the  different  parts  of  the  room.  The  eye 
does  not  perceive  the  image  of  the  mirror,  but  that  of  the  sun.  If  the  reflect- 
ing power  of  the  mirror  be  diminished  by  sprinkling  on  it  a  light  powder,  the 
solar  image  becomes  feebler,  and  the  mirror  is  visible  from  all  parts  of  the 
room.  Perfectly  smooth,  polished  reflecting  surfaces,  if  such  there  were,, 
would  be  invisible.  The  beam  of  light  itself  is  only  seen  in  the  room  owing 
to  irregular  reflections  from  the  particles  of  dust,  and  the  like,  which  are 
floating  in  the  air.  Tyndall  has  shown  that  when  this  floating  matter  in  the 
air  in  an  enclosed  space  is  completely  removed,  the  beam  of  sunlight  or  the 
electric  light  is  quite  invisible.  The  atmosphere  diffuses  the  light  which 
falls  on  it  from  the  sun  in  all  directions,  so  that  it  is  light  in  places  which  do 
not  receive  the  direct  rays  of  the  sun.  Thus,  the  upper  layers  of  the  air 
diffuse  the  light  which  they  receive  before  sunrise  and  sunset,  and  accord- 
ingly give  rise  to  the  phenomena  oi  twilight. 

519.  Intensity  of  reflected  light. — The  intensity  of  reflected  light  is 
always  less  than  that  of  the  incident  light,  for  some  of  the  original  vibrations 
are   converted   into   vibrations   of  the  reflecting  surfaces.      The   intensity 
increases  with  the  obliquity  of  the  incident  ray.     For  instance,  if  a  sheet 
of  white  paper  be  placed  before  a  candle,  and  be  looked  at  very  obliquely,, 
an  image  of  the  flame  is  seen  by  reflection,  which  is  not  the  case  if  the  eye 
receives  less  oblique  rays. 

The  intensity  of  the  reflection  varies  with  different  bodies,  even  when 
the  degree  of  polish  and  the  angle  of  incidence  are  the  same.  Thus  with  a 
perpendicular  incidence  the  reflected  light  is  f  of  the  incident  in  the  case  of 
that  reflected  from  a  metal  mirror,  f  from  mercury,  i  from  glass,  and  -j-- 
from  water.  It  also  varies  with  the  nature  of  the  medium  which  the  ray  is 
traversing  before  and  after  reflection.  Polished  glass  immersed  in  water 
loses  a  great  part  of  its  reflecting  power. 

In  the  case  of  scattered  reflection  the  actual  lustre  or  brightness  of  a 
luminous  surface  is  only  a  fraction  of  the  light 
which  falls  upon  it,  and  depends  on  the  nature  of 
the  surface.  If  we  call  the  incident  light  100, 
we  have  for  the  brightness  of  freshly  fallen  snow 
78,  white  paper  70,  white  sandstone  24,  porphyry 
II,  and  ordinary  earth  8. 

520.  Reflection  of  a  ray  of  ligrnt  in  a  ro- 
tating: mirror. — When  a  horizontal  ray  of  light 
falls  on  a  plane  mirror  which  can  rotate  about 
a  vertical  axis,  if  the  mirror  is  turned  through  an 
angle  a,  the   reflected  ray   is    turned  through 
double  the  angle. 

Let  nm  (fig.  431)  be  the  first  position  of  the  mirror,  n'm'  its  position  after 
it  has  been  turned  through  the  angle  a  ;  and  let  OD  be  the  fixed  incident 
ray.  If  from  the  centre  of  rotation  C,  with  any  radius  we  describe  the  cir- 


480 


On  Light. 


[520- 


^ 
y 


cumference  Omn,  and  from  the  point  O,  where  it  cuts  the  incident  ray, 
chords  OO'and  OO"  are  drawn  perpendicular  respectively  to  mn  and  m'n' ; 
the  points  O'  and  O"  are  the  images  of  the  point  O  in  the  two  positions  of 
the  mirror,  and  the  angles  CO'D  and  CO"D'  are  each  equal  to  COD.  The 
lines  O'D  and  O"D'  thus  making  equal  angles  with  O'C  and  O"C,  the  angle 
between  the  two  former  lines  is  equal  to  that  between  the  two  latter ;  that 
is,  it  will  be  equal  to  O'CO",  and  will  be  measured  by  the  arc  O'O". 
The  rotations  of  the  reflected  ray  and  of  the  mirror  are  thus  measured  by 
the  two  arcs  O'O"  and  mm'  respectively. 

Now,  the  two  angles  O'OO"  and  mCm'  are  equal,for  they  have  their 
sides  perpendicular  each  to  each  ;  but  the  angle  O'OO",  which  is  an  angle 
at  the  circumference,  is  measured  by  half  the  arc  O'O'',  and  the  angle 
mCm'  by  the  whole  arc  mm'  \  hence  O'O"  is  the  double  of  ;;/;«',  which 
shows  that  when  the  mirror  has  turned  through  an  angle  a,  the  reflected  ray 
has  turned  through  2a. 

521.  Hartley's  reflecting-  sextant. — The  principal  features  of  this  in- 
strument, which  is  used  to  measure  the  angular  distance  of  any  two  distant 
objects,  are  represented  in  fig.  432.  It  consists  of  a  metal  sector,  the  arc,  cd, 

of  which  is  graduated.  About 

&\  the  centre  of  the  sector,  an 

/  index  arm,  ab,  turns  ;  this  is 

provided  with  a  vernier  and 
a  micrometer  screw,  by  which 
the  index  may  be  accurately 
adjusted  and  also  clamped. 
A  mirror  at  a  is  fixed  perpen- 
dicularly to  the  arm  ab,  and 
therefore  moves  with  it.  A 
telescope  de  is  permanently 
fixed  to  the  arm  ac,  and  oppo- 


Si 


" 


site  to  it  is  a  second  mirror 
m,  also  permanently  fixed  ; 
the  lower  half  of  this  is 
silvered,  and  the  axis  of  the 
telescope  just  traverses  the 
boundary  of  the  silvered  and 

F;gi  432.  unsilvered  part  of  the  mirror. 

In  making  an  observation, 

the  sextant  is  held  so  that  its  plane  may  pass  through  both  the  objects  whose 
angular  distance  is  to  be  measured.  The  index  arm  is  at  the  zero  of  the 
graduation,  which  indicates  the  parallelism  of  the  two  mirrors.  One  of  the 
objects  is  then  viewed  in  the  direction  om,  through  the  telescope,  and  the 
unsilvered  part  of  the  mirror  m.  The  index  arm  is  then  moved  until  the 
eye  sees  simultaneously  with  this  the  image  of  another  object  g,  which 
reaches  the  eye  after  successive  reflections  from  the  mirror  «,  and  from  the 
silvered  part  of  the  mirror  m  ;  that  is,  by  the  path  gamedo.  The  angle 
mha  which  the  two  mirrors  now  form  is  measured  by  the  graduation  of  the 
sector  cd,  and  is  half  the  angle  gom.  For  when  the  two  mirrors  were  parallel 
the  angular  deflection  of  the  ray  ga,  after  two  reflections,  would  be  zero,  and 
its  deflection  is  now  the  angle  gom  ;  whence,  by  the  last  article,  the  mirror  a 


-523]  Mance's  Heliograph.  481 

must  have  turned  through  half  that  angle,  the  mirror  m  having  been  fixed 
in  position  throughout. 

522.  Measurement  of  small  angles  by  reflection  from  a  mirror. — An 

important  application  is  made  of  the  laws  of  reflection  in  measuring  small 
angles  of  deflection  in 
magnetic  and  other  ob- 
servations. The  prin- 
ciple  of  this  method 
will  be  understood 
from  fig.  433,  in  which 
AO  represents  a  tele- 
scope, underneath 
which,  and  at  right 
angles  to  its  axis,  is 
fixed  a  graduated  scale 
ss\  the  centre  of  which, 
the  zero,  corresponds 
to  the  axis  of  the  tele-  Fig.  433. 

scope. 

Let  NS  be  the  object  whose  angular  deflection  is  to  be  measured,  a  mag- 
net for  instance,  and  let  mm  represent  a  small  perfectly  plane  mirror  fixed 
rigidly  at  right  angles  to  the  axis  of  the  magnet.  If  now,  at  the  beginning 
of  the  observation,  the  telescope  is  adjusted  so  that  the  image  of  the  zero, 
appears  behind  the  cross  wires,  its  axis  is  perpendicular  to  the  mirror.  Now 
when  the  mirror  is  turned,  by  whatever  cause,  through  an  angle  «,  the  eye 
will  see,  through  the  telescope,  the  image  of  another  division  of  the  scale,  a 
for  instance,  the  ray  proceeding  from  which  makes  with  the  line  cOA.  the 
angle  2a. 

From  the  distance  of  this  division  Oa  from  the  zero  of  the  scale  and  the 

distance  Oc  from  the  mirror  we  have  tan  20.  =  -^.      Thus,  for  instance,  if  Oa 

is  12  millimetres  and  Oc  5,000  millimetres,  then  tan  2#  =    I2    ,    from  which 

5,000' 

2a  =  8'  1 5".     As  a  practised  eye  can  easily  read  ^  of  a  millimetre,  it  is  pos- 
sible by  such  an  arrangement  to  read  off  an  angular  deflection  of  two  seconds. 

523.  AXance's  heliograph. — The  reflection  of  light  from   mirrors  has 
been  applied  by  Mance  in  signalling  at  great  distances  by  means  of  the  sun's 
light. 

The  apparatus  consists  essentially  of  a  mirror  about  4  inches  in  diameter 
mounted  on  a  tripod,  and  provided  with  suitable  adjustments,  so  that  the 
sun's  light  can  be  received  upon  it  and  reflected  to  a  distant  station.  An 
observer  then  can  see  through  a  telescope  the  reflection  of  the  sun's  rays  as 
a  spot  of  light.  The  mirror  has  an  adjustment  by  which  it  can  be  made  to 
follow  the  sun  in  its  apparent  motion.  There  is  also  a  lever  key  by  which  the 
signaller  can  deflect  the  mirror  through  a  very  small  angle  either  to  the 
right  or  left,  and  thus  the  observer  at  the  distant  station  sees  corresponding 
flashes  to  the  right  or  left.  Under  the  subject  of  Telegraphy  it  will  be  seen 
how  these  alternate  motions  can  be  used  to  form  an  alphabet. 

The  heliograph  proved  of  essential  service  in  the  campaigns  in  Africa 

I  I 


\ 


482  On  Light.  [523- 

and  Afghanistan.  Instead  of  any  special  form  of  apparatus,  an  ordinary 
shaving  mirror  or  hand-glass  is  frequently  used  ;  and  the  proper  inclination 
having  been  given  so  as  to  send  the  sun's  rays  to  the  distant  station,  which  is 
very  easily  effected,  the  signals  are  produced  by  obscuring  the  mirror  by 
sliding  a  piece  of  paper  over  it  for  varying  lengths  of  time.  In  this  way 
longer  or  shorter  flashes  of  light  are  produced,  which,  properly  combined,, 
form  the  alphabet. 

Of  course  this  mode  of  signalling  can  only  be  used  where  the  sun's  light 
is  available,  but  it  has  the  advantage  of  being  cheap,  simple,  and  portable. 
Signals  have  been  sent  at  the  ra'te  of  12  words  a  minute,  through  distances,, 
in  very  fine  weather,  of  40  miles. 

REFLECTION  OF  LIGHT  FROM  CURVED  SURFACES. 

524.  Spherical  mirrors. — It  has  been  already  stated  (512)  that  there  are 
several  kinds  of  curved  mirrors ;  those  most  frequently  employed  are 
spherical  and  parabolic  mirrors. 

Spherical  mirrors  are  those  whose  curvature  is  that  of  a  sphere  ;  their 
surface  may  be  supposed  to  be  formed  by  the  revolution  of  an  arc  MN  (fig. 
434)  about  the  radius  CA,  which  unites  the  middle  of  the  arc  to  the  centre 
of  the  circle  of  which  it  is  a  part.  According  as  the  reflection  takes  place 

from  the  internal  or  from 
the  external  face  of  the 
mirror  it  is  said  to  be 
concave  or  convex.  C,  the 
centre  of  the  hollow  sphere 
of  which  the  mirror  forms 
part  is  called  the  centre  of 
curvature,  or  geometrical 
Flg-  434-  centre :  the  point  A  is  the 

centre  of  the  figure.  The  infinite  right  line  AL,  which  passes  through  A  and 
C,  is  the  principal  axis  of  the  mirror  ;  any  right  line  which  simply  passes 
through  the  centre  C,  and  not  through  the  point  A,  is  a  secondary  axis. 
The  angle  MCN,  formed  by  joining  the  centre  and  extremities  of  the 
mirror,  is  the  aperture.  A  principal  or  meridional  section  is  the  section 
made  by  a  plane  through  its  principal  axis.  In  speaking  of  mirrors  those 
lines  alone  will  be  considered  which  lie  in  the  same  principal  section. 

The  theory  of  the  reflection  of  light  from  curved  mirrors  is  easily  deduced 
from  the  laws  of  reflection  from  plane  mirrors,  by  considering  the  surface  of 
the  former  as  made  up  of  an  infinitude  of  extremely  small  plane  surfaces, 
which  are  its  elements.  The  normal  to  the  curved  surface  at  a  given  point  is 
the  perpendicular  to  the  corresponding  element,  or,  what  is  the  same  thing, 
to  its  corresponding  tangent  plane.  It  is  shown  in  geometry  that  in  spheres 
all  the  normals  pass  through  the  centre  of  curvature,  so  that  the  normal  may 
readily  be  drawn  to  any  point  of  a  spherical  mirror. 

525.  Focus  of  a  spherical  concave  mirror. —  In  a  curved  mirror  the 
focus  is  a  point  in  which  the  reflected  rays  meet  or  tend  to  meet,  if  produced 
either  backwards  or  forwards  ;  there  may  either  be  a  real  focus  or  a  virtual 
focus. 


-525]  Focus  of  a  SpJierical  Concave  Mirror.  483 

Real  focus. — We  shall  first  consider  the  case  in  which  the  rays  of  light 
are  parallel  to  the  principal  axis,  which  presupposes  that  the  luminous  body 
is  at  an  infinite  distance.  Let  GD  (fig.  434)  be  such  a  ray. 

From  the  hypothesis  that  curved  mirrors  are  composed  of  a  number  of 
infinitely  small  plane  elements,  this  ray  would  be  reflected  from  the  element 
corresponding  to  the  point  D,  according  to  the  laws  of  the  reflection  from 
plane  mirrors  (513)  ;  that  is,  that  CD  being  the  normal  at  the  point  of 
incidence  D,  the  angle  of  reflection  CDF,  is  equal  to  the  angle  of  incidence 
GDC,  and  is  in  the  same  plane.  It  follows  from  this,  that  the  point  F,  where 
the  reflected  ray  cuts  the  principal  axis,  divides  the  radius  of  curvature  AC 
very  nearly  into  two  equal  parts.  For  in  the  triangle  DFC  the  angle  DCF 
is  equal  to  the  angle  CDG,  for  they  are  alternate  and  opposite  angles  ;  likewise 
the  angle  CDF  is  equal  to  the  angle  CDG,  from  the  laws  of  reflection  ;  there- 
fore the  angle  FDC  is  equal  to  the  angle  FCD,  and  the  sides  FC  and  FD 
are  equal  as  being  opposite  to  equal  angles.  Now  the  smaller  the  arc  AD, 
the  more  nearly  does  DF  equal  AF  ;  and  when  the  arc  is  only  a  small  number 
of  degrees,  the  right  lines  AF  and  FC  may  be  taken  as  approximately  equal, 
and  the  point  F  may  be  taken  as  the  middle  of  AC.  So  long  as  the  aperture 
of  the  mirror  does  not  exceed  8  to  10  degrees,  any  other  ray  HB,  will,  after 
reflection,  pass  very  nearly  through  the  point  F.  Hence,  when  a  pencil  of  rays 
parallel  to  the  axis  falls  on  a  concave  mirror  the  rays  intersect  after  reflection 
in  the  same  point,  which  is  at  an  equal  distance  from  the  centre  of  curvature, 
and  from  the  mirror.  This  point  is  called  the  principal  focus  of  the  mirror, 
and  the  distance  AF  is  the  prin cipal  focal  distance. 

All  rays  parallel  to  the  axis  meet  in  the  point  F  ;  and,  conversely,  if  a 
luminous  point  be  placed  at  F,  the  rays  emitted  by  this  point  will  after 
reflection  take  the  direc- 
tions DG,  BH,  parallel  to 
the  principal  axis  ;  for  in 
this  case  the  angles  of  in- 
cidence and  reflection  have 
changed  places  ;  but  these 
angles  always  remain  equal. 
The  case  is  now  to  be 
considered  in  which  the  Fig.  435. 

rays  are    emitted    from    a 

luminous  point,  L  (fig.  435),  placed  on  the  principal  axis,  but  at  such  a  dis- 
tance that  they  are  not  parallel,  but  divergent.  The  angle  LKC,  which  the 
incident  ray  LK  forms  with  the  normal  KC,  is  smaller  than  the  angle  SKC, 
which  the  ray  SK,  parallel  to  the  axis,  forms  with  the  same  normal ;  and, 
consequently,  the  angle  of  reflection  corresponding  to  the  ray  LK  must  be 
smaller  than  the  angle  CKF,  corresponding  to  the  ray  SK.  And  therefore 
the  ray  LK  will  meet  the  axis  after  reflection  at  a  point  /,  between  the 
centre  C  and  the  principal  focus  F.  So  long  as  the  aperture  of  the  mirror 
does  not  exceed  a  small  number  of  degrees,  all  the  rays  from  the  point  L 
will  intersect  after  reflection  in  the  point  /.  This  point  is  called  the  conjugate 
focus  •  for  there  is  this  connection  between  the  points  L  and  /,  that  if  the 
luminous  point  were  transferred  to  /,  its  conjugate  focus  would  be  at  L,  /K 
being  the  incident  and  KL  the  reflected  ray. 


484  On  Light.  [525- 

On  considering  the  figure  435  it  will  be  seen  that  when  the  point  L  is 
brought  near  to  or  removed  from  the  centre  C,  its  conjugate  focus  approaches 
or  recedes  in  a  corresponding  manner,  for  the  angles  of  incidence  and  re- 
flection increase  or  decrease  together. 

If  the  point  L  coincides  with  the  centre  C,  the  angle  of  incidence  is 
null,  and  as  the  angle  of  reflection  must  be  the  same,  the  ray  is  reflected  on 
itself,  and  the  focus  coincides  with  the  luminous  point.  When  the  luminous 
point  is  between  the  centre  C  and  the  principal  focus,  the  conjugate  focus  in 
turn  is  on  the  other  side  of  the  centre,  and  is  further  from  the  centre  accord- 
ing as  the  luminous  point  is  nearer  the  principal  focus.  If  the  luminous  point 
coincides  with  the  principal  focus,  the  reflected  rays,  being  parallel  to  the 
axis,  will  not  meet,  and  there  is,  consequently,  no  focus. 

Virtual  focus. — There  is,  lastly,  the  case  in  which  the  point  is  placed  at 
L,  between  the  principal  focus  and  the  mirror  (fig.  436).  Any  ray  LM, 
emitted  from  the  point  L,  makes  with  the  normal  CM  an  angle  of  incidence, 
LMC,  greater  than  FMC  ;  the  angle  of  reflection  must  be  greater  than  CMS, 
and  therefore  the  reflected  ray  ME  diverges  from  the  axis  AK.  This  is  also 
the  case  with  all  rays  from  the  point  L,  and  hence  these  rays  do  not  intersect, 
and,  consequently,  form  no  conjugate  focus  ;  but  if  they  are  conceived  to  be 
prolonged  on  the  other  side  of  the  mirror,  their  prolongations  will  intersect 


Fig.  436.  Fig.  437. 

in  the  same  point,  /,  on  the  axis,  and  the  eye  experiences  the  same  impression 
as  if  the  rays  were  directly  emitted  from  the  point  /.  Hence  a  virtual  focus 
is  formed  quite  analogous  to  those  formed  by  plane  mirrors  (514). 

In  all  these  cases  it  is  seen  that  the  position  of  the  principal  focus  is 
constant,  while  that  of  the  conjugate  foci  and  of  the  virtual  foci  vary.  The 
principal  and  the  conjugate  foci  are  always  on  the  same  side  of  the  mirror  as 
the  luminous  point,  while  the  virtual  focus  is  always  on  the  other  side  of  the 
mirror. 

Hitherto  the  luminous  point  has  always  been  supposed  to  be  placed  on 
the  principal  axis  itself,  and  then  the  focus  is  formed  on  this  axis.  In  the 
case  in  which  the  luminous  point  is  situate  on  a  secondary  axis,  LB  (fig.  437), 
by  applying  to  this  axis  the  same  reasoning  as  in  the  preceding  case,  it  will 
be  seen  that  the  focus  of  the  point  L  is  formed  at  a  point  /  on  the  secondary 
axis,  and  that,  according  to  the  distance  of  the  point  L,  the  focus  may  be 
either  principal,  conjugate,  or  virtual. 

526.  Foci  of  convex  mirrors. — In  convex  mirrors  there  are  only  virtual 
foci.  Let  SI,  TK  .  .  .  (fig.  438)  be  rays  parallel  to  the  principal  axis  of  a 
convex  mirror.  These  rays,  after  reflection,  take  the  diverging  directions 
IM,  KH,  which,  when  continued,  meet  in  a  point  F,  which  is  the  principal 


-527]     Determination  of  the  Principal  Focus  of  a  Mirror.       485 

"virtual  focus  of  the  mirror.  By  means  of  the  triangle  CKF,  it  may  be  shown 
in  the  same  manner  as  with  concave  mirrors,  that  the  point  F  is  approxi- 
mately the  centre  of  the  radius  of  curvature,  CA. 


Fig.  438. 

If  the  incident  luminous  rays,  instead  of  being  parallel  to  the  axis,  pro- 
ceed from  a  point  L,  situated  on  the  axis  at  a  finite  distance,  it  is  at  once 
seen  that  a  virtual  focus  will  be  formed  at  a  point  /,  between  the  principal 
focus  F  and  the  mirror. 

527.  Determination  of  the  principal  focus  of  a  mirror. — In  the  appli- 
cations of  concave  and  convex  mirrors  it  is  often  necessary  to  know  the 
radius  of  curvature.  This  is  tantamount  to  finding  the  principal  focus  ;  for 
being  situated  at  the  middle  of  the  radius,  it  is  simply  necessary  to*  double 
the  focal  distance. 

To  find  this  focus  with  a  concave  mirror,  it  is  exposed  to  the  sun's  rays, 
so  that  its  principal  axis  is  parallel  to  them,  and  then  with  a  small  screen  of 
ground  glass  the  point  is  sought  at  which  the  image  is  formed  with  the 
greatest  intensity  ;  this  is  the  principal  focus.  The  radius  of  the  mirror  is 
double  this  distance. 

If  the  mirror  is  convex,  it  is  covered  with  paper  ;  but  two  small  portions 
H  and  I,  are  left  exposed  at 
equal  distances  from  the 
centre  of  the  figure  A,  and  on 
the  same  principal  section 
(fig.  439).  A  screen  MN,  in 
the  centre  of  which  is  an 
opening  larger  than  the  dis- 
tance HI,  is  placed  before 
the  mirror.  If  a  pencil  of 

solar  rays,  SH,  S'l,  parallel  g-  439- 

to  the  axis,  fall  on  the  mirror,  the  light  is  reaected  at  H  and  I,  on  the  parts 
where  the  mirror  is  left  exposed,  and  forms  on  the  screen  two  brilliant  images 
at  h  and  i.  By  moving  the  screen  MN  nearer  to  or  farther  from  the  mirror, 
a  position  is  found  at  which  the  distance  hi  is  double  that  of  HI.  The 
distance  AD  from  the  screen  to  the  mirror  then  equals  the  principal  focal 
distance.  For  the  arc  HAI  does  not  sensibly  differ  from  its  chord  ;  and 

because  the  triangles  FHI  and  Yki  are  similar,  —  f.  =  ^     but  HI  is  half  of 

hi     FD 
hi,  and  therefore  also  FA  is  the  half  of  FD,  and  therefore  AD  is  equal  to 


486 


On  Light. 


[527- 


AF.  Further,  FA  is  the  principal  focal  distance  ;  for  the  rays  SH  and  S'l 
are  parallel  to  the  axis  :  consequently  also  twice  the  distance  AD  equals  the 
radius  of  curvature  of  the  mirror. 

528.  Formation  of  images  in  concave  mirrors.  —  Hitherto  it  has  been 
supposed  that  the  luminous  or  illuminated  object  placed  in  frojit  of  the 
mirror  wis  simply  a  point  ;  but  if  this  object  has  a  certain  magnitude,  we 
can  conceive  a  secondary  axis  drawn  through  each  of  its  points,  and  thus  a 
series  of  real  or  virtual  foci  could  be  determined,  the  collection  of  which 
composes  the  image  of  the  object.  By  the  aid  of  the  constructions  which 
have  served  for  determining  the  foci,  we  shall  investigate  the  position  and 
magnitude  of  these  images  in  concave  and  in  convex  mirrors. 

Realimage. — We  shall  first  take  the  case  in  which  the  mirror  is  concave, 
and  the  object  AB  (fig.  440)  is  on  the  other  side  of  the  centre.  To  obtain 


Fig.  440. 

the  image  or  the  focus  of  any  point  A,  a  secondary  axis,  AE,  is  drawn  from 
this  point,  and  then  drawing  from  the  point  A  an  incident  ray  AD,  the 
normal  to  this  point,  CD,  is  taken,  and  the  angle  of  reflection  CDa  is  made 
equal  to  the  angle  of  incidence  ADC.  The  point  #,  where  the  reflected  ray 
cuts  the  secondary  axis  AE,  is  the  conjugate  focus  of  the  point  A,  because 
every  other  ray  drawn  from  this  point  passes  through  a.  Similarly  if  a 
secondary  axis,  BI,  be  drawn  from  the  point  B,  the  rays  from  this  point 
meet  after  reflection  in  b,  and  form  the  conjugate  focus  of  B.  And  as  the 
images  of  all  the  points  of  the  object  are  formed  between  a  and  b,  ab  is  the 
complete  image  of  AB.  From  what  has  been  said  about  foci  (525),  it 
follows  that  this  image  is  real,  inverted,  smaller  than  the  object,  and  placed 
between  the  centre  of  curvature  and  the  principal  focus.  This  image  may  be 

seen  in  two  ways  :  by  placing 
the  eye  in  the  continuation  of 
the  reflected  rays,  and  then  it  is 
an  aerial  image  which  is  seen  ; 
or  the  rays  are  collected  on  a 
screen,  on  which  the  image  ap- 
pears to  be  depicted. 

If  the  luminous  or  illuminated 
i'ls'441'  object  is  placed  at  ^between 

the  principal  focus  and  the  centre,  its  image  is  formed  at  AB.  It  is  then  a 
real  but  inverted  image ;  it  is  larger  than  the  object,  and  the  larger  as  the 
object,  ab,  is  nearer  the  focus. 

If  the  object  is  placed  in  the  principal  focus  itself,  no  image  is  produced ; 


-530] 


Formula  for  Spherical  Mirrors. 


487 


for  then  the  rays  emitted  from  each  point  form,  after  reflection,  as  many 
pencils  respectively  parallel  to  the  secondary  axis,  which  is  drawn  through 
the  point  from  which  they  are  emitted  (524),  and  hence  neither  foci  nor 
images  are  formed. 

When  all  points  of  the  object  AB  are  above  the  principal  axis  (fig.  441), 
by  repeating  the  preceding  construction,  it  is  readily  seen  that  the  image  of 
the  object  is  formed  at  ab. 

Virtual  image. — The  case  remains  in  which  the  object  is  placed  between 
the  principal  focus  and  the  mirror.  Let  AB  be  this  object  (fig.  442)  ;  the 
incident  rays  after  reflection 
take  the  directions  DI  andKH, 
and  their  prolongations  form  a 
virtual  image,  a,  of  the  point  A, 
on  the  secondary  axis.  Simi- 
larly, an  image  of  B  is  formed 
at  b ;  consequently  the  eye  sees 
at  ab  the  image  of  AB.  This 
image  is  virtual,  erect,  and 
larger  than  the  object. 

From  what  has  been  stated, 
it  is  seen  that,  according  to  the 

distance  of  the  object,  concave  mirrors  produce  two  kinds  of  images,  or  none 
at  all  ;  a  person  notices  this  by  placing  himself  in  front  of  a  concave  mirror. 
At  a  certain  distance  he  sees  an  image  of  himself  inverted  and  smaller  ;  this 
is  the  real  image  ;  at  a  less  distance  the  image  becomes  confused,  and  dis- 
appears when  he  is  at  the  focus  ;  still  nearer  the  image  appears  erect,  but 
larger — it  is  then  a  virtual  image. 

529.  Formation  of  images  in  convex  mirrors. — Let  AB  (fig.   443)  be 
an  object  placed  in  front  of  a  mirror  at  any  given  distance.     AC  and  BC  are 
secondary  axes,  and  it  follows, 

from    what    has    been    already        | 

stated,  that  all  the  rays  from  A 

are   divergent    after    reflection, 

and  that  their  prolongations  pass 

through  a  point  a,  which  is  the 

virtual   image  of  the   point  A. 

Similarly  the  rays  from  B  form 

a  virtual  image  of  it  in  the  point 

b.     The  eye  which  receives  the 

divergent  rays  DE,  KA  .  .  .  sees  in 

the  position  of  an  object  in  front  of  a  convex  mirror,  the  image  is  always 

virtual,  erect,  and  smaller  than  the  object. 

530.  Formulae    for    spherical    mirrors. — The   relation    between    the 
position  of  an  object  and  that  of  its  image  in  spherical  mirrors  may  be 
expressed  by  a  very  simple  formula.     In  the  case  of  concave  mirrors,  let 
R  be  its  radius  of  curvature,  p  the  distance  LA  of  the  object  L  (fig.  444), 
and  p'  the  distance  /A  of  the  image  from  the  mirror.     In  the  triangle  LM/, 
the  perpendicular  MC  divides  the  angle  LM/  into  two  equal  parts,  and  from 


Fig.  443- 

image  of  AB.     Hence,  whatever 


488  On  Light.  [530- 

geometry,  it  follows  that  the  two  segments  LC,  C7  are  to  each  other  as  the 
two  sides  containing  the  angle  ;  that  is, 

C.f-  =  ^  :  therefore  CL  x  LM  =  CL  x  /M. 
CL     LM 

If  the  arc  AM  does  not  exceed  5  or  6  degrees,  the  lines  ML  and  M/  are 

approximately  equal  to  AL  and  A/  ; 
that  is,  to/  and/'. 

Further,  C/=  CA-  A/=  R-/', 
and  also  CL  =  AL-AC  -/-R. 

The   values   substituted  in  the 
preceding  equations  give 


From  which  transposing  and  reducing  we  have 

R/  +  R/'  =  2//'     -..  (0 

If  the  terms  of  this  equation  be  all  divided  by//'R,  we  obtain 


which  is  the  usual  form  of  the  equation. 
From  the  equation  (i)   we  get 


which  gives  the  distance  of  the  image  from  the  mirror,  in  terms  of  the 
distance  of  the  object,  and  of  the  radius  of  curvature. 

531.  Discussion  of  the  formulae  for  mirrors.  —  We  shall  now  in- 
vestigate the  different  values  of  p',  according  to  the  values  of  p  in  the 
formula  (3). 

i.  Let  the  object  be  placed  at  an  infinite  distance  on  the  axis,  in  which 
case  the  incident  rays  are  parallel.  To  obtain  the  value  of/',  both  terms  of 
the  fraction  (3)  must  be  divided  by/,  which  gives 

,,  R 

P  =  —  v,   - 

2>  ....         (4) 

P 

"R  R 

as  p  is  infinite,  —  is  zero,  and  we  have  pf  =  —  ;  that  is,  the  image  is  formed 

in  the  principal  focus,  as  ought  to  be  the.  case,  for  the  incident  rays  are 
parallel  to  the  axis. 

ii.  If  the  object  approaches  the  mirror,/  decreases,  and  as  the  denomi- 
nator of  the  formula  (4)  diminishes,  the  value  of  /'  increases  ;  consequently 
the  image  approaches  the  centre  at  the  same  time  as  the  object,  but  it  is 
always  between  the  principal  focus  and  the  centre,  for  so  long  as 

/  is  >  R,  we  have     -  ~  >  —  and  <  R. 
R      2 

-v 

iii.  When  the  object  coincides  with  the  centre,  /  =  R,  and,  consequently,, 
P'  —  R  ;  that  is,  the  image  coincides  with  the  object. 


-533]  Spherical  Aberration.     Caustics.  489 

iv.  When  the  luminous  object  is  between  the  centre  and  the  principal 
focus,  /<R,  and  hence  from  the  formula  (4),  /'>R  ;  that  is,  the  image  is 
formed  on  the  other  side  of  the  centre.  When  the  object  is  in  the  focus, 

-D  T3 

p  =  _   which  gives  /'•-=-  =  oo  ;  that  is,  the  image  is  at  an  infinite  distance, 

for  the  reflected  rays  are  parallel  to  the  axis. 

v.  Lastly,  if  the  object  is  between  the  principal  focus  and  the  mirror,  we 

T3 

get/  L      ;  p'  is  then  negative,  because  the  denominator  of  the  formula  (4) 

is  negative.  Therefore,  the  distance  p'  of  the  mirror  from  the  image  must 
be  calculated  on  the  axis  in  a  direction  opposite  to  p.  The  image  is  then 
virtual,  and  is  on  the  other  side  of  the  mirror. 

Making  p'  negative  in  the  formula  (2),  it  becomes  -—^7  =  ",  ;  in  this 

p    p      R 

form  it  comprehends  all  cases  of  virtual  images  in  concave  mirrors. 

In  the  case  of  concave  mirrors  the  image  is  always  virtual  (525)  ;  p'  and 
R  are  of  the  same  sign,  since  the  image  and  the  centre  are  on  the  same  side 
of  the  mirror,  while  the  object  being  on  the  opposite  side,  p  is  of  the  contrary 
sign  ;  hence  in  the  formula  (2)  we  get 


as  the  formula  for  convex  mirrors.  It  may  also  be  found  directly  by  the 
same  geometrical  considerations  as  those  which  have  led  to  the  formula  (2) 
for  concave  mirrors. 

It  must  be  observed  that  the  preceding  formulae  are  not  rigorously  true> 
inasmuch  as  they  depend  upon  the  assumption  that  the  lines  LM  and  /M 
(fig.  444)  are  equal  to  LA  and  A/:  although  this  is  not  true,  the  error 
diminishes  without  limit  with  the  angle  MCA;  and  when  this  angle  does 
not  exceed  a  few  degrees,  the  error  is  so  small  that  it  may,  in  practice,  be 
neglected. 

532.  Calculation  of  the  magnitude  of  images.  —  By  means  of  the  above 
formulas  the  magnitude  of  an  image  may  be  calculated  when  the  distance 
of  the  object,  its  magnitude, 

and  the  radius  of  the  mirror 

are  given.     For    if    BD    be 

the  object  (fig.  445);   bd  its 

image,  and   if  the   distance 

A  and    the   radius    AC    be 

known,  A0  can  be  calculated 

by  means  of  formula  (3)  of 

article  530.     A0  known,  oC 

can  be  calculated.     But  as  the  triangles  BCD  and  dCb   are  similar,  their 

bases  and  heights  are  in  the  proportion  bd  :  BD  =  Co  :  CK,  or 

Length  of  the  image  :  length  of  the  object 
-  distance  from  image  to  centre  :  distance  from  the  object  to  the  centre. 

533.  Spherical  aberration.     Caustics.  —  In  the  foregoing  explanation  of 
the  formation  of  foci  and  images  of  spherical  mirrors,  it  has  already  been 


490  On  Light.  [533- 

observed  that  the  reflected  rays  only  pass  through  a  single  point  when  the 
aperture  of  the  mirror  does  not  exceed  8  or  10  degrees  (531).  With  a  larger 
aperture  the  rays  reflected  near  the  edges  meet  the  axis  nearer  the  mirror 
than  those  that  are  reflected  at  a  small  distance  from  the  neighbourhood  of 
the  centre  of  the  mirror.  Hence  arises  a  want  of  precision  in  these  images, 
which  is  called  spherical  aberration  by  reflection,  to  distinguish  it  from  the 
spherical  aberration  by  refraction,  which  occurs  in  the  case  of  lenses. 

Every  reflected  ray  cuts  the  one  next  to  it  (fig.  446),  and  their  points  of 
intersection  form  in  space  a  curved  surface  which  is  called  the  caustic  by 

reflection.  The  curve  FM  repre- 
sents one  of  the  branches  of  a 
section  of  this  surface  made  by  the 
plane  of  the  paper.  When  the 
light  of  a  candle  is  reflected  from 
the  inside  of  a  cup  or  tumbler,  a 
section  of  the  caustic  surface  can 
be  seen  by  partly  filling  the  cup  or 
tumbler  with  milk. 

534.  Applications  of  mirrors.     Keliostat. — The  applications  of  plane 
mirrors  in  domestic  economy  are  well  known.     Mirrors  are  also  frequently 
used  in  physical  apparatus  for  sending  light  in  a  certain   direction.     We 
have  already  seen  an  application  of  this  in  the  heliograph  (523).     The  light 
of  the  sun  can  only  be  sent  in  a  constant  direction  by  making  the  mirror  mov- 
able.    It  must  have  a  motion  which  compensates  for  the  continual  change 
in  the  direction  of  the  sun's  rays  produced  by  the  apparent  diurnal  motion 
of  the  sun.     This  result  is  obtained  by  means  of  a  clockwork  motion,    to 
which  the  mirror  is  fixed,  and  which  causes  it  to  follow  the  course  of  the 
sun.     Such  an  apparatus  is  called  a  heliostat.     The  reflection  of  light  is  alsp 
used  to  measure  the  angles  of  crystals  by  means  of  the  instruments  known 
as  reflecting  goniometers. 

Concave  spherical  mirrors  are  also  often  used.  They  are  applied  for 
magnifying  mirrors,  as  in  the  older  forms  of  shaving  mirrors.  They  have 
been  employed  for  burning  mirrors,  and  are  still  used  in  telescopes.  They 
also  serve  as  reflectors,  for  conveying  light  to  great  distances,  by  placing 
a  luminous  object  in  their  principal  focus.  For  this  purpose,  however, 
parabolic  mirrors  are  preferable. 

The  images  of  objects  seen  in  concave  or  convex  mirrors  appear  smaller 
or  larger,  but  otherwise  similar  geometrically,  except  in  the  case  where 
some  parts  of  a  body  are  nearer  the  mirror  than  others.  The  distor- 
tion of  features  observed  on  looking  into  a  spherical  garden  mirror  is  more 
marked  the  nearer  we  are  to  the  glass.  Objects  seen  in  cylindrical  or 
conical  mirrors  appear  ludicrously  distorted.  From  the  laws  of  reflection 
the  shape  of  such  a  distorted  figure  can  be  geometrically  constructed.  In 
like  manner  distorted  images  of  objects  can  be  constructed  which,  seen  in 
such  mirrors,  appear  in  their  normal  proportions.  They  are  called  anamor- 
fyses. 

535.  Parabolic  mirrors. — Parabolic  mirrors  are  concave  mirrors  whose 
surface  is  generated  by  the  revolution  of  the  arc  of  a  parabola,  AM,  about 
its  axis  AX  (fig.  447). 


-535] 


Parabolic  Mirrors. 


491 


Fig.  447. 


It  has  been  already  stated  that  in  spherical  mirrors  the  rays  parallel  to 
the  axis  converge  only  approximately  to  the  principal  focus  ;  and  reciprocally, 
when  a  source  of  light  is  placed  in 
the  principal  focus  of  these  mirrors 
the  reflected  rays  are  not  exactly 
parallel  to  the  axis.  Parabolic 
mirrors  are  free  from  this  defect  ; 
they  are  more  difficult  to  construct, 
but  are  better  for  reflectors.  It  is 
a  property  of  a  parabola  that  the 
right  line  FM,  drawn  from  the 
focus  F  at  any  point  M  of  the 
curve,  and  the  line  ML,  parallel  to 
the  axis  AF,  make  equal  angles 
with  the  tangent  TT'  at  this  point. 
Hence  all  rays  parallel  to  the  axis  alter  reflec- 
tion meet  in  the  focus  of  the  mirror  F  ;  and 
conversely,  when  a  source  of  light  is  placed 
in  the  focus,  the  rays  incident  on  the  mirror 
are  reflected  exactly  parallel  to  the  axis. 
The  light  thus  reflected  tends  to  maintain  its 
intensity  even  at  a  great  distance,  for  it  has 
been  seen  (508)  that  it  is  the  divergence  of  the 
luminous  rays  which  principally  weakens  the 
intensity  of  light. 

From  this  property  parabolic  mirrors  are 
used  in  carriage  lamps,  and  in  the  lamps  placed 
in  front  of  and  behind  railway  trains.  These  re- 
flectors were  formerly  used  for  lighthouses,  but 
have  been  replaced  by  lenticular  glasses. 

When  two  equal  parabolic  mirrors  are  cut 
by  a  plane  perpendicular  to  the  axis  passing 
through  the  focus,  and  are  then  united  at  their 
intersections  as  shown  in  fig.  448,  so  that  their  foci  coincide,  a  system 
of  reflectors  is  obtained  with  which  a  single  lamp  illuminates  in  two 
directions  at  once.  This  arrangement  is  used  in  lighting  staircases  and 
passages. 


Fig.  448. 


492  On  Light.  [536- 


CHAPTER    III. 

SINGLE   REFRACTION.      LENSES. 

536.  Phenomenon  of  refraction. — Refraction  is  the  deflection  or  bending 
which  the  rays  of  light  experience  in  passing  obliquely  from  one  medium  to- 
another  :  for  instance,  from  air  into  water.  We  say  obliquely,  because  if  the 
incident  ray  is  perpendicular  to  the  surface  separating  the  two  media,  it  is 
not  bent,  and  continues  its  course  in  a  right  line. 

The  incident  ray  being  represented  by  SO  (fig.  449),  the  refracted  ray  is 
the  direction  OH  which  light  takes  in  the  second  medium;  and  of  the  angles 
SOA  and  HOB,  which  these  rays  form  with  the  line  AB,  at  right  angles  to 
the  surface  which  separates  the  two  media,  the  first 
is  the  angle  of  incidence,  and  the  other  the  angle  of 
refraction.     According  as   the   refracted   ray   ap- 
proaches or  deviates  from  the  normal,  the  second 
medium  is  said  to  be  more  or  less  refringent  or 
refracting  than  the  first. 

All  the  light  which  falls  on  a  refracting  surface 
does  not  completely  pass  into  it ;  one  part  is  re- 
Fig  449  fleeted  and  scattered  (518),  while  another  penetrates. 

into  the  medium. 

Mathematical  analysis  shows  that  the  direction  ot  refraction  depends  on 
the  relative  velocity  of  light  in  the  two  media.  On  the  undulatory  theory 
the  more  highly  refracting  medium  is  that  in  which  the  velocity  of  propaga- 
tion is  least. 

In  uncrystallised  media,  such  as  air,  liquids,  ordinary  glass,  the  luminous- 
ray  is  singly  refracted';  but  in  certain  crystallised  bodies,  such  as  Iceland  spar, 
selenite,  &c.,  the  incident  ray  gives  rise  to  two  refracted  rays.  The  latter 
phenomenon  is  called  double  refraction,  and  will  be  discussed  in  another  part 
of  the  book.  We  shall  here  deal  exclusively  with  single  refraction. 
y  537.  Laws  of  single  refraction. — When  a  luminous  ray  is  refracted  in 
passing  from  one  medium  into  another  of  a  different  refractive  power,  the 
following  laws  prevail  : — 

I.  Whatever  the  obliqttity  of  the  incident  ray,  the  ratio  which  the  line  of 
the  incident  angle  bears  to  the  sine  of  the  angle  of  refraction  is  constant  for 
the  same  two  media,  but  varies  with  different  media. 

II.  The  incident  and  the  refracted  ray  are  in  the  same  plane,  which  is 
Perpendicular  to  the  surface  separating  the  two  media* 

These  have  been  known  as  Descartes'  law  ;  they  are,  however,  really 
due  to  Willibrod  Snell,  who  discovered  them  in  1620 ;  they  are  demon- 
strated by  the  same  apparatus  as  that  used  for  the  laws  of  reflection  (511). 
The  plane  mirror  in  the  centre  of  the  graduated  circle  is  replaced  by  a 


-539] 


Effects  produced  by  Refraction. 


493 


semi-cylindrical  glass  vessel,  filled  with  water  to  such  a  height  that  its 
level  is  exactly  the  height  of  the  centre  (fig.  450).  If  the  mirror,  M,  be 
then  so  inclined  that  a  reflected  ray,  MO,  is  directed  towards  the  centre, 
it  is  refracted  on  passing  into  the  water,  but  it  passes  out  without  refraction, 
because  then  its  direction  is  at  right  angles  to  the  curved  sides  of  the 
vessel.  In  order  to  observe  the  course 
of  the  refracted  ray,  it  is  received  on  a 
screen,  P,  which  is  moved  until  the 
image  of  the  aperture  in  the  screen  N 
is  formed  in  its  centre.  In  all  positions 
of  the  screens  N  and  P,  the  sines  of 
the  angles  of  incidence  and  refraction 
are  measured  by  means  of  two  graduated 
rules,  movable  so  as  to  be  always  hori- 
zontal, and  hence  perpendicular  to  the 
diameter  AD. 

On  reading  off  the  length  of  the  sines 
of  the  angles  MOA  and  DOP  in  the 
scales  I  and  R,  the  numbers  are  found 
to  vary  with  the  position  of  the  screens, 
but  their  ratio  is  constant  ;  that  is,  if 
the  sine  of  incidence  becomes  twice  or 
three  times  as  large,  the  sine  of  refrac- 
tion increases  in  the  same  ratio,  which 
demonstrates  the  first  law.  The  second 
law  follows  from  the  arrangement  of  the 


Fig.   450. 


r 


apparatus,  for  the  plane  of  the  graduated  limb  is  perpendicular  to  the  surface 
f  the  liquid  in  the  semi-cylindrical  vessel. 

538.  Index  of  refraction. — The  ratio  between  the  sines  of  the  incident 
and  refracted   angle  is  called  index  of  refraction,  or  refractive  index.     It 
varies  with  the  media ;  for  example,  from  air  to  water  it  is  |,  and  from  air  to 
glass  it  is  f. 

If  the  media  are  considered  in  an  inverse  order — that  is,  if  light  passes 
from  water  to  air,  or  from  glass  to  air — it  follows  the  same  course,  but  in  a 
contrary  direction,  PO  becoming  the  incident  and  O1VJ  the  refracted  ray. 
Consequently  the  index  of  refraction  is  reversed  ;  from  water  to  air  it  is  then 
|,  and  from  glass  to  air  |. 

539.  Effects  produced  by  refraction.— In  consequence  of  refraction, 
bodies  immersed  in  a  medium  more  highly  refracting  than  air,  appear  nearer 
the  surface  of  this  medium,  but  they  appear  to  be  more  distant  if  immersed 
in  a  less  refracting  medium.     Let  L  (fig.  451)  be  an  object  immersed  in  a 
mass  of  water.     In  passing  thence  into  air,  the  rays  LA,  LB  .  .  .  diverge 
from  the  normal  to  the  point  of  incidence,  and  take  the  direction  AC,  BD 
.  .  .  ,  the  prolongations  of  which  intersect  approximately  in  the  point  L', 
placed  on  the  perpendicular  L'K.     The  eye  receiving  these  rays  sees  the 
object  L  at  L'.   The  greater  the  obliquity  of  the  rays  LA,  LB  .  .  .  the  higher 
the  object  appears. 

It  is  for  the  same  reason  that  a  stick  plunged  obliquely  into  water  appears 
bent  (fig.  452),  the  immersed  part  appearing  raised. 


494 


On  Light. 


[539- 


An  experimental  illustration  of  the  effect  of  refraction  is  the  following  : — 
A  coin  is  placed  in  an  empty  porcelain  basin,  and  the  position  of  the  eye  is 
so  adjusted  that  it  is  just  not  visible.  If  now,  the  position  of  the  eye  remain- 
ing unaltered,  water  be  poured  into  the  basin,  the  coin  becomes  visible.  A 
consideration  of  fig.  451  will  suggest  the  explanation  of  this  phenomenon. 

Owing  to  an  effect  of  refraction,  stars  are  visible  to  us  even  when  they 
are  below  the  horizon.  For  as  the  layers  of  the  atmosphere  are  denser  in 
proportion  as  they  are  nearer  the  earth,  and  as  the  refractive  power  of  a  gas 


Fig.  452. 


Fig.  453- 


increases  with  its  density  (550),  it  follows  that  on  entering  the  atmosphere 
the  luminous  rays  become  bent,  as  seen  in  fig.  453,  describing  a  curve  before 
reaching  the  eye,  so  that  we  can  see  the  star  at  S'  along  the  tangent  of  this 
curve  instead  of  at  S.  In  our  climate  the  atmospheric  refraction  does  not 
raise  the  stars  when  on  the  horizon  more  than  half  a  degree. 

The  effect  of  refraction  is  that  objects  at  a  distance  appear  higher  than 
they  are  in  reality  ;  our  horizon  is  thereby  widened.  When  individual  layers 
of  air  refract  more  strongly  than  usual,  objects  may  thereby  become  visible 
which  are  usually  below  the  horizon.  Thus,  from  Hastings,  the  coast  of 
France,  which  is  at  a  distance  of  56  miles,  is  not  unfrequently  seen. 
"  540.  Total  reflection.  Critical  angle. — When  a  luminous  ray  passes 
from  one  medium  into  another  which  is  less  refracting,  as  from  water  into 

air,  it  has  been 
seen  that  the 
angle  of  inci- 
dence is  less 
than  the  angle 
of  refraction. 
Hence,  when 
light  is  propa- 
gated in  a  mass 
of  water  from  S 
to  O  (fig.  454), 
there  is  always 

a  value  of  the  angle  of  incidence  SOB,  such  that  the  angle  of  refraction  AOR 
is  a  right  angle,  in  which  case  the  refracted  ray  emerges  parallel  to  the 
surface  of  the  water. 

This  angle,  SOB,  is  called  the  critical  angle,  since  for  any  greater  angle, 
FOB,  the  incident  ray  cannot  emerge,  but  undergoes  an  internal  reflection, 


Fig-  454- 


Fig.  455- 


-541] 


Mirage. 


495 


which  is  called  total  reflection  because  the  incident  light  is  entirely  reflected. 
From  water  to  air  the  critical  angle  is  48°  35' :  from  glass  to  air,  41°  48'. 

The  occurrence  of  this  internal  reflection  may  be  observed  by  the  follow- 
ing experiment  :  —An  object,  A,  is  placed  before  a  glass  vessel  filled  with 
water  (fig.  455)  ;  the  surface  of  the  liquid  is  then  looked  at  as  shown  in  the 
figure,  and  an  image  of  the  object  A  is  seen  at  a,  formed  by  the  rays  reflected 
at  ?;z,  in  the  ordinary  manner  of  a  mirror. 

Similar  effects  of  the  total  reflection  of  the  images  of  objects  contained 
in  aquaria  are  frequently  observed,  and  add  much  to  the  interest  of  their 
appearance. 

In  total  reflection  there  is  no  loss  of  light  from  absorption  or  transmission,, 
and  accordingly  it  produces  the  greatest  brilliancy.  If  an  empty  test-tube 
be  placed  in  a  slanting  position  in  water,  its  surface,  when  looked  at  from 
above,  shines  as  brilliantly  as  pure  mercury  ;  those  rays  which  fall  obliquely 
on  the  side  cannot  pass  into  the  water,  and  are  therefore  totally  reflected 
upwards.  If  a  little  water  be  passed  into  the  tube,  that  portion  of  it  loses  its 
lustre.  Bubbles,  again,  in  water  glisten  like  pearls,  and  cracks  in  transparent 
bodies  like  strips  of  silver,  for  the  oblique  rays  are  totally  reflected.  The 
lustre  of  transparent  bodies  bounded  by  plane  surfaces,  such  as  the  lustre  of 
chandeliers,  arises  mainly  from  total  reflection.  This  lustre  is  more  frequent 
and  more  brilliant  the  smaller  the  limiting  'angle ;  the  lustre  of  diamond, 
therefore,  is  the  most  brilliant. 

K~~54i.  Mirage. — The  mirage  is  an  optical  illusion  by  which  inverted  images 
of  distant  objects  are  seen  as  if  below  the  ground  or  in  the  atmosphere.    This 


Fig.  456. 

phenomenon  is  of  most  frequent  occurrence  in  hot  climates,  and  more  espe- 
cially on  the  sandy  plains  of  Egypt.  The  ground  there  has  often  the  aspect  of 
a  tranquil  lake,  on  which  are  reflected  trees  and  the  surrounding  villages. 
Monge,  who  accompanied  Napoleon's  expedition  to  Egypt,  was  the  first  to 
give  an  explanation  of  the  phenomenon. 

It  is  a  phenomenon  of  refraction,  which  results  from  the  unequal  density 
of  the  different  layers  of  the  air  when  they  are  expanded  by  contact  with  the 
heated  soil.  The  least  dense  layers  are  then  the  lowest,  and  a  luminous  ray 


496  On  Light.  [541- 

from  an  elevated  object,  A  (fig.  456),  traverses  layers  which  are  gradually  less 
refracting  ;  for,  as  will  be  shown  presently  (550),  the  refracting  power  of  a 
gas  diminishes  with  lessened  density.  The  angle  of  incidence  accordingly 
increases  from  one  layer  to  the  other,  and  ultimately  reaches  the  critical 
angle,  beyond  which  internal  reflection  succeeds  to  refraction  (540).  The 
ray  then  rises,  as  seen  in  the  figure,  and  undergoes  a  series  of  successive  re- 
fractions, but  in  the  direction  contrary  to  the  first,  for  it  now  passes  through 
layers  which  are  gradually  more  refracting.  The  luminous  ray  then  reaches 
the  eye  with  the  same  direction  as  if  it  had  proceeded  from  a  point  below 
the  ground,  and  hence  it  gives  an  inverted  image  of  the  object,  just  as  if  it 
had  been  reflected  at  the  point  O,  from  the  surface  of  a  tranquil  lake. 

The  effect  of  the  mirage  may  be  illustrated  artificially,  though  feebly,  as 
Dr.  Wollaston  showed,  by  looking  along  the  side  of  a  red-hot  poker  at  a  word 
or  object  ten  or  twelve  feet  distant.  At  a  distance  less  than  three-eighths  of 
an  inch  from  the  line  of  the  poker,  an  inverted  image  was  seen,  and  within 
and  without  that  an  erect  image.  A  more  convenient  arrangement  than  a 
red-hot  poker  is  a  flat  box  closed  at  the  top  and  filled  with  red-hot  charcoal. 

Mariners  sometimes  see  inverted  images  in  the  air  of  ships  and  distant 
objects  which  are  still  under  the  horizon  ;  this  is  due  to  the  same  cause  as 
the  mirage,  but  is  in  a  contrary  direction.  The  lower  layers  of  the  air  being 
in  contact  with  the  water  are  cold  and  dense.  The  rays  of  an  object,  a  ship 
for  instance,  bent  in  an  upward  direction  are  more  and  more  bent  away  from 
the  vertical  as  they  are  continually  passing  into  gradually  less  dense  layers, 
and  ultimately  fall  so  obliquely  on  an  upper  attenuated  layer  that  they  are 
totally  reflected  downwards,  and  can  thus  reach  the  eye  of  an  observer  on  the 
sea  or  on  the  shore.  Scoresby  observed  several  such  cases  in  the  Polar  seas. 

The  twinkling  or  scintillation  of  the  fixed  stars  is  also  to  be  accounted 
for  by  alterations  in  the  direction  of  the  motion  of  their  light  due  to  refraction. 

TRANSMISSION   OF  LIGHT  THROUGH   TRANSPARENT  MEDIA. 

542.  Media  with  parallel  faces. — When  light  traverses  a  medium  with 
parallel  faces  the  emergent  rays  are  parallel  to  the  incident  rays. 

Let  MN  (fig.  457)  be  a  glass  plate  with  parallel  faces,  let  SA  be  the 
incident  and  DB  the  emergent  ray,  z  and  r  the  angles  of  incidence  and  of 
refraction  at  the  entrance  of  the  ray,  and,  lastly,  /'  and  r1  the  same  angles 

at  its  emergence.  At  A  the  light  undergoes 

a  first  refraction,  the  index  of  which  is  sm  z 

sin  r 
(537).     At  D  it  is  refracted  a  second  time, 

and  the  index  is  then  ~  l .     But  we  have 
sin  r' 

seen  that  the  index  of  refraction  of  glass  to 
air  is  the  reciprocal  of  its  refraction  from  air 

to  glass  ;  hence  sm_l.  =  ——. 
sin  r      sin  i 

457>  But  as  the  two  normals  AG  and  DE  are 

parallel,  the  angles  r  and  i'  are  equal,  as  being  alternate  interior  angles.    As 
the  numerators  in  the  above  equation  are  equal,  the  denominators  must  also 


-544]  Path  of  Rays  in  Prisms.  497 

be  equal ;  the  angles  r'  and  i  are  therefore  equal,  and  hence  DB  is  parallel 
to~SA. 

543.  Prism. — In  optics  a  prism  is  any  transparent  medium  comprised 
between  two  plane  faces  inclined  to  each  other.     The  intersection  of  these 
two  faces  is  the  edge  of  the  prism,  and  their  inclination  is  its  refracting  angle. 
Every  section  perpendicular  to  the  edge  is  called  a  principal  section. 

The  prisms  used 
for  experiments  are 
generally  right  trian- 
gular prisms  of  glass, 
as  shown  in  fig.  458, 
and  their  principal  sec- 
tion is  a  triangle  (fig. 
459).  In  this  section 

the  point  A  is  called  JT^  Fig.  459. 

the     summit    of    the 
prism,  and  the  right  line   BC  is  called  the  base  :   these  expressions  have 
reference  to  the  triangle  ABC,  and  not  to  the  prism. 

544.  Path  of  rays  in  prisms.     Angle  of  deviation. — When  the  laws 
of  refraction  are  known,  the  path  of  the  rays  in  a  prism  is  readily  determined. 
Let  O  be  a  luminous  point  (fig.  459)  in  the  same  plane  as  the  principal  sec- 
tion ABC  of  a  prism,  and  let  OD  be  an  incident  ray.     This ,  ray  is  refracted 
at  D,  and  approaches  the  normal,  because  it  passes  into  a  more  highly  re- 
fracting medium.     At  K  it  experiences  a  second  refraction,  but  it  then  de- 
viates from  the  normal,  for  it  passes  into  air,  which  is  less  refractive  than 
glass.   The  light  is  thus  refracted  twice  in  the  same  direction,  so  that  the  ray 
is  deflected  towards  the  base,  and  consequently  the  eye  which  receives  the 
emergent  ray  KH  sees  the  object  O  at  O' ;  that  is,  objects  seen  through  a 
prism  appear  deflected  towards  its  summit.     The  angle  OEO',  which  the 
incident  and  emergent  rays  form  with  each  other,  expresses  the  deviation  of 
light  caused  by  the  prism,  and  is  called  the  angle  of  deviation. 

Besides  this,  objects  seen  through  a  prism  appear  in  all  the  colours  of 
the  rainbow :  this  phenomenon,  known  as  dispersion,  will  be  afterwards 
described  (564). 

This  angle  increases  with  the  refractive  index  of  the  material  of  the  prism, 
and  also  with  its  refracting  angle.  It  also  varies  with  the  angle  under  which 
the  luminous  ray  enters  the  prism.  The  angle  of  deviation  increases  up  to 
a  certain  limit,  which  is  determined  by  calculation,  knowing  the  angle  of 
incidence  of  the  ray,  and  the  refracting  angle  of  the  prism. 

That  the  angle  of  deviation  increases  with  the  refractive  index  may  be 
shown  by  means  of  the  polyprism.  This  name  is  given  to  a  prism  formed 
of  several  prisms  of  the  same  angle  connected  at  their  ends  (fig.  460).  These 
prisms  are  made  of  substances  unequally  refringent,  such  as  flint  glass,  rock 
crystal,  or  crown  glass.  If  any  object — a  line,  for  instance — be  looked  at 
through  the  polyprism,  its  different  parts  are  seen  at  unequal  heights.  The 
highest  portion  is  that  seen  through  the  flint  glass,  the  refractive  index  of 
which  is  greatest ;  then  the  rock  crystal ;  and  so  on  in  the  order  of  the 
decreasing  refractive  indices. 

The  prism  with  variable  angle  (fig.  461)  is  used  for  showing  that  the 

K  K 


498  On  Light.  [544- 

angle  of  deviation  increases  with  the  refracting  angle  of  the  prism.  It  con- 
sists of  two  parallel  brass  plates,  B  and  C,  fixed  on  a  support.  Between 
these  are  two  glass  plates,  moving  on  a  hinge,  with  some  friction  against  the 


Fig.  460. 


Fig.  461. 


plates,  so  as  to  close  it.  When  water  is  poured  into  the  vessel  the  angle 
may  be  varied  at  will.  If  a  ray  of  light,  S,  be  allowed  to  fall  upon  one  of 
them,  by  inclining  the  other  more  the  angle  of  the  prism  increases,  and  the 
deviation  of  the  ray  is  seen  to  increase. 

Y        545-  Application  of  right-angled  prisms  in  reflectors. — Prisms  whose 
principal  section  is  an  isosceles  right-angled  triangle  afford  an  important 

application  of  total  reflection  (540).  For 
let  ABC  (fig.  462)  be  the  principal  section 
of  such  a  prism,  O  a  luminous  point,  and 
OH  a  ray  at  right  angles  to  the  face  BC. 
This  ray  enters  the  glass  without  being  re- 
fracted, and  makes  with  the  face  AB  an 
angle  equal  to  B — that  is,  to  45  degrees — 
and  therefore  greater  than  the  limiting 
F'ls-  462.  angle  of  glass,  which  is  41°  48'  (540).  The 

ray  OH  undergoes,  therefore,  at  H  total  reflection,  which  imparts  to  it  a 
direction  HI  perpendicular  to  the  second  face  AC.  Thus  the  hypothenuse 
surface  of  this  prism  produces  the  effect  of  the  most  perfect  plane  mirror, 
and  an  eye  placed  at  I  sees  O',  the  image  of  the  point  O.  This  property  of 
right-angled  prisms  is  frequently  used  in  optical  instruments  and  particularly 
in  the  prismatic  compass  (697)  instead  of  metal  reflectors,  which  so  readily 
tarnish.  The  newer  lighthouse  lenses  are  made  up  of  such  prisms. 

546.  Conditions  of  emergence  in  prisms. — In  order  that  any  luminous 
rays  refracted  at  the  first  face  of  a  prism  may.  emerge  from  the  second,  it 
is  necessary  that  the  refractive  angle  of  the  prism  be  less  than  twice  the 


-547]  Minimum  Deviation.  499 

critical  angle  of  the  substance  of  which  the  prism  is  composed.     For  if  LI 
(fig.  463)  be  the  ray  incident  on  the  first  face,  IE  the  refracted  ray,  PI  and 
PE  the  normals,  the  ray  IE  can  only  emerge  from  the  second  face  when 
the  incident  angle  IEP  is  less  than 
the   critical  angle  (540).     But  as  the 
incident    angle    LIN    increases,    the 
angle  EIP  also  increases,  while  IEP 
diminishes.     Hence,  according  as  the 
direction  of  the  ray  LI  tends  to  be- 
come parallel  with  the  face  AB,  does 
this  ray  tend  to  emerge  at  the  second 
face. 

Let  LI  be  now  parallel  to  AB,  the 
angle  r  is  then  equal  to  the  critical 
angle  /  of  the  prism,  because  it  has  its 
maximum  value.  Further,  the  angle 

EPK,  the  exterior  angle  of  the  triangle  IPE,  is  equal  to  r  +  i' ;  but  the  angles 
EPK  and  A  are  equal,  because  their  sides  are  perpendicular,  and  therefore 
A  =  r  +  /v;  therefore  also  A  =  /  +  zv,  for  in  this  case  r  =  L  Hence,  if  A  =  2/or 
is  >2/,  we  shall  have  zv  =  /  or  >/,  and  therefore  the  ray  would  not  emerge  at 
the  second  face,  but  would  undergo  internal  reflection,  and  would  emerge  at 
a  third  face,  BC.  This  would  be  much  more  the  case  with  rays  whose  in- 
cident angle  is  less  than  BIN,  because  we  have  already  seen  that  i'  con- 
tinually increases.  Thus  in  the  case  in  which  the  refracting  angle  of  a 
prism  is  equal  to  2/  or  is  greater,  no  luminous  ray  could  pass  through  the  faces 
of  the  refracting  angle. 

As  the  critical  angle  of  glass  is  41°  48',  twice  this  angle  is  less  than  90°, 
and,  accordingly,  objects  cannot  be  seen  through  a  glass  prism  whose  refract- 
ing angle  is  a  right  angle.  As  the  critical  angle  of  water  is  48°  35',  light 
could  pass  through  a  hollow  rectangular  prism  formed  of  three  glass  plates 
and  filled  with  water. 

If  we  suppose  A  to  be  greater  than  /  and  less  than  2/,  then  of  rays  inci- 
dent at  I,  some  within  the  angle  NIB  will  emerge  from  AC,  others  will  not 
emerge,  nor  will  any  emerge  that  are  incident  within  the  angle  NIA.  If  we 
suppose  A  to  have  any  magnitude  less  than  /,  all  rays  incident  at  I  within 
the  angle  NIB  will 
emerge  from  AC, 
as  also  will  some  of 
those  incident  with- 
in the  angle  NIA. 

547.  Minimum 
deviation. — When 
a  pencil  of  sunlight 
passes  through  an 
aperture  A,  in  the 
side  of  a  dark  cham- 
ber (fig.  464),  the  Fig.  464. 

pencil  is  projected  in  a  straight  line  AC,  on  a  distant  screen.  But  if  a  ver- 
tical prism  be  interposed  between  the  aperture  and  the  screen,  the  pencil  is 

K  K  2 


500  On  Light.  [547- 

deviated  towards  the  base  of  the  prism,  and  the  image  is  projected  at  D,  at 
some  distance  from  the  point  C.  If  the  prism  be  turned  so  that  the  incident 
angle  decreases,  the  luminous  disc  approaches  the  point  C  up  to  a  certain 
position,  E,  from  which  it  reverts  to  its  original  position  even  when  the  prism 
is  rotated  in  the  same  direction.  Hence  there  is  a  deviation,  EEC,  less  than 
any  other.  It  may  be  demonstrated  mathematically  that  this  minimum  de- 
viation takes  place  when  the  angles  of  incidence  and  of  emergence  are  equal. 
The  angle  of  minimum  deviation  may  be  calculated  when  the  incident 
angle  and  the  refracting  angle  of  the  prism  are  known.  For  when  the 
deviation  is  least,  as  the  angle  of  emergence  r'  is  equal  to  the  incident  angle 
/  (fig.  463),  r  must  equal  i'.  But  it  has  been  shown  above  (546)  that  A  =  r  +  zy  ;. 
consequently 

A  =  2r        .        .         .        .  "  '..        (i) 

If  the  minimum  angle  of  deviation  LD/  be  called  d,  this  angle  being  ex- 
terior to  the  triangle  DIE,  we  readily  obtain  the  equation 

d=  z  —  r  +  r/—i/  =  21  —  2r, 
whence  d=2i— A        .        .        .       -,./.  i ,:;,;       (2) 

which  gives  the  angle  d,  when  /  and  A  are  known. 

From  the  formulae  (i)  and  (2)  a  third  may  be  obtained,  which  serves  ta 
calculate  the  index  of  refraction  of  a  prism  when  its  refracting  angle  and  the 
minimum  of  deviation  are  known.  The  index  of  refraction,  ;/,  is  the  ratio 

of  the  sines  of  the  angles  of  incidence  and  refraction  :  hence  n  =  S_]!L!_'  re- 
sin r 

placing  i  and  r  from  their  values  in  the  above  equations  (i)  and  (2)  we  get 


n-  — 


.    A 
sin- 


(3) 


548.  Measurement  of  the  refractive  index  of  solids.— By  means  of 
the  preceding  formula  (3)  the  refractive  index  of  a  solid  may  be  calculated 
when  the  angles  A  and  d  are  known. 

In  order  to  determine  the  angle  A,  the  substance  is  cut  in  the  form  of  a 
triangle  prism,  and  the  angle  measured  by  means  of  a  goniometer  (534). 

The  angle  d  is  measured  in  the  following  manner  : — A  ray,  LI,  emitted 
from  a  distant  object  (fig.  495),  is  received  on  the  prism,  which  is  turned 

in  order  to  obtain  the 
minimum  deviation 
EDL'.  By  means  of 
a  telescope  with  a 
graduated  circle  the 
angle  EDLX  is  read 
off,  which  the  re- 
fracted ray  DE  makes 
with  the  ray  DL', 
Fig.  465.  coming  directly  from 

the  object ;  now  this  is  the  angle  of  minimum  deviation,  assuming  that  the 
object  is  so  distant  that  the  two  rays  LI  and  L'D  are  approximately  parallel. 


-550]        Measurement  of  the  Refractive  Index  of  Gases.          501 

These  values  then  only  need  to  be  substituted  in  the  equation  (3)  to  give  the 
value  ot  n. 

549.  Measurement  of  tbe  refractive  index  of  liquids. — Biot  applied 
Newton's  method  to  determining  the  refractive  index  of  liquids.     For  this 
purpose  a  cylindrical  cavity  O,  of  about  075 

in.  diameter,  is  perforated  in  a  glass  prism, 
PQ  (fig.  466),  from  the  incident  face  to  the 
face  of  emergence.  This  cavity  is  closed  by 
two  plates  of  thin  glass  which  are  cemented 
on  the  sides  of  this  prism.  Liquids  are 
introduced  through  a  small  stoppered  aper- 
ture, B.  The  refracting  angle  and  the 
minimum  deviation  of  the  liquid  prism  in 
the  cavity  O  having  been  determined,  their  Fig-  466> 

values  are  introduced  into  the  formula  (3),  which  gives  the  index. 

550.  Measurement  of  the  refractive  index  of  gases. — A  method  for 
this  purpose,  founded  on  that  of  Newton,  was  devised  by  Biot  and  Arago. 
The  apparatus  which  they  used  consists  of  a  glass  tube  (fig.  467),  bevelled  at 
its   two  ends,  and  closed  by  glass  plates,  which  are  at  an  angle  of  143°. 
This  tube  is  connected  with  a  bell-jar,  H,  in  which  there  is  a  siphon  barometer, 
and  with  a  stopcock  by  means  of  which  the  apparatus  can  be  exhausted,  and 
different   gases   introduced.     After   having  ex- 
hausted the  tube  AB,  a  ray  of  light,  SA,  is  trans- 
mitted, which   is  bent   away  from   the  normal 

through  an  angle  r  =  i  at  the  first  incidence,  and 
towards  it  through  an  angle  if  —  r'  at  the  second. 
These  two  deviations  being  added,  the  total 
deviation  d  is  r—i+i'  —  rf.  In  the  case  of  a 
minimum  deviation,  i  =  r'  and  r  =  i',  whence 
4  =  A  -  2*,  since  r  +  i  =  A  ( 547).  The  index  from 

vacuum   to   air,  which   is  evidently  ?HLT    has 

sinz 
therefore  the  value 


•     (4) 


Hence,  in   order  to   deduce  the  refractive 
index  n  from  vacuum  into   air,  which   is   the  Flg'  4<57' 

.absolute  index  or  principal  index,  it  is  merely  necessary  to  know  the  re- 
fracting angle  A,  and  the  angle  of  minimum  deviation  d.  To  obtain  the 
absolute  index  of  any  other  gas,  after  having  produced  a  vacuum,  this  gas  is 
introduced  ;  the  angles  A  and  d  having  been  measured,  the  above  formula 
.gives  the  index  of  refraction  from  gas  to  air.  Dividing  the  index  of  refrac- 
tion from  vacuum  to  air  by  the  index  of  refraction  from  the  gas  to  air,  we 
obtain  the  index  of  refraction  from  vacuum  to  the  gas  ;  that  is,  its  absolute 
index. 

The  square  of  the  refractive  index  of  a  substance,  less  unity,  that  is  n-  -  i 


502 


On  Light. 


[550 


measures  what  is  called  the  refractive  action.  On  the  undulatory  theory  ri* 
is  the  density  of  the  ether  in  the  medium,  when  i  is  the  density  of  the  ether 
in  a  vacuum.  The  refractive  action  is  therefore  a  measure  of  the  excess  of 
the  density  of  the  ether  in  the,  refracting  medium.  The  refractive  action 

divided  by  the  density,  or  n—^,  is  called  the  absolute  refractive  power. 


Table  of  refractive  indices. 


Diamond    . 

Rutile 

Phosphorus 

Sulphur       . 

Ruby  .         .  :      ... 

Flint  glass  .         •  -...•••.        • 

Bisulphide  of  carbon  . 

Iceland  spar,  ordinary  ray  . 

Iceland  spar,  extraordinary 

ray  .         .       ''„'."' 
Crown  glass        .         :..',.     • 
Oil  of  cassia        .      ;  .         . 


2-470  to  2750  Plate  glass,  St.  Gobin  .  .  1-587 

2-616  Rock  crystal .  .  ..  -..«,  -:..,  1*548 

.  2-224  Rock  salt  .  ..:'.;'  r>f|j  .  1-545 

2-215  Turpentine  .  ,  ....-.,,,  •  i'4?i 

.  1-779  Alcohol  ,'  .,  ;  V.'<— V"  .'•«:  r'363 

1702  Albumen  .  .  :  .  .  1-360 

1-678  Ether  .  .  ;,  ^.af.  ^  ..^M/  1-358 

1-654  Crystalline  lens  \ .  • .  . ,  ".  ..  1*384 

Vitreous  „  .  iV  ..  .  1*339 

1-483  Aqueous  „  v,  r;)!,-  r3S7 

i -608  Water  .  •  .  ,<_,.,,,,  .  1-336 

1-600  Ice  ..  ,  ...,.-  v  /».  t*i  i'3^c> 


Vacuum 

Hydrogen 

Oxygen . 

Air 

Nitrogen 

Ammonia 


Refractive  indices  of  gases. 

i  -oooooo  Carbonic  acid  . 

1-000138  Hydrochloric  acid 

1*000272  Nitrous  oxide   . 

i  -000294  Sulphurous  acid 

T  -000300  Olefiant  gas 

1-000385  Chlorine   . 


i  -000449 
i  -000449 
i  -000503 
i  -000665 
1-000678 
1-000772 


LENSES.   THEIR  EFFECTS. 

."<-,s  ';..;.; 
1 

551.  Different  kinds  of  lenses. — Lenses  are  transparent  media  which, 
from  the  curvature  of  their  surfaces,  have  the  property  of  causing  the  luminous 
rays  which  traverse  them  either  to  converge  or  to  diverge.  According  to 
their  curvature  they  are  either  spherical,  cylindrical,  elliptical,  or  parabolic. 
Those  used  in  optics  are  always  exclusively  spherical.  They  are  commonly 
made  either  of  crown  glass,  which  is  free  from  lead,  or  of  flint  glass,  which 
contains  lead,  and  is  more  refractive  than  crown  glass. 

The  combination  of  spherical  surfaces,  either  with  each  other  or  with 
plane  surfaces,  gives  rise  to  six  kinds  of  lenses,  sections  of  which  are  repre- 
sented in  fig.  468  ;  four  are  formed  by  two  spherical  surfaces,  and  two  by  a 
plane  and  a  spherical  surface. 

A  is  a  double  convex,  B  is  a  plano-convex,  C  is  a  converging  co?icavo- 
convex,  D  is  a  double  concave,  E  is  a  plano-concave,  and  F  is  a  diverging 
concavo-convex.  The  lenses  C  and  F  are  also  called  meniscus  lenses,  from 
their  resemblance  to  the  crescent-shaped  moon. 

The  first  three,  which  are  thicker  at  the  centre  than  at  the  borders,  are 


-552] 


Foci  in  Double  Convex  Lenses. 


503 


Fig.  468. 


converging ;  the  others,  which  are  thinner  in  the  centre,  are  diverging.     In 
the  first  group  the  double  convex  lens  only  need  be  considered,  and  in  the 
second  the  double  concave, 
as  the  properties  of  each  of 
these    lenses    apply   to    all 
those  of  the  same  group. 

In  lenses  whose  two  sur- 
faces are  spherical,  the 
centres  for  these  surfaces  are 
called  centres  of  ctirvature, 
and  the  right  line  which 
passes  through  these  two 
centres  is  the  principal  axis.  In  a  plano-concave  or  plano-convex  lens  the 
principal  axis  is  the  perpendicular  let  fall  from  the  centre  of  the  spherical 
face  on  the  plane  face. 

In  order  to  compare  the  path  of 
a  luminous  ray  in  a  lens  with  that 
in  a  prism,  the  same  hypothesis  is 
made  as  for  curved  mirrors  (525)  ; 
that  is,  the  surfaces  of  these  lenses 
are  supposed  to  be  formed  of  an 
infinity  of  small  plane  surfaces  or 
elements  (fig.  469) :  the  normal  at 
any  point  is  then  the  perpendicular 
to  the  plane  of  the  corresponding 
element.  It  is  a  geometrical  principle 
that  all  the  normals  to  the  same 
spherical  surface  pass  through  its 
centre.  On  the  above  hypothesis 
we  can  always  conceive  two  plane 
surfaces  at  the  points  of  incidence 
and  emergence,  which  are  inclined 
to  each  other,  and  thus  produce 
the  effect  of  a  prism.  Pursuing 
this  comparison,  the  three  lenses 
A,  B,  and  C  may  be  compared  to 
a  succession  of  prisms  having  their 
summits  outwards,  and  the  lenses 
D,  E,  and  F  to  a  series  having 
their  summits  inwards  :  from  this 
we  see  that  the  first  ought  to  con- 
dense the  rays,  and  the  latter  to 
disperse  them,  for  we  have  already 
seen  that  when  a  luminous  ray 
traverses  a  prism  it  is  deflected 
towards  the  base  (536). 
V  552.  Foci  in  double  convex  lenses. 


Fig.  469. 

-The  focus  of  a  lens  is  the  point 


where  the   refracted  rays,   or  their  prolongations,  meet.     Double  convex 
lenses  have  both  real  and  virtual  foci  like  concave  mirrors. 


504 


On  Light. 


[552- 


Real  foci. — We  shall  first  consider  the  case  in  which  the  luminous  rays 
which  fall  on  the  lens  are  parallel  to  its  principal  axis,  as  shown  in  fig. 
470.  In  this  case,  any  incident  ray,  LB,  in  approaching  the  normal  of  the 

point  of  incidence  B, 
and  in  diverging  from  it 
at  the  point  of  emergence 
D,  is  twice  refracted  to- 
wards the  axis,  which  it 
cuts  at  F.  As  all  rays 
parallel  to  the  axis  are 
refracted  in  the  same 
manner,  it  can  be  shown 
F[s-  470.  by  calculation  that  they 

all  pass  very  nearly  through  the  point  F,  so  long  as  the  arc  DE  does  not 
exceed  10°  to  12°.  This  point  is  called  the  principal  focus,  and  the  dis- 
tance FA  is  the  principal  focal  distance.  It  is  constant  in  the  same  lens, 
but  varies  with  the  radii  of  curvature  and  the  index  of  refraction.  In  ordi- 
nary lenses,  which  are  of  crown  glass,  and  in  which  the  radii  of  the  two 
surfaces  are  nearly  equal,  the  principal  focus  coincides  very  closely  with  the 
centre  of  curvature. 

We  shall  now  consider  the  case  in  which  the  luminous  point  is  outside  the 
principal  focus, 
but  so  near  that 
all  incident  rays 
form  a  divergent 
pencil,  as  shown 
in  fig.  471.  The 
luminous  point 
being  at  L,  by 
comparing  the 
path  of  a  di- 
verging ray,  LB,  F[s-  w- 

with  that  of  a  ray,  SB,  parallel  to  the  axis,  the  former  is  found  to  make  with 
the  normal  an  angle,  LB«,  greater  than  the  angle  SB«  ;  consequently,  after 
traversing  the  lens,  the  ray  cuts  the  axis  at  a  point,  /,  which  is  more  distant 

than  the  principal 
focus  F.  As  all 
rays  from  the  point 
L  intersect  approxi- 

I  w  S^^^^^Hm  mately  in  the  same 
point  /,  this  latter 
is  the  conjugate 
focus  of  the  point 
L ;  this  term  has 
the  same  meaning 
here  as  in  the  case 

of  mirrors,  and  expresses  the  relation  existing  between  the  two  points  L 
and  /,  which  is  of  such  a  nature  that,  if  the  luminous  point  is  moved  to  /, 
the  focus  passes  to  L. 


-554]  Determination  of  the  Focus  of  Lenses.  505 

According  as  the  luminous  point  comes  nearer  the  lens,  the  convergence 
of  the  emergent  rays  decreases,  and  the  focus  /  becomes  more  distant ; 
when  the  point  L  coin-  ^ 

cides  with  the  principal 
focus,  the  emergent  rays 
on  the  other  side  are 
parallel  to  the  axis,  and 
there  is  no  focus,  or,  what 
is  the  same  thing,  it  is 
infinitely  distant.  As  the 
refracted  rays  are  parallel 
in  this  case,  the  intensity  Fis-  473- 

of  light  only  decreases  slowly,  and  a  simple  lamp  can  illuminate  great  dis- 
tances. It  is  merely  necessary  to  place  it  in  the  focus  of  a  double  convex 
lens,  as  shown  in  fig.  472, 

Virtual  foci. — A  double  convex  lens  has  a  virtual  focus  when  the  luminous 
object  is  placed  between  the  lens  and  the  principal  focus,  as  shown  in  fig.  473. 
In  this  case  the  incident  rays  make  with  the  normal  greater  angles  than  those 
made  with  the  rays  FI  from  the  principal  focus  ;  hence,  when  the  former 
rays  emerge,  they  move  farther  from  the  axis  than  the  latter,  and  form  a 
diverging  pencil,  HK,  GM.  These  rays  cannot  produce  a  real  focus,  but 
their  prolongations  intersect  in  some  point,  /,  on  the  axis,  and  this  point  is 
the  virtual  focus  of  the  point  L  (514). 

553.  Poci  in  double  concave  lenses. — In  double  concave  lenses  there 
are  only  virtual  foci,  whatever  the  distance  of  the  object.  Let  SS'  be  any 
pencil  of  rays  parallel  to  the  axis  (fig.  474) ;  any  ray  SI  is  refracted  at  the 
point  of  incidence  I,  and  approaches  the  normal  CI.  At  the  point  of  emer- 
gence it  is  also  refracted,  but  diverges  from  the  normal  GC',  so  that  it  is 
twice  refracted  in  a  direction  which  moves  it  from  the  axis  CC'.  As  the 
same  thing  takes  place  for  every  other  ray,  S'KMN,  it  follows  that  the  rays, 
after  traversing  the  lens,  form  a  diverging  pencil,  GHMN.  Hence  there  is 
no  real  focus,  but  the  prolongations  of  these  rays  cut  one  another  in  a  point 
F,  which  is  the  principal  virtual  focus. 


Fig.  474-  Fig.  475. 

In  the  case  in  which  the  rays  proceed  from  a  point,  L  (fig.  475),  on  the 
axis,  it  is  found  by  the  same  construction  that  a  virtual  focus  is  formed  at  /, 
which  is  between  the  principal  focus  and  the  lens. 

5  54.  Experimental  determination  of  the  principal  focus  of  lenses. — 
To  determine  the  principal  focus  of  a  convex  lens,  it  may  be  exposed  to 
the  sun's  rays  so  that  they  are  parallel  to  its  axis.  The  emergent  pencil 


506  On  Light.  [554- 

being  received  on  a  ground  glass  screen,  the  point  to  which  the  rays  con- 
verge is  readily  seen;  it  is  the  principal  focus. 

Or  an  image  of  an  object  is 
formed  on  a  screen,  their  respective 
distances  from  which  are  then  mea- 
sured, and  from  these  distances  the 
focus  is  calculated  from  the  dioptric 
formula  (561). 

With  a  double  concave  lens,  the 
face  ab  (fig.  476)  is  covered  with  an 
opaque  substance,  such  as  lamp- 
Flg>  476'  black,  two  small  apertures  a  and  £, 

being  left  in  the  same  principal  section,  and  at  an  equal  distance  from  the 
axis  ;  a  pencil  of  sunlight  is  then  received  on  the  other  face,  and  the 
screen  P,  which  receives  the  emergent  rays,  is  moved  nearer  to  or  farther 
from  the  lens,  until  A  and  B,  the  spots  of  light  from  the  small  apertures  a 
and  £,  are  distant  from  each  other  by  twice  ab.  The  distance  DI  is  then 
equal  to  the  focal  distance  FD,  because  the  triangles  ¥ab  and  FAB  are 
similar.  Another  method  of  determining  the  focus  of  a  concave  lens  is 
given  in  article  560. 

555.  Optical  centre,  secondary  axis. —  In  every  lens  there  is  a  point 
called  the  optical  centre,  which  is  situate  on  the  axis,  and  which  has  the 
property  that  any  luminous  ray  passing  through  it  experiences  no  angular 
deviation  ;  that  is,  that  the  emergent  ray  is  parallel  to  the  incident  ray. 
The  existence  of  this  point  may  be  demonstrated  in  the  following  manner  : — 
Let  two  parallel  radii  of  curvature,  CA  and  C'A'  (fig.  477),  be  drawn  to  the 
two  surfaces  of  a  double  convex  lens.  Since  the  two  plane  elements  of  the 
lens  A  and  A'  are  parallel,  as  being  perpendicular  to  two  parallel  right  lines, 
it  will  be  granted  that  the  refracted  ray  A  A'  is  propagated  in  a  medium 
with  parallel  faces.  Hence  a  ray  KA,  which  reaches  A  at  such  an  inclination 
that  after  refraction  it  takes  the  direction  AA',  will  emerge  parallel  to  its  first 
direction  (542)  ;  the  point  O,  at  which  the  right  line  cuts  the  axis,  is  there- 
fore the  optical  centre.  The  position  of  this  point  may  be  determined  fot 
the  case  in  which  the  curvature  of  the  two  faces  is  the  same,  which  is  the 
usual  condition,  by  observing  that  the  triangles  COA  and  C'OA'  are  equal, 


Fig.  477.  Fig.  478. 

and  therefore  that  OC  =  OC',  which  gives  the  point  O.  If  the  curvatures  are 
unequal,  the  triangles  COA  and  CO'A'  are  similar,  and  either  CO  or  C'O  may 
be  found,  and  therefore  also  the  point  O. 


-556]          Formation  of  Images  in  Double  Convex  Lenses.          507 

In  double  concave  or  concavo-convex  lenses  the  optical  centre  may  be 
determined  by  the  same  construction.  In  lenses  with  a  plane  face  this  point 
is  at  the  intersection  of  the  axis  by  the  curved  face. 

Every  right  line  PP'  (fig.  478),  which  passes  through  the  optical  centre 
without  passing  through  the  centres  of  curvature,  is  a  secondary  axis.  From 
this  property  of  the  optical  centre,  every  secondary  axis  represents  a  luminous 
rectilinear  ray  passing  through  this  point  :  for,  from  the  slight  thickness  of  the 
lenses,  it  may  be  assumed  that  rays  passing  through  the  optical  centre  are  in 
a  right  line  ;  that  is,  that  the  small  deviation  may  be  neglected  which  rays 
experience  in  traversing  a  medium  with  parallel  faces  (fig.  457). 

So  long  as  the  secondary  axes  only  make  a  small  angle  with  the  principal 
axis,  all  that  has  hitherto  been  said  about  the  principal  axis  is  applicable  to- 
them  ;  that  is,  that  rays  emitted  from  a  point  P  (fig.  478)  on  the  secondary 
axis  PP'  nearly  converge  to  a  certain  point  of  the  axis  P',  and  according  as 
the  distance  from  the  point  P  to  the  lens  is  greater  or  less  than  the  principal 
focal  distance,  the  focus  thus  formed  will  be  conjugate  or  virtual.  This  prin- 
ciple is  the  basis  of  what  follows  as  to  the  formation  of  images. 

Y556.  Formation  of  images  in  double  convex  lenses. — In  lenses,  as  well 
as  in  mirrors,  the  image  of  an  object  is  the  collection  of  the  foci  of  its  several 
points  ;   hence  the  images  furnished  by  lenses  are  real  or  virtual  in  the  same 
case  as  the  foci,  and 
their     construction 
resolves  itself  into 
determining  the  po- 
sition of  a  series  of 
points,  as  was  the 
case   with    mirrors 
(5*8). 

i.  Real  image. 
Let  AB  (fig.  479) 
be  placed  beyond 

the  principal  focus.  If  a  secondary  axis,  A#,  be  drawn  from  the  outside 
point  A,  any  ray  AC,  from  this  point,  will  be  twice  refracted  at  C  and 
D,  and  both  times  in  the  same  direction  approaching  the  secondary  axis, 
which  it  cuts  at  a.  From  what  has  been  said  in  the  last  paragraph,  the 
other  rays  from  the  point  A  will  intersect  in  the  point  a,  which  is  accordingly 
the  conjugate  focus  of  the  point  A.  If  the  secondary  axis  be  drawn  from 
the  point  B,  it  will  be  seen,  in  like  manner,  that  the  rays  from  this  point 
intersect  in  the  point  b ;  and  as  the  points  between  A  and  B  have  their 
foci  between  a  and  b,  a  real  but  inverted  image  of  AB  will  be  formed  at  ab. 
To  see  this  image,  it  may  be  received  on  a  white  screen,  on  which  it  will 
be  depicted,  or  the  eye  may  be  placed  in  the  path  of  the  rays  emerging 
from  it. 

Conversely,  if  ab  were  the  luminous  or  illuminated  object  its  image 
would  be  formed  at  AB.  Two  consequences  important  for  the  theory 
of  optical  instruments  follow  from  this:  that,  ist,  if  an  object,  even  a  very 
large  one,  is  at  a  sufficient  distance  from  a  double  convex  lens,  the  real  ana 
inverted  image  which  is  obtained  of  it  is  very  small — it  is  near  the  prin- 
cipal focus,  but  somewhat  farther  from  the  /ens  than  this  is  ;  2nd,  if  a  very 


508  On  Light.  [556- 

small  object  be  placed  near  the  principal  focus,  but  a  little  in  front  of  it, 
the  image  which  is  formed  is  at  a  great  distance — it  is  much  larger,  and  that 
in  proportion  as  the  object  is  near  the  principal  focus.  In  all  cases  the  object 
and  the  image  are  in  the  same  proportion  as  their  distances  from  the  lens. 

These  two  principles  are  experimentally  confirmed  by  receiving  on  a 
screen  the  image  of  a  lighted  candle,  placed  successively  at  various  distances 
from  a  double  convex  lens. 

ii.  Virtual  image.  There  is  another  case  in  which  the  object  AB  (fig.  480) 
is  placed  between  the  lens  and  its  principal  focus.  If  a  secondary  axis  Oa 
be  drawn  from  the  point  A,  every  ray  AC,  after  having  been  twice  refracted, 

diverges  from 
this  axis  on 
emerging,  since 
the  point  A  is 
at  a  less  dis- 
tance than  the 
principal  focal 
distance  (552). 
This  ray,  con- 
tinued in  an 
opposite  direc- 
tion, will  cut  the 

axis  Oa  in  the  point  a,  which  is  the  virtual  focus  of  the  point  A.  Tracing 
the  secondary  axis  of  the  point  B,  it  will  be  found,  in  the  same  manner, 
that  the  virtual  focus  of  this  point  is  formed  at  b.  There  is,  therefore,  an 
image  of  AB  at  ab.  This  is  a  "virtual  image;  it  is  erect,  and  larger  than  the 
object. 

The  magnifying  power  is  greater  in  proportion  as  the  lens  is  more  con- 
vex, and  the  object  nearer  the  principal  focus.  We  shall  presently  show  how 
the  magnifying  power  may  be  calculated  by  means  of  the  formulae  relating 
to  lenses  (561).  Double  convex  lenses,  used  in  this  manner  as  magnifying 
glasses,  are  called  simple  microscopes. 

557.  Formation  of  images  in  double  concave  lenses. — Double  con- 
cave lenses,  like  convex  mirrors,  only  give  virtual  images,  whatever  the 
distance  of  the  object. 

Let  AB  (fig.  481)  be  an  object  placed  in  front  of  such  a  lens.     If  the 

secondary  axis  AO  be  drawn  from 
the  point  A,  all  rays,  AC,  AI,  from 
this  point  are  twice  refracted  in  the 
same  direction,  diverging  from  the 
axis  AO  ;  so  that  the  eye,  receiving 
the  emergent  rays  DE  and  GH, 
supposes  them  to  proceed  from  the 
point  where  their  prolongations  cut 
the  secondary  axis  AO  in  the  point 
a.  In  like  manner,  drawing  a 
secondary  axis  from  the  point  B, 
Flg  4Sl'  the  rays  from  this  point  form  a  pen- 

cil of  divergent  rays  the  directions  of  which,  prolonged,  intersect  in  b.    Hence 


-558]  Spherical  Aberration.     Caiistics.  509 

the  eye  sees  at  ab  a  virtual  image  of  AB,  which  is  always  erect,  and  smaller 
than  the  object. 

558.  Spherical  aberration.  Caustics. — In  speaking  about  foci,  and 
about  the  images  formed  by  different  kinds  of  spherical  lenses,  it  has  been 
hitherto  assumed  that  the  rays  emitted  from  a  single  point  intersect  also- 
after  refraction  in  a  single  point.  This  is  virtually  the  case  with  a  lens  whose 
aperture — that  is,  the  angle  obtained  by  joining  the  edges  to  the  principal 
focus — does  not  exceed  10°  or  12°. 

Where,  however,  the  aperture  is  larger,  the  rays  which  traverse  the  lens 
near  the  edge  are  refracted  to  a  point  F  nearer  the  lens  than  the  point  G,. 
which  is  the  focus  of  the  rays  which  pass  near  the  axis.  The  phenomenon 
thus  produced  is  named  spherical  aberration  by  refraction  ;  it  is  analogous 
to  the  spherical  aberration  produced  by  reflection  (533).  The  luminous  sur- 
faces formed  by  the  intersection  of  the  refracted  rays  are  termed  caustics  by 
refraction. 

Spherical  aberration  is  prejudicial  to  the  sharpness  and  definition  of  an 
image.  If  a  ground  glass  screen  be  placed  exactly  in  the  focus  of  a  lens, 
the  image  of  an  ob- 
ject will  be  sharply 
defined  in  the 
centre,  but  indis- 
tinct at  the  edges  ; 
and,  vice  versa,  if 
the  image  is  sharp 
at  the  edges,  it  will 
be  indistinct  in  the 
centre.  This  defect 
is  very  objection- 
able, more  espe- 
cially in  lenses  used 
for  photography.  It 

is  partially  obviated  by  placing,  in  front  of  the  lenses,  diaphragms  provided 
with  a  central  aperture,  called  stops,  which  admit  the  rays  passing  near  the 
centre,  but  cut  off  those  which  pass  near  the  edges.  The  image  thereby 
becomes  sharper  and  more  distinct,  though  the  illumination  is  less. 

If  a  screen  be  held  between  the  light  and  an  ordinary  double  convex  lens 
which  quite  covers  the  lens,  but  has  two  concentric  series  of  holes,  two  images 
are  obtained,  and  may  be  received  on  a  sheet  of  paper.  By  closing  one  or 
the  other  series  of  holes  by  a  flat  paper  ring  it  can  be  easily  ascertained 
which  image  arises  from  the  central,  and  which  from  the  marginal  rays. 
When  the  paper  is  at  a  small  distance  the  marginal  rays  produce  the  image 
in  a  point,  and  the  central  ones  in  a  ring  ;  the  former  are  converged  to  a 
point,  and  the  latter  not.  At  a  somewhat  greater  distance  the  marginal  rays 
produce  a  ring,  and  the  central  ones  a  point.  It  is  thus  shown  that  the  focus 
of  the  marginal  rays  is  nearer  the  lens  than  that  of  the  central  rays. 

Mathematical  investigation  shows  that  convex  lenses  whose  radii  of  cur- 
vature stand  in  the  ratio  expressed  by  the  formula 

r  _  4-2n*  +  n 
r,          2riz  +  n 


510  On  Light.  [558- 

are  most  free  from  spherical  aberration,  and  are  called  lenses  of  best  form  : 
in  this  formula  r  is  the  radius  of  curvature  of  the  foci  turned  to  the  parallel 
rays,  and  r^  that  of  the  other  face,  while  n  is  the  refractive  index.  Thus, 

with  a   glass  whose  refractive  index  is  ^^r^  =  6r.     Spherical  aberration  is 

also  destroyed  by  substituting  for  a  lens  of  short  focus  two  lenses  of  double 
focal  length,  which  are  placed  at  a  little  distance  apart.  Greater  length  of 
focus  has  the  result  that  for  the  same  diameter  the  aperture  and  also  the  aber- 
ration are  less  ;  and  as  it  is  not  necessary  to  stop  a  great  part  of  the  lens 
there  is  a  gain  in  luminosity,  which  is  not  purchased  by  indistinctness  of  the 
images,  while  the  combination  of  the  two  lenses  has  the  same  focus  as  that 
•of  the  single  lens  (560).  Lenses  which  are  free  from  spherical  aberration  are 
called  aplanatic. 

\^  SS9-  Formulae  relating:  to  lenses. — In  all  lenses  the  relations  between 
the  distances  of  the  image  and  object,  the  radii  of  curvature,  and  the  refrac- 
tive index,  may  be  expressed  by  a  formula.  In  the  case  of  a  double  convex 


Fig.  483. 

lens,  let  P  be  a  luminous  point  situate  on  the  axis  (fig.  483),  let  PI  be  an  in- 
cident ray,  IE  its  direction  within  the  lens,  EP'  the  emergent  ray,  so  that  P' 
is  the  conjugate  focus  of  P.  Further,  let  C'l  and  CE  be  the  normals  to  the 
points  of  incidence  and  emergence,  and  I  PA  be  put  equal  to  o,  EP'A'^/3, 
ECA'  =  y,  IC'A-8,  NIP=/,  EIO  =  r,  IEO=zv,  N'EP'  =  r. 

Because  the  angle  i  is  the  exterior  angle  of  the  triangle  PIC',  and  the 
angle  r'  the  exterior  angle  of  the  triangle  CEP',  therefore  z'  =  a  +  d,  and 
r1  =  y  + 18,  whence 

z  +  r'  =  a  +  p  +  y  +  d (i) 

But  at  the  point  I,  sin  i  =  n  sin  r,  and  at  the  point  E,  sin  r'  =  n  sin  i  (538),  n 
being  the  refractive  index  of  the  lens.  Now  if  the  arc  AI  is  only  a  small 
number  of  degrees,  these  sines  may  be  considered  as  proportional  to  the 
angles  /,  r,  z',  and  r  ;  whence,  in  the  above  formula,  we  may  replace  the  sines 
by  their  angles,  which  gives  i  =  nr  and  r'  =  ni'\  from  which  z +  r'  =  ?z  (r  +  z'}. 
Further,  because  the  two  triangles  IOE  and  COG'  have  a  common  equal 
angle  O,  therefore  r+zv  =  y  +  (5,  from  which  z  +  r'  =  n  (y  +  8).  Introducing 
this  value  into  the  equation  (i)  we  obtain 

n  (y  +  8)  =a  +  £  +  y  +  S,  from  which  (rt-l)  (y  +  8)=a  +  /3         ,          (2) 

Let  CA'  be  denoted  by  R,  C'A  by  R',  PA  by  /,  and  P'A'  by  p.  Then 
with  centre  P  and  radius  PA  describe  the  arc  Ad,  and  with  centre  P'  and 


-560]  Combination  of  Lenses.  511 

radius  P'A'  describe  the  arc  A'».  Now  when  an  angle  at  the  centre  of  a 
circle  subtends  a  certain  arc  of  the  circumference,  the  quotient  of  the  arc 
divided  by  the  radius  measures  the  angle  ;  consequently 

kd          A^    R      A'»         A'E         ,  ,      AI 

"=      or       *-'**'*"    ~~ 


Therefore  by  substitution  in  (2),  (»-i)  + 

\   K. 

Now  since  the  thickness  of  the  lens  is  very  small,  the  angles  are  also  small, 
and  Adf,  AI,  A'E,  A'/z  differ  but  little  from  coincident  straight  lines,  and  are 
therefore  virtually  equal.  Hence  the  above  equation  becomes 


This  is  the  formula  for  double  convex  lenses  ;  if/  be  =  oo  —  that  is,  if  the  rays 
are  parallel  —  we  have 


p'  being  the  principal  focal  distance.     Calling  this/j  we  get 

•         -         •          •         (4) 

from  which  the  value  of  /  is  easily  deduced.     Considered  in  reference  to 
equation  (4),  the  equation  (3)  assumes  the  -form 


which  is  that  in  which  it  is  usually  employed.     When  the  image  is  virtual, 
fi  changes  its  sign,  and  formula  (5)  takes  the  form 

I      I  _  I  .~ 

p-p>-f 

In  double  concave  lenses  p'  and  /"retain  the  same  sign,  but  that  of/ 
changes  ;  the  equation  (5)  becomes  then 


The  equation  (7)  may  be  obtained  by  the  same  reasonings  as  the  other. 

560.  Combination  of  lenses.  —  If  parallel  rays,  fall  on  a  convex  lens  A, 
which  has  the  focal  distance  f,  and  then  on  a  similar  lens  B  with  the  focal 
distance  f,  at  a  distance  d  from  A,  the  distance  from  the  lens  B  at  which 
the  image  is  formed  at  F  is  , 

1     ' 


If  the  lenses  are  close  together,  so  that  4^=0,  then 

i*i*ij 

K    f  f> 


512  On  Light.  [560- 

if  the  lenses  have  the  same  curvature,  that  is  f=f,  then  -i  =  £  ;  that  is  to 

say,  the  focal  distance  of  the  combination  is  half  that  of  a  single  lens. 

If  the  second  lens  is  a  dispersing  one  of  the   focal  distance  f,  then 

—  =  -  —   —  -  ;  and  if  the  lenses  are  close  .together,  then  _  =  --  -  l  .. 
F    /-»    f  ,  *    f    f 

This  formula  can  be  used  to  determine  the  focal  distance  of  a  concave 
lens,  by  combining  it  with  a  convex  lens  of  longer  focus,  and  then  determining 
the  focal  distance  of  the  combination. 

561.  Relative  magnitudes  of  image  and  object.  Determination  of 
focus.  —  From  the  similarity  of  the  triangles  AOB,  aO&  (fig.  479),  we  get 

for  the  relative  magnitudes  of  image  and  object  the  proportion    —  •=—  ,  ; 

whence    —  =  —  ,  where  AB  =  O  is  the  magnitude  of  the  object,  and  ab  =  \ 
O     p 

that  of  the  image  ;  while  p  and  p'  are  their  respective  distances  from  the 

lens.      Replacing  p'  by  its  value  from  the  equation     +  --  =  I  where  the 

P     P' 

image  is  real,  or  from  the  equation  —  —  _-—  -  where  it  is  virtual,  we  shall 

P     P      f 

obtain  the  different  values  of  the  ratio  -_  for  various  positions  of  the  object. 
In  the  first  case  we  have  —  .  —  ?  —  J-. 

Thus  if  p>7.f    I>O 


In  the  second  case  when  the  image  is  virtual  we  shall  have 

—  =  -  —  ,  so  that  in  all  cases  I  >O. 
O    f-p 

By  using  the  above  formula  we  may  easily  deduce  the  focal  length  of  a 
convex  lens  where  direct  sunlight  is  not  available.  For  if  it  be  placed  in 
front  of  a  scale,  and  if  a  screen  be  placed  on  the  other  side,  then,  by  altering 
the  relative  positions  of  the  lens  and  the  screen,  a  position  may  be  found  by 
trial,  such  that  an  image  of  the  object  is  formed  on  the  screen  of  exactly  the 
same  size.  Dividing  now  by  4,  the  total  distance  between  the  object  and  the 
screen,  we  get  the  focal  distance  of  the  lens. 

Another  method  is  to  place  on  one  side  of  the  lens,  and  a  little  beyond 
its  principal  focus,  a  brightly  illuminated  scale,  which  is  best  of  glass,  on  which 
a  strong  light  falls  ;  on  the  other  side  a  screen  is  placed  at  such  a  distance 
as  to  produce  a  greatly  magnified  distinct  image  of  the  scale.  Then  if  /  and 
L  are  the  lengths  of  the  scale  and  its  image  respectively,  and  d  the  distance 
of  the  screen  from  the  lens, 

f-dJ  • 

/+L 


-563] 


Laryngoscope. 


513 


Fig.  484. 


562.  Determination  of  the  refractive  index  of  a  liquid. — By  measure- 
ments of  focal  distance  the  refractive  index  of  a  liquid  may  be  ascertained  in 
cases  in  which  only  small  quantities  of  liquid  are  available. 

One  face  of  a  double  convex  lens  of  known  focal  distance/, 
and  known  curvature  r,  is  pressed  against  a  drop  of  the  liquid 
in  question  on  a  plate  glass  (fig.  484).  The  liquid  forms 
thereby  a  plano-concave  lens  whose  radius  of  curvature  is  r. 
The  focal  distance  F  of  the  whole  system  is  then  determined 
experimentally  ;  this  gives  the  focal  length  of  the  liquid  lens 
f  from  the  formula 

I  _!___! 

F    /    /' 
while  from  the  formula  _^  =  (n  —  i)  -  we  get  the  value  of  n. 

563.  laryngoscope. — As  an  application  of  lenses  may  be  adduced  the 
laryngoscope,  which  is  an  instrument  invented  to  facilitate  the  investigation 
of  the  larynx  and  the  other  cavities  of  the  mouth.     It  consists  of  a  plano- 
convex lens  L,  and  a  concave  reflector  M,  both  fixed  to  a  ring  which  can  be 
adjusted  to  any  convenient  lamp  (fig.  485).     The  flame  of  a  lamp  is  in  the 


Fig.  485. 

principal  focus  of  the  lens,  and  at  the  same  time  is  at  the  centre  of  curvature 
of  the  reflector.  Hence  the  divergent  pencil  proceeding  from  the  lamp  to 
the  lens  is  changed  after  emerging  into  a  parallel  pencil.  Moreover,  the 
pencil  from  the  lamp,  impinging  upon  the  mirror,  is  reflected  to  the  focus  of 
the  lens,  and  traverses  the  lens,  forming  a  second  parallel  pencil  which  is 
superposed  on  the  first.  This  being  directed  into  the  mouth  of  a  patient, 
its  condition  may  be  readily  observed. 


L  L 


514  On  Light  [564- 


CHAPTER   IV. 

DISPERSION   AND   ACHROMATISM. 

564.  Decomposition  of  -white  light.  Solar  spectrum. — The  pheno- 
menon of  refraction  is  by  no  means  so  simple  as  we  have  hitherto  assumed. 
When  white  light,  or  that  which  reaches  us  from  the  sun,  passes  from  one 
medium  into  another,  it  is  decomposed  into  several  kinds  of  light,  a  pheno  - 
menon  to  which  the  name  dispersion  is  given. 

In  order  to  show  that  white  light  is  decomposed  by  refraction,  a  pencil  of 
the  sun's  rays  SA  (fig.  486)  is  allowed  to  pass  through  a  small  aperture  in  the 

window  shutter  of  a 
dark  chamber.  This 
pencil  tends  to  form  a 
round  and  colourless 
image  of  the  sun  at 
K  ;  but  if  a  flint  glass 
prism,  arranged  hori- 
zontally be  interposed 
in  its  path,  the  beam 
on  emerging  from  the 
prism,  becomes  re- 
fracted towards  its 
base,  and  produces 
on  a  distant  screen  a 
Fi  486  vertical  band  rounded 

at  the  ends,  coloured 

in  all  the  tints  of  the  rainbow,  which  is  called  the  solar  spectrum,  see  Plate  I. 
In  this  spectrum  there  is,  in  reality,  an  infinity  of  different  tints,  which  im- 
perceptibly merge  into  each  other,  but  it  is  customary  to  distinguish  seven 
principal  colours.  These  are  violet,  indigo,  blue,  green,  yellow,  orange, 
red  •  they  are  arranged  in  this  order  in  the  spectrum,  the  violet  being  the 
most  refrangible,  and  the  red  the  least  so.  They  do  not  all  occupy  an 
equal  extent  in  the  spectrum,  violet  having  the  greatest  extent,  and  orange 
the  least. 

With  transparent  prisms  of  different  substances,  or  with  hollow  glass 
prisms  filled  with  various  liquids,  spectra  are  obtained  formed  of  the  same 
colours,  and  in  the  same  order  ;  but  when  the  deviation  produced  is  the 
same,  the  length  of  the  spectrum  varies  with  the  substance  of  which  the 
prism  is  made.  The  angle  of  separation  of  two  selected  rays  (say  in  the  red 
and  the  violet)  produced  by  a  prism  is  called  the  dispersion,  and  the  ratio  of 


-566]  Production  of  a  pure  Solar  Spectrum.  515 

this  angle  to  the  mean  deviation  of  the  two  rays  is  called  the  dispersive  poiver. 
This  ratio  is  constant  for  the  same  substance  so  long  as  the  refracting  angle 
of  the  prism  is  small.  For  the  deviation  of  the  two  rays  is  proportional  to 
the  refracting  angle  ;  their  difference  and  their  mean  vary  in  the  same 
manner,  and  therefore  the  ratio  of  their  difference  to  their  mean  is  constant. 
For  flint  glass  this  is  0*043  ;  for  crown  glass  it  is  0*0246  ;  for  the  dispersive 
power  of  flint  is  almost  double  that  of  crown  glass. 

The  spectra  which  are  formed  by  artificial  lights  rarely  contain  all  the 
colours  of  the  solar  spectrum  ;  but  their  colours  are  found  in  the  solar 
spectrum,  and  in  the  same  order.  Their  relative  intensity  is  also  modified. 
The  shade  of  colour  which  predominates  in  the  flame  predominates  also  in 
the  spectrum  :  yellow,  red,  and  green  flames  produce  spectra  in  which  the 
dominant  tint  is  yellow,  red,  or  green. 

^565.  Production  of  a  pure  solar  spectrum. — In  the  above  experiment, 
when  the  light  is  admitted  through  a  wide  slit,  the  spectrum  formed  is  built 
up  of  a  series  of  overlapping  spectra,  and  the  colours  are  confused  and  indis- 
tinct. In  order  to  obtain  a  pure  spectrum,  the  slit,  in  the  shutter  of  the  dark 
room  through  which  light  enters,  should  be  from  15  to  25  mm.  in  height  and 
from  i  to  2  mm.  in  breadth.  The  sun's  rays  are  directed  upon  the  slit  by  a 
mirror,  or  still  better  by  a  heliostat  (534).  An  achromatic  double  convex 
lens  is  placed  at  a  distance  from  the  slit  of  double  its  own  focal  length,  which 
should  be  about  a  metre,  and  a  screen  is  placed  at  the  same  distance  from 
the  lens.  An  image  of  the  slit  of  exactly  the  same  size  is  thus  formed  on 
the  screen  (561).  If  now  there  is  placed  near  the  lens,  between  it  and 
the  screen,  a  prism  with  an  angle  of  about  60°,  and  with  its  refracting  edge 
parallel  to  the  slit,  a  very  beautiful,  sharp,  and  pure  spectrum  is  formed  on 
the  screen.  The  prism  should  be  free  from  striae,  and  should  be  placed  so 
that  it  produces  the  minimum  deviation. 

y  566.  The  colours  of  the  spectrum  are  simple,  and  unequally  refran- 
gible.— If  one  of  the  colours  of  the  spectrum  be  isolated  by  intercepting  the 
others  by  means  of  a  screen  E,  as  shown  in  fig.  487,  and  if  the  light  thus 
isolated  be  allowed  to 
pass  through  a  second 
prism,  B,  a  refraction 
will  be  observed,  but 
the  light  remains  un- 
changed ;  that  is,  the 
image  received  on  the 
screen  H  is  violet  if  the 
violet  pencil  has  been 
allowed  to  pass,  blue  Fig-  ^7~ 

if  the  blue  pencil,  and  so  on.    Hence  the  colours  of  the  spectrum  are  simple  ; 
that  is,  they  cannot  be  further  decomposed  by  the  prism. 

Moreover,  the  colours  of  the  spectrum  are  unequally  refrangible  ;  that 
is,  they  possess  different  refractive  indices.  The  elongated  shape  of  the 
spectrum  would  be  sufficient  to  prove  the  unequal  refrangibility  of  the  simple 
colours,  for  it  is  clear  that  the  violet,  which  is  most  deflected  towards  the 
base  of  the  prism,  is  also  most  refrangible  ;  and  that  red,  which  is  least  re- 
flected, is  least  refrangible.  But  the  unequal  refrangibility  of  simple  colours 

T.  L  2 


5i6 


On  Light. 


[566- 


may  be  shown  by  numerous  experiments,  of  which  the  two  following  may  be 
adduced  : — 

i.  Two  narrow  strips  of  coloured  paper,  one  red  and  the  other  violet,  are 
fastened  close  to  each  other  on  a  sheet  of  black  paper.  On  looking  at  them 
through  a  prism,  they  are  seen  to  be  unequally  displaced,  the  red  band  to  a 
less  extent  than  the  violet  ;  hence  the  red  rays  are  less  refrangible  than  the 
violet. 

ii.  The  same  conclusion  may  be  drawn  from  Newton's  experiment  with 
crossed  prisms.  On  a  prism  A  (fig.  488),  in  a  horizontal  position,  a  pencil 


Fig.  488. 

of  white  light,  S,  is  received,  which,  if  it  had  merely  traversed  the  prism  A, 
would  form  the  spectrum  rz/,  on  a  distant  screen.  But  if  a  second  prism,  B, 
be  placed  in  a  vertical  position  behind  the  first,  in  such  a  manner  that  the 
refracted  pencil  passes  through  it,  the  spectrum  rv  becomes  deflected  towards 
the  base  of  the  vertical  prism  ;  but,  instead  of  being  deflected  in  a  direction 
parallel  to  itself,  as  would  be  the  case  if  the  colours  of  the  spectrum  were 
equally  refracted,  it  is  obliquely  refracted  in  the  direction  rV,  proving  that 
from  red  to  violet  the  colours  are  more  and  more  refrangible. 

These  different  experiments  show  that  the  refractive  index  differs  in 
different  colours  ;  even  rays  which  are  to  perception  undistinguishable  have 
not  the  same  refractive  index.  In  the  red  band,  for  instance,  the  rays  at  the 


Fig.  489. 


Fig.  490. 


extremity  of  the  spectrum  are  less  refracted  than  those  which  are  nearer  the 
orange  zone.  In  determining  indices  of  refraction  (538),  it  is  usual  to  take, 
as  the  index  of  any  particular  substance,  the  refrangibility  of  the  yellow  ray 
in  a  prism  formed  of  that  substance. 


-567] 


Recomposition  of  White  LigJit. 


517 


567.  Recomposition  of  white  light. — Not  merely  can  white  light  be 
resolved  into  lights  of  various  colours,  but  by  combining  the  different  pencils 
separated  by  the  prism  white  light  can  be  reproduced.  This  may  be  effected 
in  various  ways. 

i.  If  the  spectrum  produced  by  one  prism  be  allowed  to  fall  upon  a  second 
prism  of  the  same  material  and  the  same  refracting  angle  as  the  first,  but 
inverted,  as  shown  in  fig.  490,  the  latter  reunites  the  different  colours  of 
the  spectrum,  and  it  is  seen  that  the  emer- 
gent pencil  E,  which  is  parallel  to  the  pencil 
S,  is  colourless. 

ii.  If  the  spectrum  falls  upon  a  double 
convex  lens  (fig.  489),  a  white  image  of  the 
sun  will  be  formed  on  a  white  screen  placed 
in  the  focus  of  the  lens  ;  a  glass  globe  filled 
with  water  produces  the  same  effect  as  the  Flg  49i 

lens. 

iii.  When  the  spectrum  falls  upon  a  concave  mirror,  a  white  image  is 
formed  on  a  screen  of  ground  glass  placed  in  its  focus  (fig.  491). 

iv.  Light  may  be  recomposed  by  means  of  a  pretty  experiment,  which 
consists  in  receiving  the  seven  colours  of  the  spectrum  on  seven  small  glass 


Fig.  492. 

mirrors  with  plane  faces,  and  which  can  be  so  inclined  in  all  positions  that 
the  reflected  light  may  be  transmitted  in  any  given  direction  (fig.  492). 
When  these  mirrors  are  suitably  arranged,  the  seven  reflected  pencils  may 
be  caused  to  fall  on  the  ceiling,  in  such  a  manner  as  to  form  seven  distinct 
images — red,  orange,  yellow,  &c.  When  the  mirrors  are  moved  so  that 
the  separate  images  become  superposed,  a  single  image  is  obtained,  which 
is  white. 

v.  By  means  of  Newtori s'  disc  (fig.  493)  it  may  be  shown  that  the  seven 
colours  of  the  spectrum  form  white.  This  is  a  cardboard  disc  of  about  a 
foot  in  diameter ;  the  centre  and  the  edges  are  covered  with  black  paper, 
while  in  the  space  between  there  are  pasted  strips  of  paper  of  the  colours  of 
the  spectrum.  They  proceed  from  the  centre  to  the  circumference,  and  their 


5i8 


On  Light. 


[567- 


relative  dimensions  and  tints  are  such  as  to  represent  five  spectra  (fig.  494). 
When  this  disc  is  rapidly  rotated,  the  effect  is  the  same  as  if  the  retina  re- 
ceived simultaneously  the  impression  of  the  seven  colours. 

vi.  If  by  a  mechanical  arrangement  a  prism,  on  which  the  sun's  light 
falls,  is  made  to  oscillate  rapidly,  so  that  the  spectrum  also  oscillates,  the 
middle  of  the  spectrum  appears  white. 

These  latter  phenomena  depend  on  the  physiological  fact  that  sensation 
always  lasts  a  little  longer  than  the  impression  from  which  it  results  (625). 
If  a  new  impression  is  allowed  to  act,  before  the  sensation  arising  from  the 
former  one  has  ceased,  a  sensation  is  obtained  consisting  of  two  impressions. 
And  by  choosing  the  time  short  enough,  three,  four,  or  more  impressions 
may  be  mixed  with  each  other.  With  a  rapid  rotation  the  disc  (fig.  493) 


Fig.  493- 

is  nearly  white.  It  is  not  quite  so,  for  the  colours  cannot  be  exactly  arranged 
in  the  same  proportion  as  those  in  which  they  exist  in  the  spectrum,  and 
moreover  pigment  colours  are  not  pure  (571). 

568.  Newton's  theory  of  the  composition  of  light. — Newton  was  the 
first  to  decompose  white  light  by  the  prism,  and  to  recompose  it.  From  the 
various  experiments  which  we  have  described,  he  concluded  that  white  light 
was  not  homogeneous,  but  formed  of  seven  lights  unequally  refrangible, 
which  he  called  simple  or  primitive  lights.  Owing  to  the  difference  in  re- 
frangibility  they  become  separated  in  traversing  the  prism. 

The  designation  of  the  various  colours  of  the  spectrum  is  to  a  very  great 
extent  arbitrary ;  for,  in  strict  accuracy,  the  spectrum  is  made  up  of  an  in- 
finite number  of  simple  colours,  which  pass  into  one  another  by  imperceptible 
gradations  of  colour  and  refrangibility. 


-570]  Mixed  Colours.     Complementary  Colours.  519 

569.  Colour  of  bodies. — The  natural  colour  of  bodies  results  from  the 
fact  that  one  portion  of  the  coloured  rays  contained  in  white  light  is 
absorbed  at  the  surface  of  the  body.  If  the  unabsorbed  portion  traverses 
the  body,  it  is  coloured  and  transparent  ;  if,  on  the  contrary,  it  is  reflected, 
it  is  coloured  and  opaque.  In  both  cases  the  colour  results  from  the 
constituents  which  have  not  been  absorbed.  Those  which  reflect  or 
transmit  all  colours  in  the  proportion  in  which  they  exist  in  the  spectrum 
are  white  ;  those  which  reflect  or  transmit  none  are  black.  Between  these 
two  limits  there  are  infinite  tints  according  to  the  greater  or  less  extent  to 
which  bodies  reflect  or  transmit  some  colours  and  absorb  others.  Thus  a 
body  appears  yellow  because  it  absorbs  all  colours  with  the  exception  of  yellow. 
In  like  manner,  a  solution  of  ammoniacal  oxide  of  copper  absorbs  preferably 
the  red  and  yellow  rays,  transmits  the  blue  rays  almost  completely,  the  green 
and  violet  less  so,  hence  the  light  seen  through  it  is  blue. 

Accordingly  bodies  have  •  no  colour  of  their  own  ;  the  colour  of  the  body 
changes  with  the  nature  of  the  incident  light.  Thus,  if  a  white  body  in  a 
dark  room  be  successively  illuminated  by  each  of  the  colours  of  the  spectrum, 
it  has  no  special  colour,  but  appears  red,  orange,  green,  £c.,  according  to  the 
position  in  which  it  is  placed.  If  homogeneous  light  falls  upon  a  body,  it 
.appears  brighter  in  the  colour  of  this  light,  if  it  does  not  absorb  this  colour  ; 
but  black  if  it  does  absorb  it.  In  the  light  of  a  lamp  fed  by  spirit  in  which 
some  common  salt  is  dissolved,  everything  white  and  yellow  seems  bright, 
while  other  colours,  such  as  vermilion,  ultramarine,  and  malachite,  are 
black.  This  is  well  seen  in  the  case  of  a  stick  of  red  sealing-wax  viewed  in 
such  a  light.  In  the  light  of  lamps  and  of  candles,  which  from  the  want  ol 
blue  rays  appear  yellow,  yellow  and  white  appear  the  same,  and  blue  seems 
like  green.  In  bright  twilight  or  in  moonshine  the  light  of  gas  has  a  reddish 
tint. 

\  570.  Mixed  colours.  Complementary  colours. — By  mixed  colours  we 
understand  the  impression  of  colour  which  results  from  the  coincident  action 
of  two  or  more  colours  on  the  same  position  of  the  retina.  1'his  new  im- 
pression is  single  ;  it  cannot  be  resolved  into 
its  components ;  in  this  respect  it  differs  from 
a  complex  sound,  in  which  the  ear,  by  practice, 
can  learn  to  distinguish  the  constituents.  Mixed 
colours  may  be  produced  by  Lambert's  method, 
which  consists  in  looking  in  an  oblique  direction 
through  a  vertical  glass  plate  P  (fig.  495)  at  a 
coloured  wafer  &,  while,  at  the  same  time,  a  wafer  _ 
of  another  colour  g  sends  its  light  by  reflection  F} 

towards  the  observer's  eye  ;  if  g  is  placed  in  a 

proper  position,  which  is  easily  found  by  trial,  its  image  exactly  coincides 
with  that  of  b.  The  method  of  the  colour  disc  (567)  affords  another  means 
of  producing  mixed  colours. 

A  very  convenient  way  of  investigating  the  phenomena  of  mixed  colours 
is  that  of  MaxweWs  colour-discs.  These  consist  of  discs  of  cardboard  with 
an  aperture  in  the  centre,  by  which  they  can  be  fastened  on  the  spindle  of  the 
turning-table  (fig.  496).  Each  disc  is  painted  with  a  separate  colour,  and, 
having  a  radial  slit,  they  may  be  slid  over  each  other  so  as  to  overlap  to  any 


520 


On  Light. 


[570- 


desired  extent  (figs.  497  and  498)  ;  and  thus,  when  in  this  way  two  such  discs 
are  rotated,  we  get  the  effect  due  to  this  mixture  of  these  two  colours.  It  is 
clear  also  that  the  effect  of  three  colours  may  be  investigated  in  the  same  way. 


Fig.  496. 


Fig.  497. 


Fig.  498. 


If  in  any  of  the  methods  by  which  the  impression  of  mixed  spectral 
colours  is  produced,  one  or  more  colours  be  suppressed,  the  residue  corre- 
sponds to  one  of  the  tints  of  the  spectrum  ;  and  the  mixture  of  the  colours 
taken  away  produces  the  impression  of  another  spectral  colour.  Thus,  if  in 
fig.  495  the  red  rays  are  cut  off  from  the  lens  L,  the  light  on  the  focus  is  no 
longer  white,  but  greenish  blue.  In  like  manner,  if  the  violet,  indigo,  and 
blue  of  the  colour  disc  be  suppressed,  the  rest  seems  yellow,  while  the  mixture 
of  that  which  has  been  taken  out  is  a  bluish  violet.  Hence  white  can  always 
be  compounded  of  two  tints  ;  and  two  tints  which  together  give  white  are 
called  complementary  colours.  Thus  of  spectral  tints  red  d&&  greenish  yellow 
are  complementary,  so  are  orange  and  Prussian  blue  ;  yellow  and  indigo 
blue  ;  greenish  yellow  and  violet. 

The  method  by  which  Helmholtz  investigated  the  mixture  of  spectral 
colours  is  as  follows  : — Two  very  narrow  slits,  A.  and  B  (fig.  499),  at  right 


Fig.  499. 

angles  to  each  other,  are  made  in  the  shutter  of  a  dark  room  ;  at  a  distance 
from  this  is  placed  a  powerfully  dispersing  prism'  with  its  refracting  edge 
vertical.  When  this  is  viewed  through  a  telescope  the  slit  B  gives  the 
oblique  spectrum  LM,  while  the  slit  A  gives  the  spectrum  ST.  These  two 
spectra  partially  overlap,  and  when  this  is  the  case  two  homogeneous  spectral 
colours  mix.  Thus  at  i  the  red  of  one  spectrum  coincides  with  the  green  of 
the  other  ;  at  3,  indigo  and  yellow  coincide  ;  and  so  forth. 

When  the  experiment  is  made  with  suitable  precautions,  the  colours  ob- 
tained by  mixing  the  spectral  colours  are  given  in  the  table  on  the  next  page, 
where  the  fundamental  spectra  to  be  mixed  are  given  in  the  first  horizontal 
and  vertical  column,  and  the  resultant  colours  where  these  cross. 

The  mixture  of  mixed  colours  gives  rise  to  no  new  colours.  Only  the 
same  colours  are  obtained  as  a  mixture  of  the  primitive  spectral  colours  would 
yield,  except  that  they  are  less  saturated,  as  it  is  called  ;  that  is,  more  mixed 
with  white. 


-571] 


Spectral  Colozirs  and  Pigment  Colours. 


521 


\57i.  Spectral  colours  and  pigment  colours.— A  distinction  must  be 
made  between  spectral  colours  and  pigment  colours.  Thus  a  mixture  of 
pigment  yellow  and  pigment  blue  produces  green,  and  not  white,  as  is  the 
case  when  the  blue  and  yellow  of  the  spectrum  are  mixed.  The  reason  of 
this  is  that  in  the  mixture  of  pigments  we  have  a  case  of  subtraction  of 
colours,  and  not  of  addition.  For  the  pigment  blue  in  the  mixture  absorbs 
almost  entirely  the  yellow  and  red  light ;  and  the  pigment  yellow  absorbs 
the  blue  and  violet  light,  so  that  only  the  green  remains. 

In  the  above  series  are  two  spectral  colours  very  remote  in  the  spectrum, 
which  have  nearly  the  same  complementary  tints  ;  these  are  red,  the  com- 
plementary colour  to  which  is  greenish  blue ;  and  violet,  whose  complementary 
colour  is  greenish  yellow.  Now  when  two  pairs  of  complementary  colours 
are  mixed  together,  they  must  produce  white,  just  as  if  only  two  comple- 
mentary colours  were  mixed.  But  a  mixture  of  greenish  blue  and  of  greenish 
yellow  is  green.  Hence  it  follows  that  from  a  mixture  of  red,  green,  and 
violet,  white  must  be  formed.  This  may  easily  be  ascertained  to  be  the  case 
by  means  of  a  colour  disc  on  which  are  these  three  colours  in  suitable  pro- 
portions. 


Violet 

Blue 

Green 

Yellow 

Bed 

Red 

Purple 

Rose 

Dull 
yellow 

Orange 

Red 

Yellow 

Rose 

White 

Yellowish 
green 

Yellow 

Green 

Pale  blue 

Bluish 
green 

Green 

Blue 

Indigo 

Blue 

Violet 

Violet 

From  the  above  facts  it  follows  that  from  a  mixture  of  red,  green,  and 
violet  all  possible  colours  may  be  constructed,  and  hence  these  three  spectral 
colours  are  called  \\\t  fundamental  colours.  It  must  be  remarked  that  the 
tints  resulting  from  the  mixture  of  these  three  have  never  the  saturation  of 
the  individual  spectral  colours. 

We  have  to  discriminate  three  points  in  regard  to  colour.  In  the  first 
place,  the  tint,  or  colour  proper,  by  which  we  mean  that  special  property 
which  is  due  to  a  definite  refrangibility  of  the  rays  producing  it ;  secondly, 
the  saturation,  which  depends  on  the  greater  or  less  admixture  of  white  light 
with  the  colours  of  the  spectrum,  these  being  colours  which  are  fully  satu- 
rated ;  and  thirdly,  there  is  the  intensity,  which  depends  on  the  amplitude  of 
vibration. 


522  On  Light.  [572- 

572.  Homogeneous  light. — The  light  emitted  from  luminous  bodies  is 
seldom  or  never  quite  pure  ;  on  being  examined  by  the  prism  it  will  be  found 
to  contain  more  than  one  colour.  In  optical  researches  it  is  frequently  of 
great  importance  to  procure  homogeneous  or  monochromatic  light.  Common 
salt  in  the  flame  of  a  Bunsen's  lamp  gives  a  yellow  of  great  purity.  For  red 
light,  ordinary  light  is  transmitted  through  glass  coloured  with  suboxide  of 
copper,  which  absorbs  nearly  all  the  rays  excepting  the  red.  A  very  pure 
blue  is  obtained  by  transmitting  ordinary  light  through  a  glass  trough  con- 
taining an  ammoniacal  solution  of  sulphate  of  copper,  and  a  nearly  pure  red 
by  transmitting  it  through  a  solution  of  sulphocyanide  of  iron. 
^Y~~  573-  Properties  of  the  spectrum. — Besides  its  luminous  properties,  the 
spectrum  is  found  to  produce  calorific  and  chemical  effects. 

Luminous  properties.  It  appears  from  the  experiments  of  Fraunhofer 
and  of  Herschel,  that  the  light  in  the  yellow  part  of  the  spectrum  has  the 
greatest  intensity,  and  that  in  the  violet  the  least. 

Heating  effects.  It  was  long  known  that  the  various  parts  of  the  spectrum 
differed  in  their  calorific  effects.  Leslie  found  that  a  thermometer  placed  in 
different  parts  of  the  spectrum  indicated  a  higher  temperature  as  it  moved 
from  violet  towards  red.  Herschel  fixed  the  maximum  intensity  of  the 
heating  effects  just  outside  the  red  ;  Berard  in  the  red  itself.  Seebeck 
showed  that  those  different  effects  depend  on  the  nature  of  a  prism  \  with  a 
prism  of  water  the  greatest  calorific  effect  is  produced  in  the  yellow  ;  with 
one  of  alcohol  it  is  in  the  orange-yellow ;  and  with  a  prism  of  crown  glass  it 
is  in  the  middle  of  the  red. 

Melloni,  by  using  prisms  and  lenses  of  rock  salt,  and  by  availing  himself 
of  the  extreme  delicacy  of  the  thermo-electric  apparatus,  first  made  a  com- 
plete investigation  of  the  calorific  properties  of  the  thermal  spectrum.  This 
result  led,  as  we  have  seen,  to  the  confirmation  and  extension  of  Seebeck's 
observations. 

Chemical  properties.  In  numerous  phenomena,  light  exerts  a  chemical 
action.  For  instance,  chloride  of  silver  blackens  under  the  influence  of  light ; 
transparent  phosphorus  becomes  opaque ;  vegetable  colouring  matters  fade  ; 
hydrogen  and  chlorine  gases,  when  mixed,  combine  slowly  in  diffused  light, 
and  with  explosive  violence  when  exposed  to  direct  sunlight.  The  chemical 
action  differs  in  different  parts  of  the  spectrum.  Scheele  found  that  when 
chloride  of  silver  was  placed  in  the  violet,  the  action  was  more  energetic 
than  in  any;other  part.  Wollaston  observed  that  the  action  extended  beyond 
the  violet,  and  concluded  that,  besides  the  visible  rays,  there  are  some 
invisible  and  more  highly  refrangible  rays.  These  are  the  chemical  or  actinic 
rays. 

The  most  remarkable  chemical  action  which  light  exerts  is  in  the  growth 
of  plant  life.  The  vast  masses  of  carbon  and  hydrogen  accumulated  in  the 
vegetable  world  owe  their  origin  to  the  carbonic  acid  and  aqueous  vapour 
present  in  the  atmosphere.  The  light  which  is  absorbed  by  the  green  parts 
of  plants  acts  as  a  reducing  agent.  The  reduction  does  not  extend  to  the 
complete  isolation  of  carbon  and  hydrogen,  and  the  individual  stages  of  the 
process  are  unknown  to  us  ;  but  the  general  result  is,  undoubtedly,  that  under 
the  influence  of  the  sun's  rays  the  chemical  attraction  which  holds  together 
the  carbon  and  oxygen  is  overcome  ;  the  carbon,  which  is  set  free,  assimilates 


-574]  Dark  Lines  of  the  Spectrum.  523 

at  that  moment  the  elements  of  water,  forming  cellulose  or  woody  fibre, 
while  the  oxygen  returns  to  the  atmosphere  in  the  gaseous  form.  The 
equivalent  of  the  sunlight  which  has  been  absorbed  is  to  be  sought  in  the 
chemical  energy  of  the  separated  constituents.  When  we  burn  petroleum, 
or  coal,  we  reproduce,  in  some  sense,  the  light  which  the  sun  has  expended 
in  former  ages  in  the  production  of  a  primeval  vegetable  growth. 

The  researches  of  Bunsen  and  Roscoe  show  that  whenever  chemical 
action  is  induced  by  light,  an  absorption  of  light  takes  place,  preferably  of 
the  more  refrangible  parts  of  the  spectrum.  Thus,  when  chlorine  and 
hydrogen  unite,  under  the  action  of  light,  to  form  hydrochloric  acid,  light  is 
absorbed,  and  the  quantity  of  chemically  active  rays  consumed  is  directly 
proportional  to  the  amount  of  chemical  action. 

There  is  a  curious  difference  in  the  action  of  the  different  spectral  rays. 
Moser  placed  an  engraving  on  an  iodised  silver  plate,  and  exposed  it  to  the 
light  until  an  action  had  commenced,  and  then  placed  it  under  a  violet  glass 
in  the  sunlight.  After  a  few  minutes  a  picture  was  seen  with  great  distinct- 
ness, while  when  placed  under  a  red  or  yellow  glass  it  required  a  very  long 
time,  and  was  very  indistinct.  When,  however,  the  iodised  silver  plate  was 
first  exposed  in  a  camera  obscura  to  blue  light  for  two  minutes,  and  was  then 
brought  under  a  red  or  yellow  glass,  an  image  quickly  appeared,  but  not 
when  placed  under  a  green  glass.  It  appears  as  if  there  are  vibrations  of  a 
certain  velocity  which  could  commence  an  action,  and  that  there  are  others 
which  are  devoid  of  the  property  of  commencing,  but  can  continue  and 
complete  an  action  when  once  set  up.  Becquerel,  who  discovered  these 
properties  in  luminous  rays,  called  the  former  exciting  rays  and  the  latter 
continuing  or  phosphorogenic  rays.  The  phosphorogenic  rays,  for  instance, 
have  the  property  of  rendering  certain  objects  self-luminous  in  the  dark 
after  they  have  been  exposed  for  some  time  to  the  light.  Becquerel  found 
that  the  phosphorogenic  spectrum  extended  from  indigo  to  beyond  the 
violet. 

^574.  Dark  lines  of  tlie  spectrum. — The  colours  of  the  solar  spectrum 
are  not  continuous.  For  several  grades  of  refrangibility  rays  are  wanting, 
and,  in  consequence,  throughout  the  whole  extent  of  the  spectrum  there  are  a 
great  number  of  very  narrow  dark  lines.  To  observe  them,  a  pencil  of  solar 
rays  is  admitted  into  a  darkened  room,  through  a  narrow  slit.  At  a  distance 
of  three  or  four  yards  we  look  at  this  slit  through  a  prism  of  flint  glass, 
which  must  be  very  free  from  flaws,  taking  care  to  hold  its  edge  parallel  to 
the  slit.  We  then  observe  a  great  number  of  very  delicate  dark  lines 
parallel  to  the  edge  of  the  prism,  and  at  very  unequal  intervals. 

The  existence  of  the  dark  lines  was  first  observed  by  Wollaston  in  1802  ; 
but  Fratmhofer,  a  celebrated  optician  of  Munich,  first  studied  and  gave  a 
detailed  description  of  them.  Fraunhofer  mapped  the  lines,  and  indicated 
the  most  marked  of  them  by  the  letters  A,  a,  B,  C,  D,  E,  b,  F,  G,  H  ;  they 
are  therefore  generally  known  as  Fraunhofer's  lines. 

The  dark  line  A  (see  fig.  2  of  Plate  I.)  is  at  the  middle  and  B  half-way 
between  this  and  the  end  of  the  red  ray  ;  C  at  the  boundary  of  the  red  and 
orange  ray  ;  D  is  in  the  yellow  ray  ;  E,  in  the  green  ;  F,  in  the  blue  ;  G,  in 
the  indigo  ;  H,  in  the  violet.  There  are  certain  other  noticeable  dark  lines, 
.such  as  a  in  the  red  and  b  in  the  green.  In  the  case  of  sunlight  the  positions 


524  On  Light.  [574- 

of  the  dark  lines  are  fixed  and  definite ;  on  this  account  they  are  used  for 
obtaining  an  exact  determination  of  the  refractive  index  (538)  of  each  colour  ; 
for  example,  the  refractive  index  of  the  blue  ray  is,  strictly  speaking,  that  of  the 
dark  line  F.  In  the  spectra  of  artificial  lights,  and  of  the  stars,  the  relative 
positions  of  the  dark  lines  are  changed.  In  the  electric  light  the  dark  lines 
are  replaced  by  brilliant  lines.  In  coloured  flames — that  is  to  say,  flames  in 
which  certain  chemical  substances  undergo  evaporation — the  dark  lines  are 
replaced  by  very  brilliant  lines  of  light,  which  differ  for  different  substances. 
Lastly,  some  of  the  dark  lines  are  constant  in  position  and  distinctness,  such 
as  Fraunhofer's  lines  ;  but  some  of  the  lines  only  appear  as  the  sun  nears  the 
horizon,  and  others  are  strengthened.  They  are  also  influenced  by  the  state 
of  the  atmosphere.  The  fixed  lines  are  due  to  the  sun  ;  the  variable  lines 
have  been  proved  by  Jannsen  and  Secchi  to  be  due  to  the  aqueous  vapour 
in  the  air,  and  are  called  atmospheric  or  telluric  lines. 

Fraunhofer  counted  in  the  spectrum  more  than  600  dark  lines,  more  or 
less  distinct,  distributed  irregularly  from  the  extreme  red  to  the  extreme 
violet  ray.  Brewster  counted  2,000.  By  causing  the  refracted  rays  to  pass 
successively  through  several  analysing  prisms,  not  merely  has  the  existence 
of  3,000  dark  lines  been  ascertained,  but  several  which  had  been  supposed 
to  be^single  have  been  shown  to  be  compound. 

If575.  Applications  of  Fraunhoter's  lines. — Subsequently  to  Fraunhofer,. 
several  physicists  studied  the  dark  lines  of  the  spectrum.  In  1822  Sir  J. 
Herschel  remarked  that  by  volatilising  substances  in  a  flame  a  very  delicate 
means  is  afforded  of  detecting  certain  ingredients  by  the  colours  they  impart 
to  certain  of  the  dark  lines  of  the  spectrum  ;  and  Fox  Talbot  in  1834  sug- 
gested optical  analysis  as  probably  the  most  delicate  means  of  detecting 
minute  portions  of  a  substance.  To  Kirchhoff  and  Bunsen,  however,  is  really 
due  the  merit  of  basing  on  the  observation  of  the  lines  of  the  spectrum  a 
method  of  analysis.  They  ascertained  that  the  salts  of  the  same  metal,  when 
introduced  into  a  flame,  always  produced  lines  identical  in  colour  and  position, 
but  different  in  colour,  position,  or  number  for  different  metals  ;  and  finally, 
that  an  exceedingly  small  quantity  of  a  metal  suffices  to  disclose  its  existence. 
Hence  has  arisen  a  new  and  powerful  method  of  analysis,  known  by  the 
name  of  spectrum  analysis. 

'  576.  Spectroscope. — The  name  of  spectroscope  has  been  given  to  the 
apparatus  employed  by  Kirchhoff  and  Bunsen  for  the  study  of  the  spectrum. 
One  of  the  forms  of  this  apparatus  is  represented  in  fig.  500.  It  is  composed 
of  three  telescopes  mounted  on  a  common  foot,  and  whose  axes  converge 
towards  a  prism,  P,  of  flint  glass.  The  telescope  A  is  the  only  one  which 
can  turn  round  the  prism.  It  is  fixed  in  any  required  position  by  a  clamping 
screw  n.  The  screw-head  m  is  used  to  focus  the  eyepiece.  The  screw- 
head  n  serves  to  change  the  inclination  of  the  axis. 

To  explain  the  use  of  the  telescopes  B  and  C  we  must  refer  to  fig.  501,, 
which  shows  the  passage  of  the  light  through  the  apparatus.  The  rays 
emitted  by  the  flame  G  fall  on  the  lens  a,  and  are  caused  to  converge  to  a 
point  £,  which  is  the  principal  focus  of  a  second  lens  c.  Consequently  the 
pencil,  on  leaving  the  telescope  B,  is  formed  of  parallel  rays  (552).  This  pencil 
enters  the  prism  P.  On  leaving  the  prism  the  light  is  decomposed,  and  in 
this  state  falls  on  the  lens  x.  By  this  lens  x  a  real  and  reversed  image  of 


-576] 


Spectroscope. 


525 


the  spectrum  is  formed  at  /.  This  image  is  seen  by  the  observer  through  a 
magnifying  glass,  which  forms  at  ss'  a  virtual  image  of  the  spectrum  magni- 
fied about  eight  times. 


Fig.  500. 

The  telescope  C  serves  to  measure  the  relative  distances  of  the  lines 
of  the  spectrum.  For  this  purpose  a  micrometer  is  placed  at  ;/&,  divided 
into  25  equal  parts.  The  micrometer  is  formed  thus  : — A  scale  of  250  milli- 


Fig.  501. 

metres  is  divided  with  great  exactness  into  25  equal  parts.  A  photographic 
negative  on  glass  of  this  scale  is  taken,  reduced  to  15  millimetres.  The 
negative  is  taken  because  then  the  scale  is  light  on  a  dark  ground.  The 


526 


On  Light. 


[576- 


Fig.  502. 


scale  is  then  placed  at  m  in  the  principal  focus  of  the  lens  e  ;  conse- 
quently, when  the  scale  is  lighted  by  the  candle  F,  the  rays  emitted  from  it 
leave  the  lens  e  in  parallel  pencils  ;  a  portion  of  these,  being  reflected  from 

a  face  of  the  prism,  passes  through  a 
lens  x,  and  forms  a  perfectly  distinct 
image  of  the  micrometer  at  z,  thereby 
furnishing  the  means  of  measuring 
exactly  the  relative  distances  of  the 
different  spectral  lines. 

The  micrometric  telescope  C  (fig. 
500)  is  furnished  with  several  adjusting 
screws,  /,  o,  r  ;  of  these,  i  adjusts  the 
focus  ;  o  displaces  the  micrometer  in 
the  direction  of  the  spectrum  laterally  : 
r  raises  or  lowers  the  micrometer, 
which  it  does  by  giving  different  incli- 
nations to  the  telescope. 
The  opening  whereby  the  light  of  the  flame  G  enters  the  telescope  B 
consists  of  a  narrow  vertical  slit,  which  can  be  opened  more  or  less  by 
causing  the  movable  piece  a  to  advance  or  recede  by  means  of  the  screw  v 
(fig.  502).  When,  for  purposes  of  comparison,  the  spectra  of  two  flames 
are  to  be  examined  simultaneously,  a  small  prism,  whose  refracting  angle 
is  60°,  is  placed  over  the  upper  part  of  the  slit.  Rays  from  one  of  the 
flames,  H,  fall  at  right  angles  on  one  face  of  the  prism  ;  they  then  experience 
total  reflection  on  a  second  face,  and  leave  the  prism  by  the  third  face,  and 
in  a  direction  at  right  angles  to  that  face.  By  this  means  they  pass  into  the 
telescope  in  a  direction  parallel  to  its  axis,  without  in  any  degree  mixing  with 
the  rays  which  proceed  from  the  second  flame,  G.  Consequently  the  two 
pencils  of  rays  traverse  the  prism  P  (fig.  501),  and  form  two  horizontal  spectra, 
which  are  viewed  simultaneously  through  the  telescope  A.  In  the  flames  G 
and  H  are  platinum  wires,  e,  e'.  These  wires  have  been  dipped  beforehand 
into  solutions  of  the  salts  of  the  metals  on  which  experiment  is  to  be  made  ; 
and  by  the  vaporisation  of  these  salts  the  metals  modify  the  transmitted 
light,  and  give  rise  to  definite  lines. 

Each  of  the  flames  G  and  H  is  a  jet  of  ordinary  gas.  The  apparatus 
through  which  the  gas  is  supplied  is  known  as  a  Bunseifs  burner.  The  gas 
conies  through  the  hollow  stem  k  (fig.  500).  At  the  lower  part  of  this  there 
is  a  lateral  orifice  which  admits  air  to  support  the  combustion  of  the  gas. 
This  orifice  can  be  more  or  less  closed  by  a  small  diaphragm,  which  acts  as 
a  regulator.  If  we  allow  a  moderate  amount  of  air  to  enter,  the  gas  burns 
with  a  luminous  flame,-  and  the  lines  are  obscured.  But  if  a  strong  and 
steady  current  of  air  enters,  the  carbon  is  rapidly  oxidised,  the  flame  loses  its 
brightness,  and  burns  with  a  pale  blue  light,  but  with  an  intense  heat.  In 
this  state  it  no  longer  yields  a  spectrum.  If,  however,  a  metallic  salt  is  in- 
troduced either  in  a  solid  state  or  in  a  state  of  solution,  the  spectrum  of  the 
metal  makes  its  appearance,  and  in  a  fit  state  for  observation. 

There  are  three  chief  types  of  spectra  :  the  continuous  spectra,  or 
those  furnished  by  ignited  solids  and  liquids  (fig.  I,  Plate  I.)  ;  the  band 
or  line  spectrum,  consisting  of  a  number  of  bright  lines,  and  produced  by 


-578]  Experiments  with  the  Spectroscope.  527 

ignited  gases  or  vapours  ;  and  absorption  spectra,  or  those  furnished  by  the 
sun  or  fixed  stars.  For  an  explanation  of  these  see  art.  579.  Bodies  at  a 
red  heat  give  only  a  short  spectrum,  extending  at  most  to  the  orange  ;  as 
the  temperature  gradually  rises,  yellow,  green,  blue,  and  violet  successively 
appear,  while  the  intensity  of  the  lower  colours  increases. 

Instead  of  the  prism  very  pure  spectra  may  also  be  obtained  by  means  of 
a  grating  (647).  For  more  detailed  investigations  of  the  spectral  lines  a  train 
of  prisms  is  used,  the  light  on  emerging  from  one  prism  passing  into  another. 
By  this  means  far  greater  dispersion  is  obtained,  though  at  the  same  time 
there  is  a  great  loss  of  light.  In  the  case  of  ten  prisms  it  has  been  found 
to  amount  to  ninety-nine  per  cent. 

Christie  has  used  with  advantage  a  semi-prism  obtained  by  cutting  an 
isosceles  prism  by  a  plane  at  right  angles  to  the  base.  These  semi-prisms 
have  the  advantage  that  they  produce  as  much  dispersion  as  with  several 
prisms  without  any  appreciable  loss  in  the  sharpness  of  the  images  ;  and 
without  that  absorption  of  light  which  in  the  case  of  a  number  of  prisms 
is  so  very  considerable. 

577.  Direct  vision  spectroscope. — Prisms  may  be  combined  so  as  to 
get  rid  of  the  dispersion  without  entirely  destroying  the  refraction  (584)  ; 
they  may,  conversely,  be  combined  so  that  the  light  is  not  refracted,  but  is 
decomposed  and  produces  a  spectrum.  Combinations  of  prisms  of  this  kind 
are  used  in  what  are  called  direct  vision  spectroscopes.  Fig.  503  represents 
the  section  of  such  an  instrument  in  about  f  the  natural  size.  A  system  of 
two  flint  and  three  crown-glass  prisms  is  placed  in  a  tube  which  moves  in 
a  second  one  ;  at  the  end  of  this  is  an  aperture  0,  and  inside  it  a  slit  the 
width  of  which  can  by  a  special  arrangement  be  regulated  by  simply  turning 
a  ring  r.  A  small  achromatic  lens  is  introduced  at  aa,  the  focus  of  which  is 
at  the  slit,  so  that  the  rays  pass  parallel  through  the  train  of  lenses,  and  the 
spectrum  is  viewed  at  e. 

The  reversion  spectroscope  contains  two  equal  systems  of  direct  vision 
prisms  arranged  close  to  each  other,  but  reversed,  so  that  two  spectra 
are  obtained  with  the 
colours  in  opposite 
order.  By  suitable 
micrometric  movement 
of  a  split  lens,  the  posi- 
tion of  the  two  spectra 
may  be  moved  apart  or  s'  5°3' 

nearer  each  other.  Hence  it  is  possible  to  bring  any  two  identical  lines  so 
that  they  are  in  the  same  vertical  line.  If  now  the  position  of  these  lines 
in  the  spectrum  is  altered,  the  displacement  will  take  place  in  the  opposite 
direction  in  the  two  spectra,  and  will  therefore  be  twice  as  distinct. 
N{  578.  Experiments  with  the  spectroscope. — The  coloured  plate  at  the 
beginning  shows  certain  spectra  observed  by  means  of  the  spectroscope. 
No.  i  represents  the  continuous  spectrum. 

No.  2  shows  the  spectrum  of  sodium.  The  spectrum  contains  neither 
red,  orange,  green,  blue,  nor  violet.  It  is  marked  by  a  very  brilliant  yellow 
ray  in  exactly  the  same  position  as  Fraunhofer's  dark  line  D.  Of  all  metals 
sodium  is  that  which  possesses  the  greatest  spectral  sensibility.  In  fact,  it 


528  On  Light.  [578- 

has  been  ascertained  that  one  two-hundred-millionth  of  a  grain  of  sodium 
is  enough  to  cause  the  appearance  of  the  yellow  line.  Consequently  it  is  very 
difficult  to  avoid  the  appearance  of  this  line.  A  very  little  dust  scattered  in 
the  apartment  is  enough  to  produce  it — a  circumstance  which  shows  how 
abundantly  sodium  is  distributed  throughout  nature. 

No.  3  is  the  spectrum  of  lithium.  It  is  characterised  by  a  well-marked 
line  in  the  red  called  Lia,  and  by  the  feebler  orange  line  Li/3. 

IS!  os.  4  and  5  show  the  spectra  of  ctzsutm  and  ritbiditim,  metals  discovered 
by  Bunsen  and  Kirchhoff  by  means  of  spectrum  analysis.  The  former  is 
distinguished  by  two  blue  lines,  Csa  and  Cs/3  ;  the  latter  by  two  very  brilliant 
dark  red  lines,  Rby  and  Rb§,  and  by  two  less  intense  violet  lines,  Rba  and 
Rb/3.  A  third  metal,  thallium,  has  been  discovered  by  the  same  method 
by  Mr.  Crookes  in  England,  and  independently  by  M.  Lamy  in  France. 
Thallium  is  characterised  by  a  single  green  line.  Subsequently  to  this 
Richter  and  Reich  discovered  a  new  metal  associated  with  zinc,  and  which 
they  call  indium  from  a  couple  of  characteristic  lines  which  it  forms  in  the 
indigo  ;  and  quite  recently  Boisbaudran  has  discovered  a  new  metal  which 
he  calls  gallium  existing  in  zinc  in  very  minute  quantities. 

The  extreme  delicacy  of  the  spectrum  reactions,  and  the  ease  with  which 
they  are  produced,  constitute  them  a  most  valuable  help  in  the  qualitative 
analysis  of  the  alkalies  and  alkaline  earths.  It  is  sufficient  to  place  a  small 
portion  of  the  substance  under  examination  on  platinum  wire  as  represented 
in  fig.  502,  and  compare  the  spectrum  thus  obtained  either  directly  with  that 
of  another  substance  or  with  the  charts  in  which  the  positions  of  the  lines 
produced  by  the  various  metals  are  laid  down. 

With  other  metals  the  production  of  their  spectra  is  more  difficult,  es- 
pecially in  the  case  of  some  of  their  compounds.  The  heat  of  a  Bunsen's 
burner  is  insufficient  to  vaporise  the  metals,  and  a  more  intense  temperature 
must  be  used.  This  is  effected  by  taking  electric  sparks  between  wires  con- 
sisting of  the  metal  whose  spectrum  is  required,  and  the  electric  sparks  are 
most  conveniently  obtained  by  means  of  Ruhmkorff's  coil  or  inductorium. 
Thus  all  the  metals  may  be  brought  within  the  sphere  of  spectrum  obser- 
vations. 

The  power  of  the  apparatus  has  great  influence  on  the  nature  of  the 
spectrum  ;  while  an  apparatus  with  one  prism  only  gives  in  a  sodium  flame 
the  well-known  yellow  line,  an  apparatus  with  more  prisms  resolves  it  into 
two  or  three  lines. 

It  has  been  observed  that  the  character  of  the  spectrum  changes  with  the 
temperature  ;  thus  chloride  of  lithium  in  the  flame  of  a  Bunsen's  burner  gives 
a  single  intense  peach-coloured  line  ;  in  a  hotter  flame,  as  that  of  hydrogen, 
it  gives  an  additional  orange  line  ;  while  in  the  oxyhydrogen  jet  or  the 
voltaic  arc  a  broad  brilliant  blue  band  comes  out  in  addition.  The  sodium 
spectrum  produced  by  a  Bunsen's  burner  consists  of  a  single  yellow  line  ; 
if,  by  the  addition  of  oxygen,  the  heat  be  gradually  increased,  more  bright 
lines  appear ;  and  with  the  aid  of  the  oxyhydrogen  flame  the  spectrum  is 
continuous.  Sometimes  also,  in  addition  to  the  appearance  of  new  lines,  an 
increase  in  temperature  resolves  those  bands  which  exist  into  a  number  of 
fine  lines,  which  in  some  cases  are  more  and  in  some  less  refrangible  than  the 
bands  from  which  they  are  formed.  It  may  be  supposed  that  the  glowing 


-579]    Explanation  of  the  Dark  Lines  of  the  Solar  Spectrum.    529 

vapour  found  at  the  low  temperature  consists  of  the  oxide  of  some  difficultly 
reducible  metal,  whereas  at  the  enormously  high  temperature  of  the  spark 
these  compounds  are  decomposed,  and  the  true  bright  lines  of  the  metal  are 
formed. 

The  delicacy  of  the  reaction  increases  very  considerably  with  the  tem- 
perature. With  the  exception  of  the  alkalies,  it  is  from  40  to  400  times 
greater  at  the  temperature  of  the  electric  spark  than  at  that  of  Bunsen's 
burner. 

The  spectra  of  the  permanent  gases  are  best  obtained  by  taking  the 
electric  spark  of  a  RuhmkorfFs  coil,  or  Holtz's  apparatus,  through  glass 
tubes  of  a  special  construction,  provided  with  electrodes  of  platinum  and 
filled  with  the  gas  in  question  in  a  state  of  great  attenuation,  known  as 
Geissler's  tubes  ;  if  the  spark  be  passed  through  hydrogen,  the  light  emitted 
is  bright  red,  and  its  spectrum  consists  of  one  bright  red,  one  green,  and  one 
blue  line  No.  7,  the  first  two  of  which  appear  to  coincide  with  Fraunhofer's 
lines  C  and  F,  and  the  third  with  a  line  between  F  and  G.  No.  6  repre- 
sents the  spectrum  of  oxygen.  No.  8  is  the  spectrum  of  nitrogen.  The 
light  of  this  gas  in  a  Geissler's  tube  is  purple,  and  the  spectrum  very  com- 
plicated. 

If  the  electric  discharge  takes  place  through  a  compound  gas  or  vapour, 
the  spectra  are  those  of  the  elementary  constituents  of  the  gas.  It  seems  as 
if,  at  very  intense  temperatures,  chemical  combination  were  impossible,  and 
oxygen  and  hydrogen,  chlorine  and  the  metals,  could  coexist  in  a  separate 
form,  as  though  mechanically  mixed  with  each  other. 

The  nature  of  the  spectra  of  the  elementary  gases  is  very  materially  in- 
fluenced by  alterations  of  temperature  and  pressure.  Wiilmer  made  a  series 
of  very  accurate  observations  on  the  gases  oxygen,  hydrogen,  and  nitrogen. 
He  not  only  used  gases  in  closed  tubes,  which  by  various  electrical  means 
he  raised  to  different  temperatures  ;  but  in  one  and  the  same  series  of  ex- 
periments, in  which  a  small  inductorium  was  used,  he  employed  pressures 
varying  from  100  millimetres  to  a  fraction  of  a  millimetre  ;  while  in  another 
series  in  which  a  larger  apparatus  was  used,  he  extended  the  pressure  to 
2,000  millimetres.  At  the  lowest  pressure  of  less  than  one  millimetre,  the 
spectrum  of  hydrogen  was  found  to  be  green,  and  consisting  of  six  splendid 
groups  of  lines,  which  at  a  higher  pressure  than  I  millimetre  changed  to  con- 
tinuous bands  ;  at  2  to  3  millimetres  the  spectrum  consisted  of  the  often- 
mentioned  three  lines,  which  did  not  disappear  under  a  higher  pressure,  but 
gradually  became  less  brilliant  as  the  continuous  spectrum  increased  in 
extent  and  lustre.  From  this  point  the  light,  and  therefore  the  spectrum, 
became  feebler.  Using  the  larger  apparatus,  the  band  spectrum  appeared 
only  under  a  higher  pressure  ;  at  the  highest  pressure  of  2,000  millimetres  it 
gave  place  to  the  continuous  spectrum,  since  the  bright  lines  continually 
extended  and  ultimately  merged  into  each  other. 

X  579-  Explanation  of  the  dark  lines  of  the  solar  spectrum. — It  has 
been  already  seen  that  incandescent  sodium  vapour  gives  a  bright  yellow 
line  corresponding  to  the  dark  line  D  of  the  solar  spectrum.  Kirchhoff 
found  that,  when  the  brilliant  light  produced  by  incandescent  lime  passes 
through  a  flame  coloured  by  sodium  in  the  usual  manner,  a  spectrum  is  pro- 
duced in  which  is  a  dark  line  coinciding  with  the  dark  line  D  of  the  solar 

M  M 


530 


On  Light. 


[579- 


spectrum  ;  what  would  have  been  a  bright  yellow  line  becomes  a  dark  line 
when  formed  on  the  background  of  the  limelight.  By  allowing  in  a  similar 
manner  the  limelight  to  traverse  vapours  of  potassium,  barium,  strontium, 
&c.,  the  bright  lines  which  they  would  have  formed  were  found  to  be  con- 
verted into  dark  lines  :  such  spectra  are  called  absorption  spectra. 

It  appears,  then,  that  the  vapour  of  sodium  has  the  power  of  absorbing 
rays  of  the  same  refrangibility  as  that  which  it  emits.  And  the  same  is  true 
of  the  vapours  of  potassium,  barium,  strontium,  &c.  This  absorptive  power 
is  by  no  means  an  isolated  phenomenon.  These  substances  share  it,  for  ex- 
ample, with  the  vapour  of  nitrous  acid,  which  Brewster  found  to  possess  the 
following  property  : — when  a  tube  filled  with  this  vapour  is  placed  in  the  path 
of  the  light  either  of  the  sun  or  of  a  gas  flame,  and  the  light  is  subsequently 
decomposed  by  a  prism,  a  spectrum  is  produced  which  is  full  of  dark  lines 
(No.  9,  Plate  I.)  ;  and  Miller  showed  that  iodine  and  bromine  vapour  pro- 
duced analogous  effects. 

Hence  the  origin  of  the  above  phenomenon  is,  doubtless,  the  absorption 
by  the  sodium  vapour  of  rays  of  the  same  kind — that  is,  having  the  same 

refrangibility — as  those  which  it  has  itself 
the  power  of  emitting.  Other  rays  it  allows  to 
pass  unchanged,  but  these  it  either  totally  or 
in  great  part  suppresses.  Thus  the  parti- 
cular lines  in  the  spectrum  to  which  these 
rays  would  converge  are  illuminated  only  by 
the  feebly  luminous  sodium  flame,  and  ac- 
cordingly appear  dark  by  contrast  with  the 
other  portions  of  the  spectrum  which  receive 
light  from  the  powerful  flame  behind. 

By  replacing  one  of  the  flames  G  and  H 
(fig.  502)  by  a  ray  of  solar  light  reflected 
from  a  heliostat,  Kirchhofif  ascertained  by 
direct  comparison  that  the  bright  lines  which 
characterise  iron  correspond  to  dark  lines  in 
the  solar  spectrum.  He  also  found  the  same 
to  be  the  case  with  sodium,  magnesium, 
calcium,  nickel,  and  some  other  metals. 

This  reversal  of  the  sodium  light  may  be 
produced  even  without  a  prism  by  an  appa- 
ratus devised  by  Bunsen,  and  shown  in  fig. 
504.  It  consists  of  a  Woolf  s  bottle  in  which 
a  small  quantity  of  zinc,  dilute  sulphuric  acid, 
and  common  salt  are  placed  so  that  hydrogen 
is  slowly  liberated,  charged  with  particles  of 
sodium  chloride.  Through 'the  india-rubber 
tube  L  ordinary  coal  gas  is  admitted,  and 
issues  through  the  tubes  R  and  R'.  On  each 
of  these  tubes  is  a  metal  burner.  The  gas 
burns  at  the  top  A  with  a  broad  flat  flame,  C  ;  the  burner  B  is  cylindrical, 
and  over  it  is  placed  a  conical  mantle  closed  at  the  top  with  wire  gauze. 
In  this  way  a  small  yellow  flame  is  produced.  On  looking  through  this  against 


Fig.   504. 


579]     Explanation  of  the  Dark  Lines  of  the  Solar  Spectrum.     5  3 1 

the  wide  flame,  the  former  appears  dark,  as  if  smoky  on  a  light  back- 
ground. The  light  of  the  posterior  and  far  brighter  flame  is  absorbed  by 
the  front  and  cooler  one,  and  replaced  by  light  of  lesser  intensity,  which 
thus  appears  dark  by  contrast. 

From  such  observations  we  may  draw  important  conclusions  with  re- 
spect to  the  constitution  of  the  sun.  Since  the  solar  spectrum  has  dark 
lines  where  sodium,  iron,  &c.,  give  bright  ones  (No.  u,  Plate  I.),  it  is  pro- 
bable that  around  the  solid,  or  more  probably  liquid,  body  of  the  sun  which 
throws  out  the  light,  there  exists  a  vaporous  envelope  which,  like  the  sodium 
flame  in  the  experiment  described  above,  absorbs  certain  rays  ;  namely, 
those  which  the  envelope  itself  emits.  Hence  those  parts  of  the  spectrum 
which,  but  for  this  absorption,  would  have  been  illuminated  by  these  particular 
rays,  appear  feebly  luminous  in  comparison  with  the  other  parts,  since  they 
are  illuminated  only  by  the  light  emitted  by  the  envelope,  and  not  by 
the  solar  nucleus  ;  and  we  are  at  the  same  time  led  to  conclude  that  ,in  this 
vapour  there  exist  the  metals  sodium,  iron,  &c. 

Huggins  and  Miller  applied  spectrum  analysis  to  the  investigation  of  the 
heavenly  bodies.  The  spectra  of  the  moon  and  planets,  whose  light  is  re- 
flected from  the  sun,  give  the  same  lines  as  those  of  the  sun.  Uranus  proves 
an  exception  to  this,  and  is  probably  still  in  a  self-luminous  condition.  The 
spectra  of  the  fixed  stars  contain,  however,  dark  lines  differing  from  the  solar 
lines,  and  from  one  another.  Four  distinct  types  of  spectra  were  distinguished 
by  Secchi.  The  first  embraces  the  white  stars,  and  includes  the  well-known 
Sirius  and  a  Lyrse.  Their  spectra  (No  12,  Plate  I.)  usually  contain  a  number 
of  very  fine  lines,  and  always  contain  four  broad  dark  lines  which  coincide 
with  the  bright  lines  of  hydrogen.  Out  of  346  stars  164  were  found  to  belong 
to  this  group.  The  second  group  embraces  those  having  spectra  intersected 
by  numerous  fine  lines  like  those  of  our  sun.  About  140  stars,  among  them 
Pollux,  Capella,  </>  Aquilas,  belong  to  this  group.  The  third  group  embraces 
the  red  and  orange  stars,  such  as  a  Orionis,  /3  Pegasi  ;  the  spectra  of  these 
(Nos.  13,  14,  Plate  I.)  are  divided  into  eight  or  ten  parallel  columnar  clusters 
of  dark  and  bright  bands  increasing  in  intensity  to  the  red.  Group  four  is 
made  up  of  small  red  stars  with  spectra,  and  is  constructed  of  three  bright 
zones  increasing  in  intensity  towards  the  violet.  It  would  thus  appear  that 
these  fixed  stars,  while  differing  from  one  another  in  the  matter  of  which 
they  are  composed,  are  constructed  on  the  same  general  plan  as  our  sun. 
Huggins  has  observed  a  striking  difference  in  the  spectra  of  the  nebulas ; 
where  they  can  at  all  be  observed  they  are  found  to  consist  generally  of 
bright  lines,  like  the  spectra  of  the  ignited  gases,  instead  of,  like  the  spectra 
of  the  sun  and  stars,  consisting  of  a  bright  ground  intersected  by  dark  lines. 
It  is  hence  probable  that  the  nebulas  are  masses  of  glowing  gas,  and  do  not 
consist,  like  the  sun  and  stars,  of  a  photosphere  surrounded  by  a., gaseous 
atmosphere. 

We  can  apply  the  reasoning  of  Doppler's  principle  (233)  to  .the  case  of 
light,  and  assume  provisionally  that  the  motion  of  light  is  analogous  to  that 
of  sound.  When  a  source  of  light  is  approaching  the  earth,  the  eye  receives 
a  greater  number  of  waves  in  a  given  time,  the  waves  are  shorter  ;  as  it 
moves  away  the  opposite  is  the  case,  the  waves  are  longer.  Hence,  on  the 
approach  of  yellow  light,  for  instance,  the  bright  band  D  will  seem  displaced 

M  M  2 


532  On  Light.  [579- 

towards  the  violet  end  of  the  spectrum,  and  in  receding,  towards  the  red 
end.  This  will  also  be  the  case  with  the  corresponding  dark  line,  proving 
that  the  whole  medium  is  moved  at  the  same  time.  Accordingly,  by  observ- 
ing the  displacement  of  particular  lines,  conclusions  may  be  drawn  as  to  the 
relative  motions  of  what  are  called  the  fixed  stars.  Thus,  from  careful  ob- 
servation of  the  displacement  of  the  F  line  in  Sirius,  Huggins  has  inferred 
that  it  is  moving  away  from  the  earth  with  a  velocity  of  42  miles  per  second. 
One  of  the  most  interesting  triumphs  of  spectrum  analysis  has  been  the 
discovery  of  the  true  nature  of  the  protuberances,  which  appear  during  a 
solar  eclipse  as  mountains  or  cloud-shaped  luminous  objects  varying  in  size, 
and  surrounding  the  moon's  disc. 

During  the  eclipse  of  1868  it  had  been  ascertained  by  Jannsen  that  pro- 
tuberances emitted  certain  bright  lines  coinciding  with  those  of  hydrogen. 
They  have,  however,  been  fully  understood  only  since  Lockyer  and  Jannsen 
have  discovered  a  method  of  investigating  them  at  any  time.     The  principle 
of  this  method  is  as  follows  : — When  a  line  of  light  admitted  through  a  slit 
is  decomposed  by  a  prism  the  length  of  the  spectrum  may  be  increased  by 
passing  it  through  two  or  more  prisms  ;  as  the  quantity  of  light  is  the  same, 
it  is  clear  that  the  intensity  of  the  spectrum  will  be  diminished.     This  is  the 
case  with  the  ordinary  sources  of  light,  such  as  the  sun ;    if  the  light  be 
homogeneous,  it  will  be  merely  deviated,  and  not  reduced  in  intensity,  by 
dispersion.     And  if  the  source  of  light  emit  light  of  both  kinds,  the  image 
of  the  slit  of  light  of  a  definite  refrangibility,  which  the  mixture  may  contain, 
will  stand  out,  by  its  superior  intensity,  on  the  weaker  ground  of  the  con- 
tinuous spectrum.     This  is  the  case  with  the  spectrum  of  the  protuberances. 
Viewed  through  an  ordinary  spectroscope,  the  light  they  emit  is  overshadowed 
by  that  of  the  sun  ;  but  by  using  prisms  of  great  dispersive  power  the  sun's 
light  becomes  weakened,  and  the  spectrum  of  the  protuberances  may  be 
observed.     Lockyer's  researches  leave  no  doubt  that  they  are  ignited  gas 
masses,  principally  of  hydrogen.     By  altering  the  position  of  the  slit  a  series 
of  sections  of  the  prominences  is  obtained,  by  collating  which  the  form  of 
the  prominence  may  be  inferred.     They  are  thus  found  to  enclose  the  sun 
usually  to  a  depth  of  about  5,000  miles,  but  sometimes  in  enormous  local 
accumulations,  which  reach  the  height  of  70,000  miles.     Lockyer  has  not 
merely  examined  these  phenomena  right  on  the  edge  of  the  sun  ;  but  he  has 
been  able  to  observe  them  on  the  disc  itself.     He  has  shown  that  some  of 
these  protuberances  are  the  results  of  sudden  outbursts  or  storms,  which 
move  with  the  enormous  velocity  of  120  miles  in  a  second  ;  and,  by  reasoning 
as  above,  the  direction  of  this  motion  has  been  determined. 

For  a  fuller  account  of  this  branch  of  physics,  which  is  incompatible  with 
the  limits  of  this  work,  the  reader  is  referred  to  Sir  H.  Roscoe's  'Lectures  on 
Spectrum  Analysis,'  and  to  the  same  writer's  articles,  and  those  of  Schuster, 
in  Watts's  '  Dictionary  of  Chemistry,'  or  to  Schellen's  *  Spectrum  Analysis,* 
translated  by  Lassell,  or  to  Lockyer  (  On  the  Spectroscope.' 

580.  Uses  of  the  spectroscope. — When  a  liquid  placed  in  a  glass  tube 
or  in  a  suitable  glass  cell  is  interposed  between  a  source  of  light  and  the 
slit  of  the  spectroscope,  the  spectrum  observed  on  looking  through  the 
telescope  will  in  many  cases  be  found  to  be  traversed  by  dark  bands. 
No.  10,  Plate  I.,  represents  the  appearance  of  the  spectrum  when  a  solution 


—581]  Abnormal  Dispersion.  533 

>of  chlorophyl^  the  green  colouring  matter  of  plants,  is  thus  interposed. 
In  the  red,  the  yellow,  and  the  violet  parts,  dark  bands  are  formed,  and  the 
blue  gives  way  to  a  reddish  shimmer.  If,  instead  of  chlorophyl,  arterial 
blood  greatly  diluted  be  used,  the  red  of  the  spectrum  appears  brighter,  but 
green  and  violet  are  nearly  extinguished.  As  these  bands  thus  differ  in 
different  liquids  as  regards  position,  breadth,  and  intensity,  in  many  cases 
they  afford  the  most  suitable  means  of  identifying  bodies.  Sorby  and 
Browning  have  devised  a  combination  of  the  microscope  and  spectroscope 
called  the  microspectroscope,  which  renders  it  possible  to  examine  even  very 
minute  traces  of  substances. 

This  application  of  the  spectroscope  has  been  very  useful  in  investigating 
substances  which  have  special  importance  in  physiology  and  pathology ; 
thus  in  examining  normal  and  diseased  blood,  and  in  ascertaining  the  rate 
.at  which  certain  substances  pass  into  the  various  fluids  of  the  system.  The 
characteristic  absorption  bands  with  certain  liquids,  such  as  wine,  beer,  &c., 
present  in  their  normal  state,  compared  with  those  yielded  by  adulterated 
substances,  furnish  a  delicate  and  certain  means  of  detecting  the  latter. 

Thus  the  adulteration  of  claret  with  the  juice  of  elderberries  is  detected 
by  the  appearance  of  faint  bands  near  line  D,  which  are  not  seen  with  pure 
red  wine.  The  colouring  matter  of  malt  and  hops  is  quite  distinct  from 
that  of  many  other  substances  with  which  it  is  alleged  to  be  adulterated. 
An  alkaline  solution  of  blood  to  which  ammonium  sulphide  is  added,  gives 
two  very  powerful  absorption  bands  between  D  and  E,  and  between  E  and 
b  ;  this  is  the  most  valuable  test  for  toxicological  cases.  Blood  charged 
with  carbonic  oxide  is  unchanged  on  the  addition  of  ammonium  sulphide, 
and  thus  the  poisoning  by  carbonic  oxide  can  be  detected.  So,  too,  the 
appearance  of  the  characteristic  bands  of  gall  in  blood,  and  of  albumen  in 
urine,  are  indications  of  jaundice  and  of  B  right's  disease  respectively. 

Suppose  the  slit  of  the  spectroscope  be  divided  into  two  halves,  S,,  and  S2 
(fig.  505),  the  aperture  of  each  of  which  can  be  varied  to  any  measured  extent 
by  means  of  micrometric  screws.   If  then  a  layer  of  a  substance  of  known  thick- 
ness be  placed  in  front  of  the  slit  S15  for  instance, 
and  the  spectrum  of  a  particular  portion  be  observed, 
there  will  be  a  difference  between  the  luminosity 
of  the  two  parts  of  the  spectrum  ;  but  by  regulating 
the  width  of  the  slit  they  may  be  made  the  same. 
The  luminosities  will  then  be  inversely  as  the  width 
of  the  slit.     Thus,  if  the  widths  of  each  were  origi- 
nally i,  and  the  uncovered  slit  had  to  be  narrowed 
to  0-4,  the  intensity  of  the  light  transmitted  through 

the  screen  would  only  be  0*4  of  the  incident.  Vierordt  has  based  on 
this  a  method  of  quantitative  spectrum  analysis ;  thus,  if  the  absorption 
produced  by  a  definite  thickness  of  known  strength  be  known,  the  relative 
concentration  of  any  other  solution  of  the  same  substance  for  the  same  thick- 
ness may  be  determined. 

r""58l.  Abnormal  dispersion. — A  remarkable  exception  to  the  ordinary 
law  of  dispersion  was  discovered  by  Christiansen,  and  subsequently  confirmed 
and  extended  by  Soret  and  Kundt — that  the  solutions  of  certain  substances, 
such  as  indigo  and  permanganate  of  potassium,  give  spectra  in  which  the 


534  On  Light.  [581- 

order  of  tfye  colours  is  not  the  same  as  in  the  prismatic  spectrum.  Thus,  when 
a  hollow  glass  prism  is  filled  with  an  alcoholic  solution  of  fuchsine,  the  order 
of  the  colours  in  the  spectrum  which  it  yields  is  as  follows.  Violet  is  least 
refracted,  then  red,  and  then  yellow,  which  is  most  refracted.  If  we  imagine 
that  the  central  green  of  an  ordinary  spectrum  is  removed,  and  then  the 
position  of  the  rest  is  interchanged,  we  get  an  idea  of  the  abnormal  spectrum 
of  fuchsine.  Kundt  examined  a  great  number  of  substances  in  this  direc- 
tion, mostly  the  colours  derived  from  aniline,  and  found  that  the  abnormal 
dispersion  is  exhibited  by  all  substances  with  surface  colour.  These  bodies 
have  the  peculiarity  that  when  viewed  in  diffused  light  they  exhibit  a 
different  colour  from  that  which  they  transmit.  Thus  a  thin  flake  of  fuchsine 
appears  green  in  diffused,  but  red  in  transmitted  light. 

The  substances  in  solution  are  examined  by  placing  them  in  hollow  glass 
prisms  ;  if  the  solutions  are  weak,  the  abnormal  dispersion  of  the  substance 
is  concealed  by  that  of  the  solvent,  while  stronger  solutions  absorb  so  much 
light  as  to  be  almost  opaque,  and  prisms  of  very  small  refracting  angle  have 
to  be  used.  Soret  gets  rid  of  this  difficulty  by  immersing  the  prism  contain- 
ing the  solution  in  glass  vessels  with  parallel  sides  filled  with  the  solvent. 
The  dispersion  due  to  the  solvent  is  thereby  eliminated,  and  only  that  of  the 
substance  comes  into  play.  Cyanine  gives  a  well-marked  abnormal  spec- 
trum, the  order  of  the  colours  being  the  following  :  green,  light  blue,  dark 
blue,  a  dark  space,  red,  and  traces  of  orange,  the  green  being  the  colour  which 
is  least  diffused. 

The  same  explanation  cannot  be  given  of  this  as  of  the  ordinary  colour 
of  bodies  (569),  but  must  be  ascribed  to  the  fact  that  the  bodies  in  question 
totally  reflect  light  of  certain  wave-lengths  (637)  at  almost  all  incidences, 
and  that  these  colours  are  reflected  on  the  surface.  Hence  it  follows  that 
the  colour  of  these  bodies  in  diffused  light  must  be  almost  complementary 
to  the  transmitted  light— a  prevision  which  experiment  confirms. 

582.  Fluorescence. — Stokes  made  the  remarkable  discovery  that  under 
certain  circumstances  the  rays  of  light  are  capable  of  undergoing  a  change 
of  refrangibility.  The  discovery  originated  in  the  study  of  a  phenomenon 
observed  by  Sir  J.  Herschel,  that  certain  solutions  when  looked  at  by  trans- 
mitted light  appear  colourless,  but  when  viewed  in  reflected  light  present  a 
bluish  appearance.  Stokes  has  found  that  this  property,  which  he  calls 
fluorescence,  is  characteristic  of  a  large  class  of  bodies. 

The  phenomenon  is  best  seen  when  a  solution  of  sulphate  of  quinine 
contained  in  a  trough  with  parallel  sides,  is  placed  in  different  positions  in 
the  solar  spectrum.  No  change  is  observed  in  the  upper  part  of  the  spec- 
trum, but  from  about  the  middle  of  the  lines  G  and  H  (coloured  Plate)  to 
!some  distance  beyond  the  extreme  range  of  the  violet,  rays  of  a  beautiful 
sky-blue  colour  are  seen  to  proceed.  These  invisible  ultra-violet  rays  also 
become  visible  when  the  spectrum  is  allowed  to  fall  on  paper  impregnated 
with  a  solution  of  czscitUne  (a  substance  extracted  from  horse-chestnut),  an 
alcoholic  solution  of  stramonium,  or  a  plate  of  canary  glass  (which  is  coloured 
by  means  of  uranium).  This  change  arises  from  a  diminution  in  the  re- 
frangibility of  those  rays  outside  the  violet,  which  are  ordinarily  too  refran- 
'gible  to  affect  the  eye. 

Glass  appears  to  absorb  many  of  these  more  refrangible  rays,  which  is 


-583J  CJiromatic  Aberration.  535 

not  the  case  nearly  to  the  same  extent  with  quartz.'  When  a  prism  and 
trough  formed  of  plates  of  quartz  are  used,  and  the  spectrum  is  received 
on  a  sheet  of  paper  on  which  a  wash  of  solution  of  sulphate  of  quinine  has 
been  made,  two  juxtaposed  spectra  can  be  obtained.  That  which  is  on  the 
part  coated  with  sulphate  of  quinine  extends  beyond  the  line  H  to  an  extent 
equal  to  that  of  the  visible  spectrum.  In  the  spectrum,  thus  made  visible, 
dark  lines  may  be  seen  like  those  in  the  ordinary  spectrum. 

The  phenomena  may  be  observed  without  the  use  of  a  prism.  When  an 
aperture  in  a  dark  room  is  closed  by  means  of  a  piece  of  blue  glass,  and  the 
light  is  allowed  to  fall  upon  a  piece  of  canary  glass,  it  instantly  appears  self- 
luminous  from  the  emission  of  the  altered  rays.  If  a  test-tube  be  half-filled 
with  a  solution  of  sulphate  of  quinine,  and  on  it  be  poured  an  ethereal  solu- 
tion of  chlorophyl,  the  respective  layers  appear  colourless,  and  green  in 
transmitted,  and  sky-blue  and  blood-red  in  reflected  light. 

In  most  cases  it  is  the  violet  and  ultra-violet  rays  which  undergo  an 
alteration  of  refrangibility,  but  the  phenomenon  is  not  confined  to  them.  A 
decoction  of  madder  in  alum  gives  yellow  and  violet  light  from  about  the 
line  D  to  beyond  the  violet  ;  an  alcoholic  solution  of  chlorophyl  gives  red 
light  from  the  line  B  to  the  limit  of  the  spectrum.  In  these  cases  the  yellow, 
the  green,  and  the  blue  rays  experience  diminution  of  refrangibility  ;  the 
change  produces  more  highly  refrangible  rays.  An  exception  to  this  rule 
is  met  with  in  the  case  of  Magdala  red.  If  on  a  solution  of  this  substance 
contained  in  a  rectangular  glass  vessel  a  solar  spectrum  be  allowed  to  fall, 
an  orange-yellow  fluorescence  is  found  even  in  the  red  part  of  the  spectrum. 

The  electric  light  gives  a  very  remarkable  spectrum.  With  quartz  ap- 
paratus Stokes  obtained  a  spectrum  six  or  eight  times  as  long  as  the  ordinary 
one.  Several  flames  of  no  great  illuminating  power  emit  very  peculiar 
light.  Characters  traced  on  paper  with  solution  of  stramonium,  which  are 
almost  invisible  in  daylight,  appear  instantaneously  when  illuminated  by  the 
flame  of  burning  sulphur  or  of  bisulphide  of  carbon.  Robinson  has  found 
that  the  light  of  the  aurora  is  peculiarly  rich  in  rays  of  high  refrangibility. 

583.  Chromatic  aberration. — The  various  lenses  hitherto  described 
(551)  possess  the  inconvenience  that,  when  at  a  certain  distance  from  the 
eye,  they  give  images  with  coloured  edges.  This  defect,  which  is  most 
observable  in  condensing  lenses,  is  due  to  the  unequal  refrangibility  of  the 
simple  colours  (564),  and  is  called  chromatic  aberration. 

For,  since  a  lens  may  be  compared  to  a  series  of  prisms  with  infinitely 
small  faces,  and  united  at  their  bases  (551),  it  not  only  refracts  light,  but  also 
decomposes  it  like  a  prism.  On 
account  of  this  dispersion,  there- 
fore, lenses  have  really  a  dis- 
tinct focus  for  each  colour.  In 
condensing  lenses,  for  example, 
the  red  rays,  which  are  the  least 
refrangible,  form  their  focus  at 
a  point  R  on  the  axis  of  the 
lens  (fig.  506)  ;  while  the  violet 
rays,  which  are  most  refrangible, 
coincide  in  the  nearer  point  V.  The  foci  of  the  orange,  yellow,  green,  blue, 


536  On  Light.  [583- 

and  indigo  are  between  these  points.  The  chromatic  aberration  is  more 
perceptible  in  proportion  as  the  lenses  are  more  convex,  and  as  the  point 
at  which  the  rays  are  incident  is  farther  from  the  axis  ;  for  then  the  deviation, 
and  therefore  the  dispersion,  are  increased. 

If  a  pencil  of  rays  which  has  passed  through  a  condensing  lens  be  re- 
ceived on  a  screen  placed  at  mm  within  the  focal  distance,  a  bright  spot  is 
seen  with  a  red  border ;  if  it  is  placed  at  ss  the  bright  spot  has  a  violet 
border. 

The  inequality  in  the  refraction  of  the  blue  and  red  rays  may  be  demon- 
strated by  closing  a  small  aperture,  half  with  red  and  half 
with  blue  glass  (fig.  507)  ;  on  each  half  a  black  arrow  is 
painted,  and  a  lamp  is  placed  behind  it.  By  means  of  a 
lens  of  60  cm.  focus  an  image  is  formed  on  a  screen  at  a 
distance  of  about  2  metres.  If  the  screen  be  placed  so 
that  a  sharp  image  is  obtained  of  the  black  object  on  the 
blue  ground,  the  outlines  of  the  other  are  confused.  To 
get  a  sharp  image  of  the  arrow  on  the  red  ground  the 
screen  must  be  moved  farther  away. 

584.  Achromatism. — By  combining  prisms  which  have  different  refracting 
angles  (544),  and  are  formed  of  substances  of  unequal  dispersive  powers  (564), 
white  light  may  be  refracted  without  being  dispersed.  The  same  result  is 
obtained  by  combining  lenses  of  different  substances,  the  curvatures  of  which 
are  suitably  combined.  The  images  of  objects  viewed  through  such  lenses  do 
not  appear  coloured,  and  they  are  accordingly  called  achromatic  lenses  ; 
achromatism  being  the  term  applied  to  the  phenomenon  of  the  refraction 
of  light  without  decomposition. 

By  observing  the  phenomenon  of  the  dispersion  of  colours  in  prisms  of 
water,  of  oil  of  turpentine,  and  of  crown  glass,  Newton  was  led  to  suppose 
that  dispersion  was  proportional  to  refraction.  He  concluded  that  there 
could  be  no  refraction  without  dispersion,  and,  therefore,  that  achromatism 
was  impossible.  Almost  half  a  century  elapsed  before  this  was  found  to  be 
incorrect.  Hall,  an  English  philosopher,  in  1733,  was  the  first  to  construct 
achromatic  lenses,  but  he  did  not  publish  his  discovery.  It  is  to  Dollond, 
an  optician  in  London,  that  we  owe  the  greatest  improvement  which  has 
been  made  in  optical  instruments.  He  showed  in  1757  that  by  combining 
two  lenses — one  a  double  convex  crown  glass  lens,  the  other  a  concavo- 

convex  lens  of  flint   glass  (fig.  509)— a  lens  is  * 

obtained  which  is  virtually  achromatic. 

To  explain  this  result,  let  two  prisms,  BFC 
and  CDF,  be  joined  and  turned  in  a  contrary 
direction,  as  shown  in  fig.  508.  Let  us  suppose  in 
the  first  case,  that  both  prisms  are  of  the  same 
material,  but  that  the  refracting  angle  of  the 
second,  CDF,  is  less  than  the  refracting  angle 
of  the  first ;  the  two  prisms  will  produce  the 
same  effect  as  a  single  prism,  BAF  ;  that  is  to 

say,  that  white  light  which  traverses  it  will  not  only  be  refracted,  but  also 
decomposed.  If,  on  the  contrary,  the  first  prism  BCF  were  of  crown  glass, 
and  the  other  CFD  of  flint  glass,  the  dispersion  might  be  destroyed  without 


-584]  Achromatism.  537 

destroying  the  refraction.  For,  as  flint  glass  is  more  dispersive  than  crown, 
and  as  the  dispersion  produced  by  a  prism  diminishes  with  its  refracting 
angle  (564),  it  follows  that  by  suitably  lessening  the  refracting  angle  of 
the  flint  glass  prism  CFD,  as  compared  with  the  refracting  angle  of  the 
crown  glass  prism  BCF,  the  dispersive  power  of  these  prisms  may  be 
equalised  ;  and  as,  from  their  position,  the  dispersion  takes  place  in  a 
contrary  direction,  it  is  neutralised  ;  that  is,  the  emergent  rays  EO  are 
parallel,  and  therefore  give  white  light.  Nevertheless,  the  ratio  of  the  angles 
BCF  and  CFD,  which  is  suitable  for  the  parallelism  of  the  red  rays  and 
violet  rays,  is  not  so  for  the  intermediate  rays,  and,  consequently,  only  two 
of  the  rays  of  the  spectrum  can  be  exactly  combined,  and  the  achromatism 
is  not  quite  perfect.  To  obtain  perfect  achromatism,  several  prisms  would 
be  necessary,  of  unequally  dispersive  materials,  and  the  angles  of  which  were 
suitably  combined. 

The  refraction  is  not  destroyed  at  the  same  time  as  the  dispersion  ;  that 
could  only  happen  if  the  refracting  power  of  a  body  varied  in  the  same  ratio 
as  its  dispersive  power,  which  is  not  the  case.     Consequently, 
the  emergent  ray  EO  is  not  exactly  parallel  to  the  incident  ray, 
and  there  is  a  refraction  without  appreciable  decomposition. 

Achromatic  lenses  are  made  of  two  lenses  of  unequal  dis- 
persive materials  :  one,  A,  of  flint  glass,  is  a  diverging  concavo- 
convex  (fig.  509)  ;  the  other,  B,  of  crown  glass,  is  double  convex, 
and  one  of  its  faces  may  exactly  coincide  with  the  concave  face 
of  the  first.  As  with  prisms,  several  lenses  would  be  necessary 
to  obtain  perfect  achromatism  ;  but  for  optical  instruments  two 
are  sufficient,  their  curvatures  being  such  as  to  combine  not  the 
extreme  red  and  violet,  but  the  blue  and  orange  rays,  while  at  the  same  time 
regard  is  had  to  the  correction  for  spherical  aberration. 


Fig.  509. 


'V 


On  Light.  [585- 


CHAPTER  V. 

OPTICAL    INSTRUMENTS. 

585.  The  different  kinds  of  optical  instruments. — By  the  term  optical 
instrument  is  meant  any  combination  of  lenses,  or  of  lenses  and  mirrors. 
Optical  instruments  may  be  divided  into  three  classes,  according  to  the 
ends  they  are  intended  to  answer,  viz.  : — i.  Microscopes,  which  are  designed 
to  obtain  a  magnified  image  of  any  object  whose  real  dimensions  are  too 
small  to  admit  of  its  being  seen  distinctly  by  the  naked  eye.  ii.  Telescopes, 
by  which  very  distant  objects,  whether  celestial  or  terrestrial,  may  be 
observed,  iii.  Instruments  designed  to  project  on  a  screen  a  magnified  or 
diminished  image  of  any  object  which  can  thereby  be  either  depicted  or 
rendered  visible  to  a  crowd  of  spectators ;  such  as  the  camera  lucida, 
the  camera  obscura,  photographic  apparatus,  the  magic  lantern,  the  solar 
microscope,  the  photo-electric  microscope,  &c.  The  two  former  classes  yield 
virtual  images ;  the  last,  with  the  exception  of  the  camera  lucida,  yield  real 
images. 

MICROSCOPES. 


,  sss. 


The  simple  microscope. — The  simple  microscope,  or  magnifying 
glass,  is  merely  a  convex  lens  of  short  focal  length,  by  means  of  which  we 
look  at  objects  placed  between  the  lens  and  its  principal  focus.  Let  AB 
(fig.  510)  be  the  object  to  be  observed,  placed  between  the  lens  and  its 

principal  focus,  F. 
Draw  the  second- 
ary axes  AO  and 
BO,  and  also  from 
A  and  B  rays  paral- 
lel to  the  axis  of 
the  lens  FO.  Now 
these  rays,  on  pass- 
ing out  of  the 
lens,  tend  to  pass 
through  the  second 
principal  focus  F' ; 
consequently  they 

Fig   510.  ,.  .  / 

are  divergent  with 

reference  to  the  secondary  axes,  and  therefore,  when  produced,  will  cut  those 
axes  in  A'  and  B'  respectively.  These  points  are  the  virtual  foci  of  A  and 
B  respectively.  The  lens,  therefore,  produces  at  A'B'  an  erect  and  magnified 
virtual  image  of  the  object  AB. 


-587] 


Conditions  of  Distinctness  of  the  Images. 


539 


The  position  and  magnitude  of  this  image  depend  on  the  distance  of  the 
object  from  the  focus.  Thus,  if  AB  is  moved  to  ab,  nearer  the  lens,  the 
secondary  axis  will  contain  a  greater  angle,  and  the  image  will  be  formed  at 
a'bf,  and  will  be  much  smaller,  and  nearer  the  eye.  On  the  other  hand,  if 
the  object  is  moved  farther  from  the  lens,  the  angle  between  the  secondary 
axes  is  diminished,  and  their  intersection  with  the  prolongation  of  the  re- 
fracted rays  taking  place  beyond  A'B',  the  image  is  formed  farther  from  the 
lens,  and  is  larger. 

In  a  simple  microscope  both  chromatic  aberration  and  spherical  aberra- 
tion increase  with  the  degree  of  magnification.     We  have  already  seen  that 
the  former  can  be  corrected 
by  using  achromatic  lenses 
(584),  and  the  latter  by  using 
stops,  which  allow  the  pas- 
sage   of  such   rays    only   as 
are    nearly   parallel     to    the 
axis,  the  spherical  aberration  Flg>  5II< 

of  these  rays  being  nearly  inappreciable.  Spherical  aberration  may  be  still 
further  corrected  by  using  two  plano-convex  lenses,  instead  of  one  very 
convergent  lens.  When  this  is  done,  the  plane  face  of  each  lens  is  turned 
towards  the  object  (fig.  511).  Although  each  lens  is  less  convex  than  the 
simple  lens  which  together  they  replace,  yet  their  joint  magnifying  power  is 
as  great,  and  with  a  less  amount  of  spherical  aberration,  since  the  first  lens- 
diverts  towards  the  axis  the  rays  which 
fall  on  the  second  lens.  This  combination 
of  lenses  is  known  as  Wollastoris  doublet. 

There  are  many  forms  of  the  simple 
microscope.  One  of  the  best  is  that  re- 
presented in  fig.  512.  On  a  horizontal 
support  E,  which  can  be  raised  and 
lowered  by  a  rack  K  and  pinion  D,  there 
is  a  black  eyepiece  m,  in  the  centre  ot 
which  is  fitted  a  small  convex  lens.  Below 
this  is  the  stage  b,  which  is  fixed,  and  on 
which  the  object  is  placed  between  glass 
plates.  In  order  to  illuminate  the  object 
powerfully,  diffused  light  is  reflected  from 
a  concave  glass  mirror,  M,  so  that  the 
reflected  rays  fall  upon  the  object.  In 
using  this  microscope  the  eye  is  placed 
very  near  the  lens,  which  is  lowered  or 
raised  until  the  position  is  found  at  which  the  object  appears  in  its  greatest 
distinctness. 

?  587.  Conditions  of  distinctness  of  the  images.  — In  order  that  objects 
looked  at  through  a  microscope  should  be  seen  with  distinctness  they  must 
have  a  strong  light  thrown  upon  them,  but  this  is  by  no  means  enough.  It 
is  necessary  that  the  image  be  formed  at  a  determinate  distance  from  the 
eye.  In  fact,  there  is  for  each  person  a  distance  of  most  distinct  vision — a 
distance,  that  is  to  say,  at  which  an  object  must  be  placed  from  an  observer's 


Fig.  512. 


540 


On  Light. 


[587- 


•eye  in  order  to  be  seen  with  greatest  distinctness.  This  distance  is  different 
for  different  observers,  but  ordinarily  is  between  10  and  12  inches.  It  is, 
therefore,  at  this  distance  from  the  eye  that  the  image  ought  to  be  formed. 
Moreover,  this  is  why  each  observer  has  to  focus  the  instrument ;  that  is,  to 
adapt  the  microscope  to  his  own  distance  of  most  distinct  vision.  This  is 
•effected  by  slightly  varying  the  distance  from  the  lens  to  the  object,  for  we 
have  seen  above  that  a  slight  displacement  of  the  object  causes  a  great  dis- 
placement of  the  image.  With  a  common  magnifying  glass,  such  as  is  held 
in  the  hand,  the  adjustment  is  effected  by  merely  moving  it  nearer  to  or 
farther  from  the  object.  In  the  microscope  the  adjustment  is  effected  by 
means  of  a  rack  and  pinion,  which  in  the  case  of  the  instrument  shown  in 
-fig.  512  moves  the  instrument,  but  moves  the  object  in  the  case  of  the 
instrument  depicted  in  fig.  517.  What  has  been  said  about  focussing  the 
microscope  applies  equally  to  telescopes.  In  the  latter  instrument  the  eye- 
piece is  generally  adjusted  with  respect  to  the  image  formed  in  the  focus  of 
the  object-glass. 

In  respect  of  the  distinctness  of  the  image  the  general  rules  for  convex 
lenses  apply. 

In  order  to  lessen  dispersion  lenses  have  been  constructed  of  diamond, 
of  ruby,  and  of  other  precious  stones,  which  for  a  small  amount  of  dispersion 
have  a  great  degree  of  refrangibility.  Drops  of  water  or  of  Canada  balsam 
in  minute  apertures,  in  a  thin  piece  of  wood  or  of  metal,  act  as  microscopes, 
f  588.  Apparent  magnitude  of  an  object. — The  apparent  magnitude 
or  apparent  diameter  of  a  body  is  the  angle  it  subtends  at  the  eye  of  the 


Fig.  514- 

observer.  Thus,  if  AB  is  the  object,  and  O  the  observer's  eye  (figs.  513,  514), 
the  apparent  magnitude  of  the  object  is  the  angle  AOB  contained  by  two 
visual  rays  drawn  from  the  centre  of  the  pupil  to  the  extremities  of  the  object. 
In  the  case  of  objects  seen  through  optical  instruments,  the  angles 
which  they  subtend  are  so  small  that  the  arcs  which  measure  the  angles  do 
not  differ  sensibly  from  their  tangents.  The  ratio  of  two  such  angles  is 
therefore  the  same  as  that  of  their  tangents.  Hence  we  deduce  the  two 
following  principles  :  — 


—  589J  Measure  of  Magnification.  541 

i.  When  the  same  object  is  seen  at  unequal  distances,  the  apparent  diameter 
varies  inversely  as  the  distance  from  the  observer's  eye. 

ii.  In  the  case  of  two  objects  seen  at  the  same  distance,  the  ratio  of  the 
apparent  diameters  is  the  same  as  that  of  their  absolute  magnitudes. 

These  principles  may  be  proved  as  follows  :  —  i.  In  fig.  513,  let  AB  be  the 
object  in  its  first  position,  and  ab  the  same  object  in  its  second  position. 
For  the  sake  of  distinctness  these  are  represented  in  such  positions  that  the 
line  OC  passes  at  right  angles  through  their  middle  points  C  and  c  respec- 
tively. It  is,  however,  sufficient  that  ab  and  AB  should  be  the  bases  of 
isosceles  triangles  having  a  common  vertex  at  O.  Now,  by  what  has  been 
said  above,  AB  is  virtually  an  arc  of  a  circle  described  with  centre  O  and 
radius  OC  ;  likewise  ab  is  virtually  an  arc  of  a  circle  whose  centre  is  O  and 
radius  Qc.  Therefore, 

AOB  :aO&  =  ^  :f*=JL  .  JL. 
OC      Oc    OC   '  Qc 

Therefore,  AOB  varies  inversely  as  OC. 

ii.  Let  AB  and  A'B'  be  two  objects  placed  at  the  same  perpendicular 
distance,  OC,  from  the  eye,  O,  of  the  observer  (fig.  514).  Then  they  are 
virtually  arcs  of  a  circle  whose  centre  is  O  and  radius  OC.  Therefore, 


AOB  :  A'OB'  =         :  =  AB  :  A'B' 


a  proportion  which  expresses  the  second  principle. 

589.  measure  of  magnification  —  In  the  simple  microscope  the  mea- 
sure of  the  magnification  produced  is  the  ratio  of  the  apparent  diameter  of 
the  image  to   that   of 
the  object,  both  being 
at  the  distance  of  most 
distinct     vision.     The 
same  rule  holds  good 
for  other  microscopes 
It  is,  however,  impor- 
tant to  obtain  an  ex- 
pression for  the  mag- 
nification     depending 
on   data   that    are    of 
easier  determination. 

In  fig.  515  let  AB 
be  the  object,  and  A'B  '  Fis-  &* 

its  image  formed  at  the  distance  of  most  distinct  vision.  Let  a'b'  be  the 
projection  of  AB  on  A'B'.  Then,  since  the  eye  is  very  near  the  glass, 

A'OTV  A'TV  A'TV 

the  magnification  equal       /^r,  or  ~£  ;  that  is,  ~~-.     But  since  the  tri- 

S      &  \JO  Ct  O  zx-t> 

angles  A'OB'  and  AOB  are  similar,  A'B'  :  AB  =  DO  :  CO.  Now  DO  is  the 
distance  of  most  distinct  vision,  and  CO  is  very  nearly  equal  to  FO,  the  focal 
length  of  the  lens.  Therefore,  the  magnification  equals  the  ratio  of  the  dis- 
tance of  most  distinct  vision  to  the  focal  length  of  the  lens.  Hence  we  con- 
clude that  the  magnification  is  greater,  ist,  as  the  focal  length  of  the  lens  is 


542  On  Light.  [589- 

smaller— in  other  words,  as  the  lens  is  more  convergent;  2ndly,  as  the 
observer's  distance  of  most  distinct  vision  is  greater. 

A  simpler  and  more  general  definition  of  the  measure  of  magnification 
may  be  stated  thus  : — Let  a  be  the  angular  magnitude  of  the  object  as  seen 
T)y  the  naked  eye,  /3  the  angular  magnitude  of  the  image,  whether  real  or 
virtual,  actually  present  to  the  eye,  then  the  magnification  is  /3-f-a.  This 
'rule  applies  to  telescopes. 

By  changing  the  lens  the  magnification  can  be  increased,  but  only  within 
certain  limits  if  we  wish  to  obtain  a  distinct  image.  By  means  of  a  simple 
microscope  distinct  magnification  may  be  obtained  up  to  120  diameters. 

The  magnification  we  have  here  considered  is  linear  magnification. 
Superficial  magnification  equals  the  square  of  the  linear  magnification  ;  for 
instance,  the  former  will  be  1,600  when  the  latter  is  40. 

Y  59°-  Principle  of  the  compound  microscope. — The  compound  micro- 
scope in  its  simplest  form  consists  of  two  condensing  lenses  :  one,  with  a 
short  focus,  is  called  the  object-glass,  or  objective,  because  it  is  turned  towards 
the  object ;  the  other  is  less  condensing,  and  is  called  the  eyepiece,  or  power, 
because  it  is  close  to  the  observer's  eye. 

Fig.  516  represents  the  path  of  the  luminous  rays  and  the  formation  of 
the  image  in  the  simplest  form  of  a  compound  microscope.  An  object  AB 

being  placed  very 
near  the  principal 
focus  of  the  object- 
glass  M,  but  a  little 
farther  from  the 
glass,  a  real  image 
ab,  inverted  and 
somewhat  magni- 
fied, is  formed  on  the  other  side  of  the  object-glass  (556).  Now  the  distance 
of  the  two  lenses  M  and  N  is  such  that  the  position  of  the  image  ab  is 
between  the  eyepiece  N  and  its  focus  F.  From  this  it  follows  that  for  the 
eye  at  E,  looking  at  the  image  through  the  eyepiece,  this  glass  produces  the 
same  effect  as  a  simple  microscope,  and  instead  of  this  image  ab,  another 
image,  a'b',  is  seen,  which  is  virtual,  and  still  more  magnified.  This  second 
image,  although  erect  as  regards  the  first,  is  inverted  in  reference  to  the 
object.  It  may  thus  be  said  that  the  compound  microscope  is  in  effect  a 
simple  microscope  applied  not  to  the  object,  but  to  its  image  already  magni- 
fied by  the  first  lens. 

V  591.  compound  microscope. — The  principle  of  the  compound  micro- 
scope has  been  already  ($90)  explained  ;  the  principal  accessories  to  the 
instrument  remain  to  be  described. 

Fig.  517  represents  a  perspective  view,  and  fig.  518  a  section  of  a  com- 
pound microscope.  The  body  of  the  microscope  consists  of  a  series  of  brass 
tubes,  DD',  H,  and  I ;  in  H  is  fitted  the  eyepiece  O,  and  in  the  lower  part 
of  DD'  the  object-glass  o.  The  tube  I  moves  with  gentle  friction  in  the  tube 
DD',  which  in  turn  can  also  be  moved  in  a  larger  tube  fixed  in  the  ring  E. 
This  latter  is  fixed  to  a  piece  BB',  which  by  means  of  a  very  fine  screw, 
worked  by  the  milled  head  T,  can  be  moved  up  and  down  an  inner  rod,  c,  not 
represented  in  the  figure.  The  whole  body  of  the  microscope  is  raised 


-591] 


Compound  Microscope. 


543 


and  lowered  with  the  piece  BB',  so  that  it  can  be  placed  near  or  far 
from  the  object  to  be  examined.  Moreover,  the  rod  c,  and  all  the  other 
pieces  of  the  apparatus,  rest  on  a  horizontal  axis  A,  with  which  they  turn 
under  so  much  friction  as  to  remain  fixed  in  any  position  in  which  they  may 
be  placed. 

The  objects  to  be  observed  are  placed  between  two  glass  plates,  V,  on 
a  stage,  R.  This  is  perforated  in  the  centre,  so  that  light  can  be  reflected 
upon  it  by  a  concave  reflecting  glass  mirror,  M.  The  mirror  is  mounted  on 


Fig.  5*7- 

an  articulated  support  so  that  it  can  be  placed  in  any  position  whatever,  so 
as  to  reflect  to  the  object  either  the  diffused  light  of  the  atmosphere,  or  that 
from  a  candle  or  lamp.  Between  the  reflector  and  the  stage  is  a  diaphragm 
or  stop,  K,  perforated  by  four  holes  of  different  sizes,  any  one  of  which  can 
be  placed  over  the  perforation  in  the  stage,  and  thus  the  light  falling  on  the 
object  may  be  regulated  ;  the  light  can,  moreover,  be  regulated  by  raising, 
by  a  lever  n,  the  diaphragm  K,  which  is  movable  in  a  slide.  Above  the 
diaphragm  is  a  piece,  m,  to  which  can  be  attached  either  a  very  small  stop, 
so  that  only  very  little  light  can  reach  the  object,  or  a  condensing  lens, 


544  On  Light.  [59K 

which  illuminates  it  strongly,  or  an  oblique  prism,  represented  at  X.  The 
rays  from  the  reflector  undergo  two  total  reflections  in  this  prism,  and 
emerge  by  a  lenticular  face  that  concentrates  them  on  the  object,  but  in  an 
oblique  direction,  which  in  some  microscopic  observations  is  an  advantage. 
Objects  are  generally  so  transparent  that  they  can  be  lighted  from  below ; 
but  where,  owing  to  their  opacity,  this  is  not  possible,  they  are  lighted  from 
above  by  means  of  a  condensing  lens  mounted  on  a  jointed  support,  and  so 
placed  that  they  receive  the  diffused  light  of  the  atmosphere. 

Fig.  518  shows  the  arrangement  of  the  lenses  and  the  path  of  the  rays 
in  the  microscope.  At  o  is  the  object-glass,  consisting  of  three  small  con- 
densing lenses,  represented  on  a  larger  scale  at  L,  on  the  right  of  the  figure. 
The  effect  of  these  lenses  being  added  to  each  other  is  that  they  act  like  a 
single  very  powerful  condensing  lens.  The  object  being  placed  at  /,  a  very 
little  beyond  the  principal  focus  of  the  system,  the  emerging  rays  fall  upon  a 
fourth  condensing  lens,  72,  the  use  of  which  will  be  seen  presently  (592,  593). 
Having  become  more  convergent,  owing  to  their  passage  through  the  lens 
#,  the  rays  form  at  aaf  a  real  and  amplified  image  of  the  object  z.  This 
image  is  between  a  fifth  condensing  lens,  O,  and  the  principal  focus  of  this 
lens.  Hence,  on  looking  through  this,  it  acts  as  a  magnifier  (556),  and  gives 
at  AA'  a  virtual  and  highly  magnified  image  of  aa\  and  therefore  of  the 
,  object.  The  two  glasses  n  and  O  constitute  the  eyepiece,  in  the  same 
manner  as  the  three  glasses  o  constitute  the  object-glass. 

The  first  image,  aa\  must  not  merely  be  formed  between  the  glass  O 
and  its  principal  focus,  but  at  such  a  distance  from  this  glass  that  the  second 
image,  AA',  is  formed  at  the  observer's  distance  of  distinct  vision.  This 
result  is  obtained  in  moving,  by  the  hand,  the  body  DH  of  the  microscope 
in  the  larger  tube  fixed  to  the  ring  E,  until  a  tolerably  distinct  image  is 
obtained ;  then  turning  the  milled  head  T  in  one  direction  or  the  other, 
the  piece  BB',  and  with  it  the  whole  microscope,  are  moved  until  the  image 
AA'  attains  its  greatest  distinctness,  which  is  the  case  when  the  image  acf 
is  formed  at  the  distance  of  distinct  vision  :  a  distance  which  can  always  be 
ultimately  obtained,  for  as  the  object-glass  approaches  or  recedes  from  the 
object,  the  image  aa'  recedes  from  or  approaches  the  eyepiece,  and  at  the 
same  time  the  image  AA'. 

This  operation  is  called  the  focussing.  In  the  microscope,  where  the 
distance  from  the  object-glass  to  the  eyepiece  is  constant,  it  is  effected  by 
altering  their  distance  from  the  object.  In  telescopes,  where  the  objects 
are  inaccessible,  the  object  is  effected  by  varying  the  distance  of  the  eye- 
piece and  the  object-glass. 

The  microscope  possesses  numerous  eyepieces  and  object-glasses,  by 
means  of  which  a  great  variety  of  magnifying  power  is  obtained.  A  small 
magnifying  power  is  also  obtained  by  removing  one  or  two  of  the  lenses  of 
the  object-glass. 

The  above  contains  the  essential  features  of  the  microscope  ;  it  is  made 
in  a  great  variety  of  forms,  which  differ  mainly  in  the  construction  of  the 
stand,  the  arrangement  of  the  lenses,  and  in  the  illumination.  For  descrip- 
tions of  these  the  student  is  referred  to  special  works  on  the  microscope. 

592.  Achromatism  of  the  microscope.  Campani's  eyepiece. — When 
a  compound  microscope  consists  of  two  single  lenses,  as  in  fig.  517,  not  only 


-592]  Achromatism  of  the  Microscope.  545 

is  the  spherical  aberration  uncorrected,  but  also  the  chromatic  aberration, 
the  latter  defect  causing  the  images  to  be  surrounded  by  fringes  of  the 
prismatic  colours,  these  fringes  being  larger  as  the  magnification  is  greater. 
It  is  with  a  view  to  correcting  these  aberrations  that  the  object-glass  (see 
fig.  517)  is  composed  of  three  achromatic  lenses,  and  the  eyepiece  of  two 
lenses,  n  and  m  ;  for  the  first  of  these,  n,  would  be  enough  to  produce  colour 
unless  the  magnifying  power  were  low. 

The  effect  of  this  eyepiece  in  correcting  the  colour  may  be  explained 
as  follows  : — It  will  be  borne  in  mind  that  with  respect  to  red  rays  the  focal 
length  of  a  lens  is  greater  than  the  focal  length  of  the  same  lens  with 
reference  to  the  violet  rays.  ^ 

In  fact,  if  in  the  equation  (4)  (559)  we  write  R/  =  oo,  we  obtain /=  — y, 

which  gives  the  focal  length  of  a  plano-convex  lens  whose  refractive  index 
is  n.  Now,  in  flint  glass,  and  for  the  red  ray,  n  —  I  equals  0-63,  and  for  the 
violet  ray  n  —  I  equals  0*67. 

Let  ab  be  the  object,  O  the  object-glass,  which  is  corrected  for  colour. 
Consequently,  a  pencil  of  rays  falling  from  a  on  O  would  converge  to  the 


Fig.  519- 

focus  A  without  any  separation  of  colours  ;  but  falling  on  the  field-glass  C, 
the  red  rays  would  converge  to  r,  the  violet  rays  to  -z/,  and  intermediate 
colours  to  intermediate  points.  In  like  manner  the  rays  from  b,  after 
passing  through  the  field-glass,  would  converge  to  r7,  or  T/,  and  interme- 
diate points.  So  that  on  the  whole  there  would  be  formed  a  succession  of 
coloured  images  of  ab ;  viz.  a  red  image  at  rr'^  a  violet  image  at  T'T/,  and 
between  them  images  of  intermediate  colours.  Let  d  be  the  point  of  the 
object  which  is  situated  on  the  axis.  The  rays  from  d  will  converge  to  R, 
V,  and  intermediate  points.  Now  suppose  the  eye-glass  O'  to  be  placed  in 
such  a  manner  that  R  is  the  principal  focus  of  O'  for  the  red  rays,  then  V 
will  be  its  principal  focus  for  the  violet  rays.  Consequently,  the  red  rays, 
after  emerging  from  O,  will  be  parallel  to  the  axis,  and  so  will  the  violet 
rays  emerging  from  V,  and  so  of  any  other  colour.  Accordingly,  the 
colours  of  d,  which  are  separated  by  C,  are  again  combined  by  O'.  The 
same  is  very  nearly  true  of  r  and  v,  and  of  r'  and  v'.  Hence  a  combination 
of  lenses  C  and  O'  corrects  the  chromatic  aberration  that  would  be  produced 
by  the  use  of  a  single  eye-glass.  Moreover,  by  drawing  the  rays  towards  the 
axis,  it  diminishes  the  spherical  aberration,  and,  as  we  shall  see  in  the  next 
article,  enlarges  the  field  of  view. 

In  all  eyepieces  consisting  of  two  lenses  the  lens  to  which  the  eye  is 
applied  is  called  the  eye-lens ;  the  one  towards  the  object-glass  is  called  the 
field-lens.  The  eyepiece  above  described  was  invented  by  Huyghens,  who 
was  not,  however,  aware  of  its  property  of  achromatism.  He  designed  it  for  use 
with  the  telescope.  It  was  applied  to  the  microscope  by  Campani.  The  rela- 

NN 


546 


On  Light. 


[592- 


tion  between  the  focal  length  of  the  lenses  is  as  follows  : — The  focal  length 
of  the  field-glass  is  three  times  that  of  the  eye-lens,  and  the  distance  between 
their  centres  is  half  the  sum  of  the  focal  length.  It  easily  follows  from  this 
that  the  image  of  the  point  d  would,  but  for  the  interposition  of  the  field-lens, 
be  formed  at  D,  which  is  so  situated  that  CD  is  three  times  DO'  ;  then  the 
mean  of  the  coloured  images  would  be  formed  midway  between  C  and  CK 
~  593.  Field  of  view. — By  the  field  of  view  of  an  optical  instrument  is 
eant  all  those  points  which  are  visible  through  the  eyepiece.  The  advan- 
tage, obtained  by  the  use  of  an  eyepiece  in  enlarging  the  field  of  view  will  be 
readily  understood  by  an  inspection  of  the  accompanying  figure.  As  before, 
O  is  the  object-glass,  C  the  field-lens,  O'  the  eye-lens,  and  E  the  eye  placed 
on  the  axis  of  the  instrument.  Let  a  be  a  point  of  the  object ;  if  we  suppose 
the  field-lens  removed,  the  pencil  of  rays  from  a  would  be  brought  to  a 
focus  at  A,  and  none  of  them  would  fall  on  the  eye-lens  O',  nor  pass  into  the 


Fig.  520. 

eye  E.  Consequently,  a  is  beyond  the  field  of  view.  But  when  the  field- 
glass  C  is  interposed,  the  pencil  of  rays  is  brought  to  a  focus  at  A',  and 
emerges  from  O'  into  the  eye.  Consequently,  a  is  now  within  the  field  ot 
view.  It  is  in  this  manner  that  the  substitution  of  an  eyepiece  for  a  single 
eye-lens  enlarges  the  field  of  view. 

594.  IKag-nifyingr  power.  Micrometer. — The  magnifying  power  of  any 
optical  instrument  is  the  ratio  of  the  magnitude  of  the  image  to  the  mag- 
nitude of  the  object.  The  magnifying  power  in  a 
compound  microscope  is  the  product  of  the  respec- 
tive magnifying  powers  of  the  object-glass  and  of 
the  eyepiece  ;  that  is,  if  the  first  of  these  magnifies 
20  times,  and  the  other  10,  the  total  magnifying 
power  is  200.  The  magnifying  power  depends  on 
the  greater  or  less  convexity  of  the  object-glass 
and  of  the  eyepiece,  as  well  as  on  the  distance  be- 
tween these  two  glasses,  together  with  the  distance 
of  the  object  from  the  object-glass.  A  magnifying 
power  of  1,500  and  even  upwards  has  been  ob- 
tained ;  but  the  image  then  loses  in  sharpness 
what  it  gains  in  extent.  To  obtain  precise  and 


Fig.  521. 


well-illuminated  images,  the  magnifying  power  ought  not  to  exceed  500  to 
600  diameters,  which  gives  a  superficial  enlargement  250,000  to  360,000  times 
that  of  the  object. 

The  magnifying  power  is  determined  experimentally  by  means  of  the 
micrometer :  this  is  a  small  glass  plate,  on  which,  by  means  of  a  diamond, 
a  series  of  lines  is  drawn  at  a  distance  from  each  other  of  —  or  T~  of  a 
millimetre.  The  micrometer  is  placed  in  front  of  the  object-glass,  and 
then,  instead  of  viewing  directly  the  rays  emerging  from  the  eyepiece 


-595]  Astronomical  Telescope.  547 

O,  they  are  received  on  a  piece  of  glass  A  (fig.  521),  inclined  at  an  angle 
of  45°,  and  the  eye  is  placed  above  so  as  to  see  the  image  of  the  micro- 
meter lines,  which  is  formed  by  reflection  on  a  screen  E,  on  which  is  a 
scale  divided  into  millimetres.  By  counting  the  number  of  divisions  of  this 
scale  corresponding  to  a  certain  number  of  lines  of  the  image,  the  magni- 
fying power  may  be  deduced.  Thus,  if  the  image  occupies  a  space  of  45 
millimetres  on  the  scale  and  contains  1 5  lines  of  the  micrometer,  the  distance 
between  each  of  which  shall  be  assumed  at  ^  niili metre,  the  absolute 
magnitude  of  the  object  will  be  ^  millimetre  ;  and  as  the  image  occupies  a 
space  of  45  millimetres,  the  magnification  will  be  the  quotient  of  45  by  i"5, 
or  300.  The  eye  in  this  experiment  ought  to  be  at  such  a  distance  from  the 
screen  E  that  the  screen  is  distinctly  visible  :  this  distance  varies  with 
different  obververs,  but  is  usually  10  to  12  inches.  The  magnifying  power 
of  the  microscope  can  also  be  determined  by  means  of  the  camera  lucida. 

When  once  the  magnifying  power  is  known,  the  absolute  magnitude  of 
objects  placed  under  the  microscope  is  easily  deduced.  For,  as  the  magni- 
fying power  is  the  quotient  of  the  size  of  the  image  by  the  size  of  the  object, 
it  follows  that  the  size  of  the  image  divided  by  the  magnifying  power  gives 
the  size  of  the  object  :  in  this  manner  the  diameters  of  all  microscopic  objects 
are  determined. 

TELESCOPES. 

>/  595.  Astronomical  telescope. — The  astronomical  telescope  is  used  for 
observing  the  heavenly  bodies  ;  like  the  microscope,  it  consists  of  a  con- 
densing eye- 
piece  and 
object-glass. 
The  object- 
glass,  M  (fig 
522),  forms 
between  the 
eyepiece,  N, 
and  its  prin- 
cipal focus 

an  inverted  image  of  the  heavenly  body  ;  and  this  eyepiece,  which  acts  as 
a  magnifying  glass,  then  gives  a  virtual  and  highly  magnified  image,  a'b'^  of 
the  image  ab.  The  astronomical  telescope  appears,  therefore,  analogous  to 
the  microscope  :  but  the  two  instruments  differ  in  this  respect,  that  in  the 
microscope,  the  object  being  very  near  the  object-glass,  the  image  is  formed 
much  beyond  the  principal  focus,  and  is  greatly  magnified,  so  that  both  the 
object-glass  and  the  eyepiece  magnify  ;  while  in  the  astronomical  telescope, 
the  heavenly  body  being  at  a  great  distance,  the  incident  rays  are  parallel, 
and  the  image  formed  in  the  principal  focus  of  the  object-glass  is  much 
smaller  than  the  object.  There  is,  therefore,  no  magnification  except  by 
the  eyepiece,  and  this  ought,  therefore,  to  be  of  very  short  focal  length. 

Fig.  523  shows  an  astronomical  telescope  mounted  on  its  stand.  Above 
it  there  is  a  small  telescope  which  is  called  the  finder.  Telescopes  with  a 
large  magnifying  power  are  not  convenient  for  finding  a  star,  as  they  have 
but  a  small  field  of  view  :  the  position  of  the  star  is,  accordingly,  first  sought 

N  N  2 


548 


On  Light. 


[595- 


by  the  finder,  which  has  a  much  larger  field  of  view — that  is,  takes  in  a  far 
greater  extent  of  the  heavens  ;  it  is  then  viewed  by  means  of  the  telescope. 

The  magnification  (589)  equals    ^     (fig.  513);   that  is,  it  equals   v~, 

CF 

and  therefore  is  approximately  equal  to— — ,  F  being  the  focus  of  the  object. 

glass  M,  and 
being  supposed 
very  nearly  to 
coincide  with 
the  focus  of 
the  eyepiece  N ; 
it  may,  there- 
fore, be  con- 
cluded that  the 
magnifying 
power  is 
greater  in  pro- 
portion as  the 
object-glass  is 
less  conver- 
gent, and  the 
eyepiece  more 
so. 

When  the 
telescope  is 
used  to  make 
an  accurate  ob- 
servation of  the  stars — for  example,  the  zenith  distance,  or  their  passage 
over  the  meridian — a  cross  wire  is  added.  This  consists  of  two  very  fine 
metal  wires  or  spider  threads  stretched  across  a  circular  aperture  in  a  small 
metal  plate  (fig.  524).  The  wires  ought  to  be  placed  in  the  position  where 
the  inverted  image  is  produced  by  the  object-glass,  and  the  point  where 
the  wires  cross  ought  to  be  on  the  optical  axis  of  the  telescope,  which  thus 
becomes  the  line  of  sight  or  collimation. 

^C  596.  Terrestrial  telescope. — The  terrestrial  telescope  differs  from  the 
astronomical  telescope  in  producing  images  in  their  right  positions.  This  is 
effected  by  means  of  two  condensing  glasses,  P  and  Q  (fig.  525),  placed 
between  the  object-glass  M  and  the  eyepiece  R.  The  object  being  sup- 
posed to  be  at 
AB,  at  a  greater 
distance  than 
can  be  shown 
in  the  drawing, 
an  inverted  and 
Fis-  525-  much  smaller 

image  is  formed 

at  ba  on  the  other  side  of  the  object-glass.  But  the  second  lens,  P,  is  at 
such  a  distance  that  its  principal  focus  coincides  with  the  image  ab  •  from 
which  it  follows  that  the  luminous  rays  which  pass  through  £,  for  example, 
after  traversing  the  lens  P,  take  a  direction  parallel  to  the  secondary  axis 


Fig.  523- 


-597] 


Galileo's  Telescope. 


549 


^O  (552)*  Similarly,  the  rays  passing  by  a  take  a  direction  parallel  to  the 
axis  <zO.  After  crossing  in  H,  these  various  rays  traverse  a  third  lens  O, 
whose  principal  focus  coincides  with  the  point  H.  The  pencil  B£H  con- 
verges towards  b\  on  a  secondary  axis  O'^',  parallel  to  its  direction  ;  the 
pencil  A&H  converging  in  the  same  manner  at  a',  an  erect  image  of  the 
object  AB  is  produced  at  a'b'.  This  image  is  viewed,  as  in  the  astrono- 
mical telescope,  through  a  condensing  eyepiece  R,  so  placed  that  it  acts  as 
a  magnifying  glass ;  that  is,  its  distance  from  the  image  a'b'  is  less  than  the 
principal  focal  distance  ;  hence  there  is  formed,  at  a"b",  a  virtual  image  of 
a'b',  erect  and  much  magnified.  The  lenses  P  and  Q,  which  only  serve  to 
rectify  the  position  of  the  image,  are  fixed  in  a  brass  tube,  at  a  constant 
distance,  which  is  equal  to  the  sum  of  their  principal  focal  distances.  The 
object-glass  M  moves  in  a  tube,  and  can  be  moved  to  or  from  the  lens  P, 
so  that  the  image  ab  is  always  formed  in  the  focus  of  the  lens,  whatever  be 
the  distance  of  the  object.  The  distance  of  the  lens  R  may  also  be  varied 
so  that  the  image  a"b"  may  be  formed  at  the  distance  of  distinct  vision. 

This  instrument  may  also  be  used  as  an  astronomical  telescope  by  using 
a  different  eyepiece  :  this  must  have  a  much  greater  magnifying  power  than 
in  the  former  case. 

In  the  terrestrial  telescope  the  magnifying  power  is  the  same  as  in  the 
astronomical  telescope,  provided  always  that  the  correcting  glasses,  P  and 
O,  have  the  same  convexity. 

In  order  to  determine  directly  the  magnifying  power  of  a  telescope  when 
this  is  not  great,  a  divided  scale  at  a  distance,  or  the  tiles  of  a  house  may 
be  viewed  through  the  telescope  with  one  eye  and  directly  with  the  other.  This 
with  a  little  practice  is  not  difficult.     It  is  thus  observed 
how  many  unmagnified  divisions  correspond  to  a  single 
magnified  one.     Thus,  if  two  seen  through  the  telescope 
appear  like  seven,  the  magnifying  power  is  3^. 

The  excellence  of  a  telescope  depends  also  on  the 
sharpness  of  the  images.  To  test  this  various  circular 
and  angular  figures  are  painted  in  black  on  a  white 
ground,  as  shown  in  fig.  526,  in  about  TT5  the  full  size. 
When  these  are  looked  at  through  the  telescope  at  a 
distance  of  80  or  100  paces  they  should  appear  sharply  defined,  perfectly 
black,  without  distortion,  and  without  coloured  edges. 

^597.    Galileo's   telescope.— Galileo's    telescope    is  the   simplest   of    all 
telescopes,  for  it  only  consists  of  two  lenses  ;  namely,  an  object-glass,  M,  and 
a  diverging  or  double  con- 
cave eyepiece,  R  (fig.  527), 
and  it  gives  at  once  an  erect 
image.      Opera-glasses  are 
constructed    on  this    prin- 
ciple. 

If  the  object   be  repre-  Fig.  527. 

sented  by  the  right  line  AB, 

a  real  but  inverted  and  smaller  image  would  be  formed  at  ba\  but  in 
traversing  the  eyepiece  R,  the  rays  emitted  from  the  points  A  and  B  are 
refracted  and  diverge  from  the  secondary  axis  £O'  and  aO',  which  corre- 
pond  to  the  points  b  and  a  of  the  image.  Hence,  these  rays  produced 


Fig.  526. 


550 


On  Light. 


[597- 


backward  meet  their  axes  in  a'  and  b'  ;  the  eye  which  receives  them  sees 
accordingly  an  erect  and  magnified  image  in  a'b',  which  appears  nearer 
because  it  is  seen  under  an  angle,  a'Q'b',  greater  than  the  angle,  AOB, 
under  which  the  object  is  seen. 

The  magnifying  power  is  equal  to  the  ratio  of  the  angle  a'Q'b'  to  the 
angle  AOB,  and  is  usually  from  2  to  4. 

The  distance  of  the  eyepiece  R  from  the  image  ab  is  pretty  nearly  equal 
to  the  principal  focal  distance  of  this  eyepiece ;  it  follows,  therefore,  that  the 
distance  between  the  two  lenses  is  the  distance  between  their  respective 
focal  distances;  hence  Galileo's  telescope  is  very  short  and  portable.  It 
has  the  advantage  of  showing  objects  in  their  right  position ;  and,  further, 
as  it  has  only  two  lenses,  it  absorbs  very  little  light :  in  consequence,  how- 
ever, of  the  divergence  of  the  emergent  rays,  it  has  only  a  small  field  of  view, 
and  in  using  it  the  eye  must  be  placed  very  near  the  eyepiece.  The  eye- 
piece can  be  moved  to  or  from  the  object-glass,  so  that  the  image  afb'  is 
always  formed  at  the  distance  of  distinct  vision. 

The  opera-glass  is  usually  double,  so  as  to  produce  an  image  in  each  eye, 
by  which  greater  brightness  is  attained. 

The  time  at  which  telescopes  were  invented  is  not  known.  Some  attri- 
bute their  invention  to  Roger  Bacon  in  the  thirteenth  century  ;  others  to  J.  B. 
Porta  at  the  end  of  the  sixteenth  ;  others,  again,  to  a  Dutchman,  Jacques 
Metius,  who,  in  1609,  accidentally  found  that  by  combining  two  glasses,  one 
concave  and  the  other  convex,  distant  objects  appeared  nearer  and  much 
larger.  Galileo's  was  the  first  telescope  directed  towards  the  heavens.  By 

its  means  Galileo  discovered  the 
mountains  of  the  moon,  Jupiter's 
satellites,  and  the  spots  on  the  sun. 

598.  Reflecting:   telescopes. — 
The  telescopes  previously  described 
are  refracting  or  dioptric  telescopes. 
It  is,  however,  only  in  recent  times 
that  it  has  been  possible  to  con- 
struct  achromatic  lenses   of  large 
size  ;  before  this  a  concave  metallic 
mirror   was    used    instead   of  the 
object-glass.      Telescopes    of   this 
kind     are     called     reflecting     or 
catoptric  telescopes.     The  principal 
forms  are  those  devised  by  Gregory, 
Newton,  Herschel,  and  Cassegrain. 

599.  The  Gregorian  telescope. 
— Fig.  528   is   a  representation  of 
Gregory's  telescope ;  it  is  mounted 
on  a  stand,  about  which  it  is  mov- 
able, and   can  be  inclined  at   any 

Flg>  528>  angle.     This  mode  of  mounting  is 

optional ;  it  may  be  equatorially  mounted.  Fig.  529  gives  a  longitudinal 
section.  It  consists  of  a  long  brass  tube  closed  at  one  end  by  a  concave  me- 
tallic mirror,  M,  which  is  perforated  in  the  centre  by  a  round  aperture  through 


-600] 


The  Newtonian  Telescope. 


551 


which  rays  reach  the  eye.  There  is  a  second  concave  metal  mirror,  N,  near 
the  end  of  the  tube  :  it  is  somewhat  larger  than  the  central  aperture  in  the 
large  mirror,  and  its  radius  of  curvature  is  much  smaller  than  that  of  the 
large  mirror.  The  axes  of  both  mirrors  coincide  with  the  axis  of  the  tube. 
As  the  centre  of  curvature  of  the  large  mirror  is  at  O,  and  its  focus  at  ab, 
rays  such  as  SA  emitted  from  a  heavenly  body  are  reflected  from  the 
mirror  M,  and  form  at  ab  an  inverted  and  very  small  image  of  the  heavenly 
body.  The  distance  of  the  mirrors  and  their  curvatures  is  so  arranged  that 
the  position  of  this  image  is  between  the  centre,  0,  and  the  focus,  f^  of  the 
small  mirror ;  hence  the  rays,  after  being  reflected  a  second  time  from  the 
mirror  N,  form  at  a'b'  a  magnified  and  inverted  image  of  ab,  and  therefore 
in  the  true  position  of  the  heavenly  body.  This  image  is  viewed  through 
an  eyepiece,  P,  which  may  either  be  simple  or  compound,  its  object 
being  to  magnify  it  again,  so  that  it  is  seen  at  a"b". 


Fig.  529. 

As  the  objects  viewed  are  not  always  at  the  same  distance,  the  focus  of 
the  large  mirror,  and  therefore  that  of  the  small  one,  vary  in  position. 

And  as  the  distance  of  distinct  vision  is  not  the  same  with  all  eyes,  the 
image  a"b"  ought  to  be  formed  at  different  distances.  The  required  adjust- 
ments may  be  obtained  by  bringing  the  small  mirror  nearer  to  or  farther 
from  the  larger  one  ;  this  is  effected  by  means  of  a  milled  head,  A  (fig.  528), 
which  turns  a  rod,  and  this  by  a  screw  moves  a  piece  to  which  the  mirror  is 
fixed. 

600.  The  Newtonian  telescope. — This  instrument  does  not  differ  much 
from  that  of  Gregory ;  the  large  mirror  is  not  perforated,  and  there  is  a 
small  plane  mirror  inclined  at  an  angle  of  45°  towards  an  eyepiece  placed  in 
the  side  of  the  telescope. 


Fig.  53°. 


The  difficulty  of  constructing  metallic  mirrors  caused  telescopes  of 
Gregorian  and  Newtonian  construction  to  fall  into  disuse.  Of  late,  how- 
ever, the  process  of  silvering  glass  mirrors  has  been  carried  to  a  high  state 


552 


On  Light. 


[600- 


of  perfection,  and  Foucault  applied  these  mirrors  to  Newtonian  telescopes 
with  great  success.  His  first  mirror  was  only  four  inches  in  diameter,  but 
he  has  successively  constructed  mirrors  of  8,  12,  and  13  inches,  and  at  the 
time  of  his  death  had  completed  one  of  32  inches  in  diameter. 

Fig.  531    represents  a  Newtonian  telescope  mounted  on  an  equatorial 


stand,  and  fig.  530  gives  a  horizontal  section  of  it.  This  section  shows 
how  the  luminous  rays  reflected  from  the  parabolic  mirror  M  meet  a  small 
rectangular  prism,  m,  which  replaces  the  inclined  plane  mirror  used  in  the 
old  form  of  Newtonian  telescope.  After  undergoing  a  total  reflection  from 
;/z,  the  rays  form  at  ab  a  very  small  image  of  the  heavenly  body.  This 
image  is  viewed  through  an  eyepiece  with  four  lenses  placed  on  the  side  of 


-601]  The  Herschelian  Telescope.  553 

the  telescope,  and  magnifying  from  50  to  800  times  according  to  the  size  of 
the  silvered  mirror. 

In  reflectors  the  mirror  acts  as  object-glass,  but  there  is,  of  course,  no 
chromatic  aberration.  The  spherical  aberration  is  corrected  by  the  form 
given  to  the  reflector,  which  is  paraboloid,  but  slightly  modified  by  trial  to 
suit  the  eyepiece  fitted  to  the  telescope. 

The  mirror  when  once  polished  is  immersed  in  a  silvering  liquid,  which 
consists  essentially  of  ammoniacal  solution  of  nitrate  of  silver,  to  which  some 
reducing  agent  is  added.  When  a  polished  glass  surface  is  immersed  in 
this  solution,  silver  is  deposited  on  the  surface  in  the  form  of  a  brilliant 
metallic  layer,  which  adheres  so  firmly  that  it  can  be  polished  with  rouge  in 
the  usual  manner.  These  new  telescopes  with  glass  mirrors  have  the  ad- 
vantage over  the  old  ones  that  they  give  purer  images,  they  weigh  less,  and 
are  much  shorter,  their  focal  distance  being  only  about  six  times  the  diameter 
of  the  mirror. 

These  details  known,  the  whole  apparatus  remains  to  be  described.  The 
body  of  the  telescope  (fig.  531)  consists  of  an  octagonal  wooden  tube.  The  end 
G  is  open  ;  the  mirror  is  at  the  other  end.  At  a  certain  distance  from  this 
end  two  axles  are  fixed,  which  rest  on  bearings  supported  by  two  wooden 
uprights,  A  and  B.  These  are  themselves  fixed  to  a  table,  PQ,  which  turns 
on  a  fixed  plate,  RS,  placed  exactly  parallel  to  the  equator.  On  the  circum- 
ference of  the  turning-table  there  is  a  brass  circle  divided  into  360  degrees  ; 
and  beneath  it,  but  also  fixed  to  the  turning-table,  there  is  a  circular  toothed 
wheel,  in  which  an  endless  screw,  V,  works.  By  moving  this  in  either 
direction  by  means  of  the  handle  m,  the  table  PQ,  and  with  it  the  telescope, 
can  be  turned.  A  vernier,  x,  fixed  to  the  plate  RS,  gives  the  fractions  of  a 
degree.  On  the  axis  of  the  motion  of  the  telescope  there  is  a  graduated 
circle,  O,  which  serves  to  measure  the  declination  of  the  star — that  is,  its 
angular  distance  from  the  equator  ;  while  the  degrees  traced  round  the  table 
RS  serve  to  measure  the  right  ascension — that  is,  the  angle  which  the  de- 
clination circle  of  the  star  makes  with  the  declination  circle  passing  through 
the  first  point  of  Aries. 

In  order  to  fix  the  telescope  in  declination,  there  is  a  brass  plate,  E,  fixed 
to  the  upright ;  it  is  provided  with  a  clamp,  in  which  the  limb  O  works,  and 
which  can  be  screwed  tight  by  means  of  a  screw  with  a  milled  head  r.  On 
the  side  of  the  apparatus  there  is  the  eyepiece  <?,  which  is  mounted  on  a 
sliding  copper  plate,  on  which  there  is  also  the  small  prism  m,  represented 
in  section  in  fig.  530.  To  bring  the  image  to  the  right  place,  this  plate  may 
be  moved  by  means  of  a  rack  and  a  milled  head  a.  The  handle  n  serves  to 
clamp  or  unclamp  the  screw  V.  The  drawing  was  one  taken  from  a  tele- 
scope the  mirror  of  which  is  only  6|  inches  in  diameter,  and  which  gives  a 
magnifying  power  of  150  to  200. 

601.  The  Herschelian  telescope. — Sir  W.  Herschel's  telescope,  which 
until  recently  was  the  most  celebrated  instrument  of  modern  times,  was  con- 
structed on  a  method  differing  from  those  described.  The  mirror  was  so  in- 
clined that  the  image  of  the  star  was  formed  at  ab  on  the  side  of  the  telescope 
near  the  eyepiece  o  :  hence  it  is  termed  the  front-view  telescope.  As  the 
rays  in  this  telescope  only  undergo  a  single  reflection,  the  loss  of  light  is  less 
than  in  either  of  the  preceding  cases,  and  the  image  is  therefore  brighter. 


554  On  Light.  [601- 

The  magnifying  power  is  the  quotient  of  the  principal  focal  distance  of  the 
mirror  by  the  focal  distance  of  the  eyepiece. 

Herschel's  great  telescope  was  constructed  in  1789  ;   it  was  40  feet  in 
length,  the  great  mirror  was  50  inches  in  diameter.     The  quantity  of  light 

obtained  by  this  instru- 
ment was  so  great  as 
to  enable  its  inventor  to 
use  magnifying  powers 
far  higher  than  anything 
which  had  hitherto  been 
attempted. 

HerscheFs  telescope 
has  been  exceeded  by 
one  constructed  by  the 

late  Earl  of  Rosse.  This  magnificent  instrument  has  a  focal  distance  of  53 
feet,  the  diameter  of  the  spectrum  being  six  feet.  It  is  at  present  used  as 
a  Newtonian  telescope,  but  it  can  also  be  arranged  as  a  front-view  tele- 
scope. 


INSTRUMENTS   FOR    FORMING   PICTURES   OF   OBJECTS. 

602.  Camera  obscura. — The  camera  obscura  (dark  chamber)  is,  as  its 
name  implies,  a  closed  space  impervious  to  light.  There  is,  however,  a  small 
aperture  by  which  luminous  rays  enter,  as  shown  in  fig.  533.  The  rays  pro- 


ceeding from  external  objects,  and  entering  by  this  aperture,  form  on  the 
opposite  side  an  image  of  the  objects  in  their  natural  colours,  but  of  reduced 
dimensions,  and  in  an  inverted  position. 

Porta,  a  Neapolitan  physician,  the  inventor  of  this  instrument,  found  that 


-603] 


Camera  Lucida. 


555 


by  fixing  a  double  convex  lens  in  the  aperture,  and  placing  a  white  screen  in 
the  focus,  the  image  was  much  brighter  and  more  definite. 

Fig.  533  represents  a  camera  obscura,  such  as  is  used  for  drawing.  It 
consists  of  a  rectangular  wooden  box,  formed  of  two  parts  which  slide  in  and 
out.  The  luminous  rays  R  pass  into  the  box  through  a  lens  B,  and  form  an 
image  on  the  opposite  side  O,  which  is  at  the  focal  distance  of  the  lens. 
But  the  rays  are  reflected  from  a  glass  mirror  M,  inclined  at  an  angle  of  45°, 
and  form  an  image  on  the  ground -glass  plate  N.  When  a  piece  of  tracing- 
paper  is  placed  on  this  screen,  a  drawing  of  the  image  is  easily  made.  A 
wooden  door,  A,  cuts  off  extraneous  light. 

The  box  is  formed  of  two  parts,  sliding  one  within  the  other,  like  the 
joints  of  a  telescope,  so  that,  by  elongating  it  more  or  less,  the  reflected 
image  may  be  made  to  fall  exactly 
on  the  screen  N,  at  whatever  dis- 
tance the  object  may  be  situated. 

Fig.  534  shows  another  kind  of 
camera  obscura,  which  is  occasionally 
erected  in  summer-houses.  In  a 
brass  case,  A,  there  is  a  triangular 
prism,  P  (fig.  535),  which  acts  both 
.as  condensing  lens  and  as  mirror. 
One  of  its  faces  is  plane,  but  the 
others  have  such  curvatures  that  the 
combined  refractions,  on  entering 
and  emerging  from  the  prism,  pro- 
duce the  effect  of  a  meniscus  lens. 
Hence  rays  from  an  object  AB, 
after  passing  into  the  prism  and  un- 
dergoing total  reflection  from  the 
face  cd>  form  at  ab  a  real  image  of 
AB. 

In  fig.  534  the  small  table  B  corre- 
sponds to  the  focus  of  the  prism  in 
the  case  A,  and  an  image  forms 
on  a  piece  of  paper  placed  on  the 
table.  The  whole  is  surrounded  by 
a  black  curtain,  so  that  the  observer  can  place  himself  in  complete  dark- 
ness. 

603.  Camera  lucida. — The  camera  lucida  is  a  small  instrument  depend- 
ing on  internal  reflection,  and  serves  for  taking  an  outline  of  any  object.  It 
was  invented  by  Wollaston  in  1804.  It  consists  of  a  small  four-sided  glass 
prism,  of  which  fig.  536  gives  a  section  perpendicular  to  the  edges.  A  is  a 
right  angle,  and  C  an  angle  of  135° ;  the  other  angles,  B  and  D,  are  67 1°. 
The  prism  rests  on  a  stand,  on  which  it  can  be  raised  or  lowered,  and  turned 
more  or  less  about  an  axis  parallel  to  the  prismatic  edges.  When  the  face 
AB  is  turned  towards  the  object,  the  rays  from  the  object  fall  nearly  per- 
pendicular on  this  face,  pass  into  the  prism  without  any  appreciable  refrac- 
tion, and  are  totally  reflected  from  BC  ;  for  as  the  line  abis  perpendicular  to 
BC,  and  «L  to  AB,  the  angle  anL  will  equal  the  angle  B  ;  that  is,  it  will  con- 


Fig.  534- 


556 


On  Light. 


[603- 


tain  67^°,  and  this  being  greater  than  the  critical  angle  of  glass  (540),  the  ray 
Ln  will  undergo  total  reflection.  The  rays  are  again  totally  reflected  from 
o,  and  emerge  near  the  summit,  D,  in  a  direction  almost  perpendicular  to 
the  face  DA,  so  that  the  eye  which  receives  the  rays  sees  at  L'  an  image 
of  the  object  L.  If  the  outlines  of  the  image  are  traced  with  a  pencil,  a 
very  correct  design  is  obtained  ;  but  unfortunately 
there  is  a  great  difficulty  in  seeing  both  the  image 
and  the  point  of  the  pencil,  for  the  rays  from  the 
object  give  an  image  which  is  farther  from  the  eye 
than  the  pencil.  This  is  corrected  by  placing  be- 
tween the  eye  and  prism  a  lens,  I,  which  gives  to- 
the  rays  from  the  pencil  and  those  from  the  object 
the  same  divergence.  In  this  case,  however,  it  is 
necessary  to  place  the  eye  very  near  the  edge  of  the 
prism,  so  that  the  aperture  of  the  pupil  is  divided 
into  two  parts,  one  of  which  sees  the  image  and  the 
other  the  pencil. 

Amici's  camera  lucida,  represented  in  fig.  537,  is  preferable  to  that  of 
Wollaston,  inasmuch  as  it  allows  the  eye  to  change  its  position  to  a  con- 
siderable extent  without  ceasing  to  see  the  image  and  the  pencil  at  the 

same  time.  It  con- 
sists of  a  rectangular 
glass  prism  ABC, 
having  one  of  its 
perpendicular  faces 
turned  towards  the 

—    object  to  be  depicted, 
while  the  other  is  at 

right  angles  to  an  in- 
clined plate  of  glass,, 
mn.  The  rays  LI, 


proceeding  from  the 


object,  and  entering  the  prism,  are  totally  reflected  from  its  base  at  D,  and 
emerge  in  the  direction  KH.  They  are  then  partially  reflected  from  the 
glass  plate  mn  at  H,  and  form  a  vertical  image  of  the  object  L,  which  is 
seen  by  the  eye  in  the  direction  OL/.  The  eye  at  the  same  time  sees 
through  the  glass  the  point  of  the  pencil  applied  to  the  paper,  and  thus 
the  outline  of  the  picture  may  be  traced  with  great  exactness. 

604.  Magic  lantern.  —  This  is  an  apparatus  by  which  a  magnified  image 
of  small  objects  may  be  projected  on  a  white  screen  in  a  dark  room.  The 
best  is  the  sriopticon,  fig.  538.  The  box  C,  the  side  of  which  is  shown  re- 
moved, is  constructed  of  sheet  iron  ;  e  is  the  flame  of  a  lamp  V,  with  two  long 
flat  wicks,  fed  by  petroleum  from  the  reservoir  B.  The  box  is  airtight,  and 
the  chimney  F  producing  a  good  draught,  the  air  is  compelled  to  pass  through 
the  wicks,  by  which  smoke  and  smell  are  avoided,  and  a  flame  of  high 
illuminating  power  is  produced. 

The  ends  of  the  box  are  closed  by  glass  plates  i  and  /,.  G  is  a  hinged 
door,  and  on  its  inside  is  a  concave  mirror  ;  o  and  ot  are  two  plano-convex 
lenses  ;  p  a  spring  clamp,  in  which  is  placed  the  transparent  picture.  The: 


-605] 


Solar  Microscope. 


557 


sliding  piece  supports  the  lens  tube,  in   which  are  two  achromatic  lenses 
^  and  £,  the  fine  adjustment  of  which  is  effected  by  the  screw  S. 

The  rays  from  the  flame  £,  reinforced  by  the  reflection  from  G,  falling 
upon  the  lenses  o,  <?,,  are  made  parallel,  or,  at  all  events,  very  slightly  diver- 
gent ;  their  lenses  are  accordingly  called  the  condensing  lenses.  Passing 
through  the  object 
which  is  depicted  on 
the  slide  placed  in^, 
they  are  concentrated 
to  an  image  which  is 
received  on  a  screen. 
The  image  is  in- 
verted, and  hence,  if 
objects  are  to  be  seen 
in  their  erect  posi- 
tion, they  must  be 
drawn  inverted.  But 
ordinary  drawings 
are  easily  adjusted 
by  fixing  an  equila- 
teral rectangular  prism,  P  (fig.  539),  in 
front  of  the  lens  tube,  so  that  the  hypo- 
then  use  surface  is  horizontal.  The  parallel 
rays  falling  on  the  prism  are  inverted  in  /, 
consequence  of  refraction  at  the  sides  and 
total  reflection  from  the  hypothenuse  sur- 
face, so  that  an  upright  position  is  obtained 
instead  of  a  reverse  one.  The  dotted  lines 
abcde  vxi&fghik  give  the  path  of  two  rays. 

The  apparatus   can  be  used  for  pro- 


Fig.  538. 


Fig-  539- 


jecting  on  a  screen  not  only  flat  images,  but  also  simple  physical  experiments, 
such  as  the  expansion  of  a  liquid  in  a  thermometer,  the  divergence  of  the  gold 
leaves  of  an  electroscope,  and  so  forth. 

Dissolving  mews  are  obtained  by  arranging  two  magic  lanterns,  which 
are  quite  alike,  with  different  pictures,  in  such  a  manner  that  both  pictures 
are  produced  on  exactly  the  same  part  of  a  screen.  The  object-glasses  of 
both  lanterns  are  closed  by  shades,  which  are  so  arranged  that  according  as 
one  is  raised  the  other  is  lowered,  and  vice  versa.  In  this  way  one  picture 
is  gradually  seen  to  change  into  the  other. 

The  magnifying  power  of  the  magic  lantern  is  obtained  by  dividing  the 
distance  of  the  lens  from  the  image  by  its  distance  from  the  object.  If  the 
image  is  100  or  1,000  times  farther  from  the  lens  than  the  object,  the  image 
will  be  loo  or  1,000  times  as  large.  Hence  a  lens  with  a  very  short  focus 
can  produce  a  very  large  image,  provided  the  screen  is  sufficiently  large. 

605.  Solar  microscope. — The  solar  microscope  is  in  reality  a  magic 
lantern  illuminated  by  the  sun's  rays  ;  it  serves  to  produce  highly  magnified 
images  of  very  small  objects.  It  is  worked  in  a  dark  room  :  fig.  540  repre- 
sents it  fitted  in  the  shutter  of  a  room,  and  fig.  541  gives  the  internal  details. 

The  sun's  rays  fall  on  a  plane  mirror,  M,  placed  outside  the  room,  and 


558 


On  Light. 


[605- 


are  reflected  towards  a  condensing  lens,  /,  and  thence  to  a  second  lens,. 
o  (fig.  541),  by  which  they  are  concentrated  at  its  focus.  The  object  to  be 
magnified  is  at  this  point ;  it  is  placed  between  two  glass  plates,  which,  by 
means  of  a  spring,  «,  are  kept  in  a  firm  position  between  two  metal  plates,. 
m.  The  object  thus  strongly  illuminated  is  very  near  the  focus  of  a  sys- 


Fig.  540. 

tern  of  three  condensing  lenses,  x^  which  forms  upon  a  screen  at  a  suitable 
distance  an  inverted  and  greatly  magnified  image,  ab.  The  distance  of  the 
lenses  o  and  x  from  the  object  is  regulated  by  means  of  screws,  C  and  D. 

As  the  direction  of  the  sun's  light  is  continually  varying,  the  position  of 
the  mirror  outside  the  shutter  must  also  be  changed,  so  that  the  reflection  is 
always  in  the  direction  of  the  axis  of  the  microscope.  The  most  exact  appa- 


Fig.  541- 


ratus  for  this  purpose  is  the  heliostat  (534)  ;  but  as  this  instrument  is  very 
expensive,  the  object  is  usually  attained  by  inclining  the  mirror  to  a  greater 
or  less  extent  by  means  of  an  endless  screw  B,  and  at  the  same  time  turning 
the  mirror  itself  round  the  lens  /  by  a  knob  A,  which  moves  in  a  fixed  slide. 
The  solar  microscope  labours  under  the  objection  of  concentrating  great 


-606] 


Photo-electric  Microscope. 


559 


heat  on  the  object,  which  soon  alters  it.  This  is  partially  obviated  by  inter- 
posing a  layer  of  a  saturated  solution  of  alum,  which,  being  a  powerfully 
athermanous  substance  (434),  cuts  off  a  considerable  portion  of  the  heat. 

The  magnifying  power  of  the  solar  microscope  may  be  deduced  experi- 
mentally by  substituting  for  the  object  a  glass  plate  marked  with  lines  at  a 
distance  of  i  or  ^  of  a  millimetre.  Knowing  the  distance  of  these  lines  on 
the  image,  the  magnifying  power  may  be  calculated.  The  same  method  is 
used  with  the  photo-electric  light.  According  to  the  magnifying  power  which 


Fig.  542. 

it  is  desired  to  obtain,  the  objective  x  is  formed  of  one,  two,  or  three  lenses, 
which  are  all  achromatic. 

The  solar  microscope  furnishes  the  means  of  exhibiting  to  a  large  audience 
many  curious  phenomena,  such,  for  instance,  as  the  circulation  of  blood  in 
the  smaller  animals,  the  crystallisation  of  salts,  the  occurrence  of  minute 
organisms  in  water,  vinegar,  &c.  &c. 

606.  Photo-electric  microscope. — This  is  nothing  more  than  the  solar 
microscope  which  is  illuminated  by  the  electric  light  instead  of  by  the  sun's 
rays.  The  electric  light,  by  its  intensity,  its  steadiness,  and  the  readiness 
with  which  it  can  be  produced  at  any  time  of  the  day,  is  far  preferable  to  the 


56o  On  Light.  [606- 

solar  light.  The  photo-electric  microscope  alone  will  be  described  here  : 
the  electric  light  will  be  considered  under  the  head  of  Galvanism. 

Fig.  542  represents  the  arrangement  devised  by  Duboscq.  A  solar 
microscope,  ABD,  identical  with  that  already  described,  is  fixed  on  the 
outside  of  a  brass  box.  In  the  interior  are  two  charcoal  points  which  do 
not  quite  touch,  the  space  between  them  being  exactly  on  the  axis  of  the 
lenses.  The  electricity  of  one  end  of  a  powerful  battery  reaches  the  charcoal 
a  by  means  of  a  copper  wire  K  ;  while  the  electricity  from  the  opposite  end 
of  the  battery  reaches  c  by  a  second  copper  wire  H. 

During  the  passage  of  the  electricity  a  luminous  arc  is  formed  between 
the  two  ends  of  the  carbons,  which  gives  a  most  brilliant  light,  and  power- 
fully illuminates  the  microscope.  This  is  effected  by  placing  at  D  in  the 
inside  of  the  tube  a  condensing  lens,  whose  principal  focus  corresponds  to 
the  space  between  the  two  charcoals.  In  this  manner  the  luminous  rays 
which  enter  the  tubes  D  and  B  are  parallel  to  their  axis,  and  the  same 
effects  are  produced  as  with  the  ordinary  solar  microscope  ;  a  magnified 
image  of  the  object  placed  between  two  plates  of  glass  is  produced  on  the 
screen. 

In  continuing  the  experiment  the  two  carbons  become  consumed,  and 
to  an  unequal  extent,  a  more  quickly  than  c.  Hence,  their  distance  increasing, 
the  light  becomes  weaker,  and  is  ultimately  extinguished.  In  speaking 
afterwards  of  the  electric  light,  the  working  of  the  apparatus  P,  which  keeps 
these  charcoals  at  a  constant  distance,  and  thus  ensures  a  constant  light, 
will  be  explained. 

The  part  of  the  apparatus  MN  may  be  considered  as  a  universal  photo- 
genic apparatus.  The  microscope  can  be  replaced  by  the  headpieces  of  the 
phantasmagoria,  the  polyorama,  the  megascope,  by  polarising  apparatus,  &c., 
and  in  this  manner  is  admirably  adapted  for  exhibiting  optical  phenomena 
to  a  large  auditory.  Instead  of  the  electric  light,  we  may  use  with  this 
apparatus  the  oxyhydrogen  or  Drummond's  light,  which  is  obtained  by  heat- 
ing a  cylinder  of  lime  in  the  flame  produced  by  the  combustion  of  a  mixture 
of  hydrogen  or  of  coal  gas  with  oxygen  gas. 

607.  lighthouse  lenses. — Lenses  of  large  dimensions  are  very  difficult 
of  construction ;  they  further  produce  a  considerable  spherical  aberration, 
and  their  thickness  causes  the  loss  of  much  light.  In  order  to  avoid  these 
inconveniences,  echelon  lenses  have  been  constructed.  They  consist  of  a 
plano-convex  lens,  C  (figs.  543  and  544),  surrounded  by  a  series  of  annular 
and  concentric  segments,  A,  B,  each  of  which  has  a  plane  face  on  the  same 
side  as  the  plane  face  of  the  central  lens,  while  the  faces  on  the  other  side 
have  such  a  curvature  that  the  foci  of  the  different  segments  coincide  in  the 
same  point.  These  rings  form,  together  with  the  central  lens,  a  single  lens, 
a  section  of  which  is  represented  in  fig.  544.  The  drawing  was  made  from 
a  lens  of  about  2  feet  in  diameter,  the  segments  of  which  are  formed  of  a 
single  piece  of  glass  ;  but,  with  larger  lenses,  each  segment  is  likewise  formed 
of  several  pieces. 

Behind  the  lens  there  is  a  support  fixed  by  three  rods,  on  which  a  body 
can  be  placed  and  submitted  to  the  sun's  rays.  As  the  centre  of  the  support 
coincides  with  the  focus  of  the  lens,  the  substances  placed  there  are  melted 
and  volatilised  by  the  high  temperature  produced.  Gold,  platinum,  and 


-607] 


Lighthouse  Lenses. 


quartz  are  melted.  The  experiment  proves  that  heat  is  refracted  in  the  same 
way  as  light :  for  the  position  of  the  calorific  focus  is  identical  with  that  of 
the  luminous  focus. 

Formerly  parabolic  mirrors  were  used  in  sending  the  light  of  beacons 
and  lighthouses  to  great  distances,  but  they  have  been  supplanted  by  the 
use  of  lenses  of  the  above  construction.  In  most  cases  oil  is  used  in  a  lamp 
of  peculiar  construction,  which  gives  as  much  light  as  20  moderators.  The 
light  is  placed  in  the  principal  focus  of  the  lens,  so  that  the  emergent  rays 
form  a  parallel 
beam  (fig.  472), 
which  loses  in- 
tensity only  by 
absorption  in  the 
atmosphere,  and 
can  be  seen  at  a 
distance  of  above 
40  miles.  In  order 
that  all  points  of 
the  horizon  may 
be  successively 
illuminated,  the 
lens  is  continually 
moved  round  the 
lamp  by  a  clock- 
work motion,  the 
rate  of  which  va- 
ries with  differ- 
ent lighthouses. 
Hence,  in  different 
parts  the  light 
alternately  ap- 
pears and  disap- 
pears after  equal 
intervals  of  time. 
These  alternations 
serve  to  distin- 
guish lighthouses 
from  an  accidental 
fire  or  a  star.  By  Fig'  543' 

means,  too,  of  the  number  of  times  the  light  disappears  in  a  given  time,  and 
by  the  colour  of  the  light,  sailors  are  enabled  to  distinguish  the  lighthouses 
from  one  another,  and  hence  to  know  their  position. 

Of  late  years  the  use  of  the  electric  light  has  been  substituted  for  that 
of  oil  lamps.  A  description  of  the  apparatus  will  be  given  in  a  subsequent 
chapter. 


O  O 


562 


On  Light. 


[608- 


PHOTOGRAPHY. 

608.  Photography  is  the  art  of  fixing  the  images  of  the  camera  obscura 
on  substances  sensitive  to  light.  The  various  photographic  processes  may 
be  classed  under  three  heads  :  photography  on  metal,  photography  on  paper, 
and  photography  on  glass. 

Wedgwood  was  the  first  to  suggest  the  use  of  chloride  of  silver  in  fixing 
the  image,  and  Davy,  by  means  of  the  solar  microscope,  obtained  images  of 
small  objects  on  paper  impregnated  with  chloride  of  silver  ;  but  no  method 
was  known  of  preserving  the  images  thus  obtained,  by  preventing  the  further 
action  of  light.  Niepce,  in  1814,  obtained  permanent  images  of  the  camera 
by  coating  glass  plates  with  a  layer  of  a  varnish  composed  of  bitumen  dis- 
solved in  oil  of  lavender.  This  process  was  tedious  and  inefficient,  and  it 
was  not  until  1839  that  the  problem  was  solved.  In  that  year  Daguerre 
described  a  method  of  fixing  the  images  of  the  camera,  which,  with  the  sub- 
sequent improvements  of  Talbot  and  Archer,  has  rendered  the  art  of  photo- 
graphy one  of  the  most  marvellous  discoveries  ever  made,  whether  as  to  the 
beauty  and  perfection  of  the  results,  or  as  to  the  celerity  with  which  they  are 
produced. 

In  Daguerre's  process,  the  Dagucrrotype,  the  picture  is  produced  on  a 
plate  of  copper  coated  with  silver.  This  is  first  very  carefully  polished — an 
operation  on  which  much  of  the  success  of  the  subsequent  operations  depends. 
It  is  then  rendered  sensitive  by  exposing  it  to  the  action  of  iodine  vapour, 
which  forms  a  thin  layer  of  iodide  of  silver  on  the  surface.  The  plate  is  now 
fit  to  be  exposed  in  the  camera  ;  it  is  sensitive  enough  for  views  which  re- 
quire an  exposure  of  ten  minutes  in  the  camera,  but  when  greater  rapidity  is 
required,  as  for  portraits,  &c.,  it  is  further  exposed  to  the  action  of  an  accele- 
rator, such  as  bromine  or  hypobromite  of  calcium.  All  the  operations  must 
be  performed  in  a  room  lighted  by  a  candle,  or  by  the  daylight  admitted 
through  yellow  glass,  which  cuts  off  all  chemical  rays.  The  plate  is  preserved 

from  the  action  of  light  by 
placing  it  in  a  small  wooden 
case  provided  with  a  slide  on 
the  sensitive  side. 

The  third  operation  con- 
sists in  exposing  the  sensitive 
plate  to  the  action  of  light, 
placing  it  in  that  position  in 
the  camera  where  the  image 
is  produced  with  greatest 
delicacy.  For  photographic 
purposes  a  camera  obscura 
of  peculiar  construction  is 
used.  The  brass  tube  A  (fig. 
545)  contains  an  achromatic 
Flg'  545'  condensing  lens,  which  can 

be  moved  by  means  of  a  rackwork  motion,  to  which  is  fitted  a  milled  head 
U.     At  the  opposite  end  of  the  box  is  a  ground-glass  plate,  E,  which  slides 


-609] 


Photographs  on  Paper. 


563 


in  a  groove,  B,  in  which  the  case  containing  the  plate  also  fits.  The 
camera  being  placed  in  a  proper  position  before  the  object,  the  sliding  part 
of  the  box  is  adjusted  until  the  image  is  produced  on  the  glass  with  the 
utmost  sharpness  •  this  is  the  case  when  the  glass  slide  is  exactly  in  the 
focus.  The  final  adjustment  is  made  by  means  of  the  milled  head  D. 

The  glass  slide  is  then  replaced  by  the  case  containing  the  sensitive 
plate  ;  the  slide  which  protects  it  is  raised,  and  the  plate  exposed  for  a  time, 
the  duration  of  which  varies  in  different  cases,  and  can  only  be  hit  exactly 
by  great  practice.  The  plate  is  then  removed  to  a  dark  room.  No  change 
is  perceptible  to  the  eye,  but  those  parts  on  which  the  light  has  acted  have 
acquired  the  property  of  condensing  mercury  :  the  plate  is  next  placed 
in  a  box  and  exposed  to  the  action  of  mercurial  vapour  at  60  or  70  degrees. 

The  mercury  is  deposited  on  the  parts  affected,  in  the  form  of  globules 
imperceptible  to  the  naked  eye.  The  shadows,  or  those  parts  on  which 
the  light  has  not  acted,  remain  covered  with  the  layer  of  iodide  of  silver. 
This  is  removed  by  treatment  with  hyposulphite  of  sodium,  which  dis- 
solves iodide  of  silver  without  affecting  the  rest  of  the  plate.  The  plate  is 
next  immersed  in  a  solution  of  chloride  of  gold  in  hyposulphite  of  sodium, 
which  dissolves  the  silver,  while  some  gold  combines  with  the  mercury  and 
silver  of  the  parts  attacked,  and  greatly  increases  the  intensity  of  the  lustre. 

Hence  the  light  parts  of  the  image  are  those  on  which  the  mercury  has 
been  deposited,  and  the  shaded  those  on  which  the  metal  has  retained  its 
reflecting  lustre. 

Fig.  546  represents  a  section  of  the  camera  and  the  object-glass.  At  first 
it  consisted  of  a  double  convex  lens,  but  now  double  achromatic  lenses,  LI/, 


Fig.  546. 

are  used  as  object-glasses.  They  act  more  quickly  than  objectives  with  a 
single  lens,  have  a  shorter  focus,  and  can  be  more  easily  focussed  by  moving 
the  lens  L'  by  means  of  the  rack  and  pinion  D. 

609.  Photographs  on  paper. — In  Daguerre's  process,  which  has  just 
been  described,  the  images  are  produced  directly  on  metal  plates.  With 
paper  and  glass,  photographs  of  two  kinds  may  be  obtained  :  those  in  which 
an  image  is  obtained  with  reversed  tints,  so  that  the  lightest  parts  have  be- 
come the  darkest  on  paper,  and  vice  versd  ;  and  those  in  which  the  lights 
and  shades  are  in  their  natural  position.  The  former  are  called  negative 
and  the  latter  positive  pictures. 

A  negative  maybe  taken  either  on  glass  or  on  paper  ;  it  serves  to  produce 
a  positive  picture. 

002 


564  On  Light.  [609- 

Negatives  on  glass. — A  glass  plate  of  the  proper  size  is  carefully  cleaned 
and  coated  with  a  uniformly  thick  layer  of  collodion  impregnated  with  iodide 
of  potassium.  The  plate  is  then  immersed  for  about  a  minute  in  a  bath  of 
nitrate  of  silver  containing  30  grains  of  the  salt  in  an  ounce  of  water.  This 
operation  must  be  performed  in  a  dark  room.  The  plate  is  then  removed, 
allowed  to  drain,  and,  when  somewhat  dry,  placed  in  a  closed  flame,  and 
afterwards  exposed  in  the  camera,  for  a  shorter  time  than  in  the  case  of  a 
Daguerrotype.  On  removing  the  plate  to  a  dark  room  no  change  is  visible  ; 
but  on  pouring  over  it  a  solution  called  the  developer,  an  image  gradually 
appears.  The  principal  substances  used  for  developing  are  protosulphate 
of  iron  and  pyrogallic  acid.  The  action  of  light  on  iodide  of  silver  appears 
to  produce  some  molecular  change,  or  else  some  actual  chemical  decom- 
position, in  virtue  of  which  the  developers  have  the  property  of  reducing 
to  the  metallic  state  those  parts  of  the  iodide  of  silver  which  have  been  most 
acted  upon  by  the  light.  When  the  picture  is  sufficiently  brought  out,  water 
is  poured  over  the  plate,  in  order  to  prevent  the  further  action  of  the  deve- 
loper. The  parts  on  which  light  has  not  acted  are  still  covered  with  iodide 
of  silver,  which  would  be  affected  if  the  plate  were  now  exposed  to  the  light. 
It  is,  accordingly,  washed  with  solution  of  hyposulphite  of  sodium,  which  dis- 
solves the  iodide  of  silver  and  leaves  the  image  unaltered.  The  picture  is  then 
coated  with  a  thin  layer  of  spirit  varnish,  to  protect  it  from  mechanical  injury. 

When  once  the  negative  is  obtained,  it  may  be  used  for  printing  an  in- 
definite number  of  positive  pictures.  For  this  purpose  paper  is  impregnated 
with  chloride  of  silver,  by  immersing  it  first  in  solution  of  nitrate  of  silver  and 
then  in  one  of  chloride  of  sodium  ;  chloride  of  silver  is  thus  formed  on  the 
paper  by  double  decomposition.  The  negative  is  placed  on  a  sheet  of  this 
paper  in  a  copying  frame,  and  exposed  to  the  action  of  light  for  a  certain 
time.  The  chloride  of  silver  becomes  acted  upon — the  light  parts  of  the 
negative  being  most  affected,  and  the  dark  parts  least  so.  A  copy  is  thus 
obtained,  on  which  the  lights  of  the  negative  are  replaced  by  shades,  and 
inversely.  In  order  to  fix  the  picture  it  is  washed  in  a  solution  of  hyposul- 
phite of  sodium,  which  dissolves  the  unaltered  chloride  of  silver.  The  pic- 
ture is  afterwards  immersed  in  a  bath  of  chloride  of  gold,  which  gives  it  tone. 

610.  Positives  on  glass. — Very  beautiful  positives  are  obtained  by  pre- 
paring the  plates  as  in  the  preceding  cases ;  the  exposure  in  the  camera, 
however,  is  not  nearly  so  long  as  for  the  negatives.     The  picture  is  then 
developed  by  pouring  over  it  a  solution  of  protosulphate  of  iron,  which  pro- 
duces a  negative  image  ;  and  by  afterwards  pouring  a  solution  of  cyanide  of 
potassium  over  the  plate,  this  negative  is  rapidly  converted  into  a  positive. 
It  is  then  washed  and  dried,  and  a  coating  of  varnish  poured  over  the  picture. 

611.  Photographs  on  albumenised  paper  and  glass. — In  some  cases, 
paper  impregnated  with  a  solution  of  albumen  containing  iodide  of  potassium 
is  used  instead  of  collodion,  over  which  it  has  the  advantage  that  it  can  be 
prepared  for  some  time  before  it  is  used,  and  that  it  produces  certain  effects 
in  the  middle  tints.     It  has  the  disadvantage  of  not  being  nearly  so  sensitive. 
It  requires,  therefore,  longer  exposure,  and  is  unsuitable  for  portraits,  but  in 
some  cases  can  be  advantageously  used  for  views. 


-612] 


Structure  of  the  Human  Eye. 


565 


CHAPTER   VI. 

THE   EYE   CONSIDERED   AS   AN   OPTICAL   INSTRUMENT. 

\  612.  Structure  of  the  human  eye. — The  eye  is  the  organ  of  vision  ; 
that  is  to  say,  of  the  phenomenon  by  virtue  of  which  the  light  emitted 
or  reflected  from  bodies  excites  in  us  the  sensation  which  reveals  their 
presence. 

The  eye  is  placed  in  a  bony  cavity  called  the  orbit ;  it  is  maintained 
in  its  position  by  the  muscles  which  serve  to  move  it,  by  the  optic  nerve, 
the  conjunctiva,  and  the  eyelids. 
Its  size  is  much  the  same  in  all 
persons  ;  it  is  the  varying  aper- 
ture of  the  eyelids  that  makes 
the  eye  appear  larger  or  smaller. 

Fig.  547  represents  a  trans- 
verse section  of  the  eye  from 
back  to  front.  The  general 
shape  is  that  of  a  spheroid,  the 
curvature  of  which  is  greater  in 
the  anterior  than  in  the  poste- 
rior part.  It  is  composed  of  the 
following  parts  :  the  cornea,  the 
sclerotica,  the  iris,  the  pupil, 
the  aqueous  humour,  the  crys- 
talline, the  vitreous  body,  the 
hyaloid  membrane,  the  choroid,  the  retina,  and  the  optic  nerve. 

Cornea. — The  cornea,  a,  is  a  transparent  membrane  situated  in  front  of 
the  ball  of  the  eye.  In  shape  it  resembles  a  small  watch-glass,  and  it  fits 
into  the  sclerotica,  i ;  in  fact,  these  membranes  are  so  connected  that  some 
anatomists  have  considered  them  as  one  and  the  same,  and  have  distin- 
guished them  by  calling  the  cornea  the  transparent,  and  the  sclerotica  the 
opaque  cornea. 

Sclerotica. — The  sclerotica,  i,  or  sclerotic  coat,  is  a  membrane  which, 
together  with  the  cornea,  envelops  all  parts  of  the  eye.  In  front  there  is 
an  almost  circular  aperture,  into  which  the  cornea  fits ;  a  perforation  behind 
gives  passage  to  the  optic  nerve. 

Iris. — The  iris,  d,  is  an  annular,  opaque  diaphragm,  placed  between  the 
cornea  and  the  crystalline  lens.  It  constitutes  the  coloured  part  of  the  eye, 
and  is  perforated  by  an  aperture  called  the /&/*'/,  which  in  man  is  circular. 
In  some  animals,  especially  those  belonging  to  the  genus  Felis^  it  is  narrow 
and  elongated  in  a  vertical  direction  ;  in  the  ruminants  it  is  elongated  in  a 


566  On  Light.  [612- 

transverse  direction.  It  is  a  contractile  membrane,  and  its  diameter  varies 
in  the  same  individual  between  0-12  and  0-28  of  an  inch  ;  but  these  limits 
may  be  exceeded.  The  luminous  rays  pass  into  the  eye  through  the  pupil. 
The  pupil  enlarges  in  darkness,  but  contracts  under  the  influence  of  a  bright 
light.  These  alternations  of  contraction  and  enlargement  take  place  with 
extreme  rapidity  ;  they  are  very  frequent,  and  play  an  important  part  in  the 
act  of  vision.  The  movements  of  the  iris  are  involuntary. 

It  appears  from  this  description  that  the  iris  is  a  screen  with  a  variable 
aperture,  whose  function  is  to  regulate  the  quantity  of  light  which  penetrates 
into  the  eye  ;  for  the  size  of  the  pupil  diminishes  as  the  intensity  of  light 
increases.  The  iris  serves  also  to  correct  the  spherical  aberration,  as  it 
prevents  the  marginal  rays  from  passing  through  the  edges  of  the  crystalline 
lens.  It  thus  plays  the  same  part  with  reference  to  the  eye  that  a  stop  does 
in  optical  instruments  (558). 

Aqueous  humour. — Between  the  posterior  part  of  the  cornea  and  the 
front  of  the  crystalline  there  is  a  transparent  liquid  called  the  aqueous 
humour.  The  space,  e,  occupied  by  this  humour  is  divided  into  two  parts 
by  the  iris ;  the  part  b,  between  the  cornea  and  the  iris,  is  called  the  anterior 
chamber ;  the  part  c,  which  is  between  the  iris  and  the  crystalline,  is  the 
posterior  chamber. 

Crystalline  lens. — This  is  a  double  convex  transparent  body  placed  im- 
mediately behind  the  iris,  the  inner  margin  of  which  is  in  contact  with 
its  anterior  surface,  though  not  attached  to  it.  The  lens  is  enclosed  in  a 
transparent  membrane,  called  its  capsule  it  is  less  convex  on  its  anterior 
than  on  its  posterior  surface,  and  is  composed  of  almost  concentric  layers, 
which  decrease  in  density  and  refracting  power  from  the  centre  to  the 
circumference. 

To  the  anterior  surface  of  the  capsule,  near  its  margin,  is  fixed  a  firm 
transparent  membrane,  which  is  attached  behind  to  the  front  of  the  hyaloid 
membrane,  and  is  known  as  the  suspensory  ligament.  This  ligament  exerts 
attraction,  all  round,  on  the  front  surface  of  the  lens,  and  renders  it  less 
convex  than  it  would  otherwise  be,  and  its  relaxation  plays  an  important 
part  in  the  adaptation  of  the  eye  for  sight  at  different  distances. 

Vitreous  body.  Hyaloid  membrane. — The  vitreous  body,  or  vitreous 
humour,  is  a  transparent  mass  resembling  the  white  of  an  egg,  which  occu- 
pies all  the  part  of  the  ball  of  the  eye,  h,  behind  the  crystalline.  The  vitreous 
humour  is  surrounded  by  the  hyaloid  membrane,  /,  which  lines  the  posterior 
face  of  the  crystalline  capsule,  and  also  the  interior  face  of  another  mem- 
brane called  the  retina. 

Retina.  Optic  nerve. — The  retina,  ;;/,  is  a  membrane  which  receives  the 
impression  of  light,  and  transmits  it  to  the  brain  by  the  intervention  of  a 
nerve,  n,  called  the  optic  nerve,  which,  proceeding  from  the  brain,  enters  the 
eye  from  behind,  rather  to  the  inner  side  of  its  posterior  hemisphere,  and 
extends  over  the  retina  in  the  form  of  a  nervous  network.  The  nerve-fibres 
themselves  are  not  sensitive  to  light,  but  are  only  stimulated  by  it  indirectly 
through  the  intervention  of  certain  structures  called  the  rods  and  cones. 
The  rods  are  slender  cylinders  ;  the  cones  or  bulbs  somewhat  thicker  flask- 
shaped  structures.  All  are  ranged  perpendicular  to  the  surface  of  the 
retina,  closely  packed  together  so  as  to  form  a  regular  mosaic  layer  behind  it. 


-614]  Dimensions  of  Parts  of  the  Human  Eye.  567 

Each  rod  is  connected  with  one  of  the  minutest  nerve-fibres,  each  cone  with 
one  somewhat  thicker.  This  layer  of  rods  and  cones  has  been  proved  to  be 
the  really  sensitive  layer  of  the  retina,  the  structure  in  which  alone  the  action 
of  light  is  capable  of  producing  nervous  excitation. 

In  the  retina  is  a  remarkable  spot  which  is  placed  near  its  centre,  a  little 
to  the  outer  side,  and  from  its  colour  is  called  the  yellow  spot.  The  retina 
is  here  somewhat  thick,  but  in  the  middle  of  the  yellow  spot  is  found  a 
depression,  \hefovea  centralis,  where  the  retina  is  reduced  to  those  elements 
alone  which  are  absolutely  necessary  for  exact  vision.  Thisfovea,  or  pit  of 
the  retina,  is  of  great  importance  for  vision,  since  it  is  the  spot  where  the 
most  exact  discrimination  of  distance  is  made.  Only  those  parts  of  the 
retinal  image  which  fall  on  the  yellow  spot  are  sharp,  all  the  rest  are  more 
inaccurate  the  nearer  they  fall  to  the  limits  of  the  retina.  The  field  of  view 
of  the  eye  is  like  a  drawing  the  centre  of  which  is  done  with  great  accuracy 
and  delicacy  while  the  surrounding  part  is  only  roughly  sketched.  Where 
the  optic  nerve  enters  there  are  no  rods  or  cones  ;  this  part  of  the  retina, 
therefore,  is  insensitive  to  light,  and  is  called  the  punctum  ccecum. 

The  only  property  of  the  retina  and  optic  nerve  is  that  of  receiving  and 
transmitting  to  the  brain  the  impression  of  objects.  These  organs  have  been 
cut  and  pricked  without  causing  any  pain  to  the  animals  submitted  to  these 
experiments  ;  but  there  is  reason  to  believe  that  irritation  of  the  optic  nerve 
causes  the  sensation  of  a  flash  of  light. 

Choroid. — The  choroid,  k,  is  a  membrane  between  the  retina  and  the 
sclerotica.  It  is  completely  vascular,  and  is  covered  on  the  internal  face 
with  a  black  substance  which  resembles  the  colouring  matter  of  a  negro's 
skin,  and  which  absorbs  all  rays  not  intended  to  co-operate  in  producing 
vision. 

The  choroid  elongates  in  front,  and  forms  a  series  of  convoluted  folds, 
called  ciliary  processes,  which  penetrate  between  the  iris  and  the  crystalline 
capsule  to  which  they  adhere,  forming  round  it  a  disc,  resembling  a  radiated 
flower.  By  its  vascular  tissue  the  choroid  serves  to  carry  the  blood  into  the 
iru^rior  of  the  eye,  and  especially  to  the  ciliary  processes. 
X  613.  Refractive  indices  of  the  transparent  media  of  the  eye. — The 
refractive  indices  from  air  into  the  transparent  parts  of  the  eye  were  deter- 
mined by  Brewster.  His  results  are  contained  in  the  following  table,  com- 
pared with  water  as  a  standard  :  — 

Water  ....  .  ....  13358 

Aqueous  humour .         .  .  I  '3366 

Vitreous  humour ....  .         .         .         .  I  '3394 

Exterior  coating  of  the  crystalline        .  .         .  1-3767 

Centre  of  the  crystalline        ...  .         .         .  i  -3990 

Mean  refraction  of  the  crystalline        .....  i  '3839 

,/"*- 
'    614.  Curvatures  and  dimensions  of  various  parts  of  the  human  eye. 

Radius  of  curvature  of  the  sclerotica     .....  0^40  to  0-44  in. 

„  „.  cornea 0-28  to  0-32  „ 

„  „  anterior  face  of  the  crystalline    .  0*28  to  0-40  „ 

i,  „  posterior  face  of  the  crystalline  .  0-20  to  0-24  „ 


568  On  Lio-ht,  [614- 

Diameter  of  the  iris 0-44  to  0-48  in, 

i>  »         pupil    .  .     0-12  to  0-28  „ 

„  „         crystalline    .  .       ,  ..;  ,  ^  :  0-40,, 

Thickness  of  the  crystalline 0-20 

Distance  from  the  pupil  to  the  cornea  ...  ,  .-<  •  ,  0-08  „ 

Length  of  the  axis  of  the  eye         .         .         .  ...  crSS  to  0-96  „ 

615.  Path  of  rays  in  the  eye. — From  what  has  been  said  as  to  the 
structure  of  the  eye,  it  may  be  compared  to  a  camera  obscura  (602),  of  which 
the  pupil  is  the  aperture,  the  crystalline  is  the  condensing  lens,  and  the 
retina  is  the  screen  on  which  the  image  is  formed.  Hence,  the  effect  is  the 
same  as  when  the  image  of  an  object  placed  in  front  of  a  double  convex  lens 
is  formed  at  its  conjugate  focus.  Let  AB  (fig.  548)  be  an  object  placed 
before  the  eye,  and  let  us  consider  the  rays  emitted  from  any  point  of  the 
object  A.  Of  all  these  rays,  those  which  are  directed  towards  the  pupil  are 
the  only  ones  which  penetrate  the  eye,  and  are  operative  in  producing  vision. 
These  rays,  on  passing  into  the  aqueous  humour,  experience  a  first  refraction 
which  brings  them  near  the  secondary  axis  Aa  drawn  through  the  optic  centre 
of  the  crystalline ;  they  then  traverse  the  crystalline,  which  again  refracts  them 
like  a  double  convex  lens,  and,  having  experienced  a  final  refraction  by  the 


Fig.  548. 

vitreous  humour,  they  meet  in  a  point  a,  and  form  the  image  of  the  point  A. 
The  rays  issuing  from  the  point  B  form  in  like  manner  an  image  of  it  at  the 
point  £,  so  that  a  very  small,  real,  and  inverted  image  is  formed  exactly  on 
the  retina,  provided  the  eye  is  in  its  normal  condition. 

X  616.  Inversion  of  images. — In  order  to  show  that  the  images  formed 
on  the  retina  are  really  inverted,  the  eye  of  an  albino  or  any  animal  with 
pink  eyes  may  be  taken  ;  this  has  the  advantage  that,  as  the  choroid  is 
destitute  of  pigment,  light  can  traverse  it  without  loss.  This  is  then  deprived 
at  its  posterior  part  of  the  cellular  tissue  surrounding  it,  and  fixed  in  a  hole 
in  the  shutter  of  a  dark  room  ;  by  means  of  a  lens  it  may  be  seen  that  the 
inverted  images  of  external  objects  are  depicted  on  the  retina. 

The  inversion  of  images  in  the  eye  has  greatly  occupied  both  physicists 
and  physiologists,  and  many  theories  have  been  proposed  to  explain  how  it 
is  that  we  do  not  see  inverted  images  of  objects.  The  chief  difficulty  seems 
to  have  arisen  from  the  conception  of  the  mind  or  brain  as  something 
behind  the  eye,  looking  into  it,  and  seeing  the  image  upon  the  retina  ; 
whereas  really  this  image  simply  causes  a  stimulation  of  the  optic  nerve, 
which  produces  some  molecular  change  in  some  part  of  the  brain  ;  and  it  is 
only  of  this  change,  and  not  of  the  image  as  such,  that  we  have  any  conscious- 
ness. The  mind  has  thus  no  direct  cognisance  of  the  image  upon  the  retina, 


-618]        Estimation  of  the  Distance  and  Size  of  Objects.  569 

nor  of  the  relative  positions  of  its  parts,  and,  sight  being  supplemented  by 
touch  in  innumerable  cases,  it  learns  from  the  first  to  associate  the  sensations 
brought  about  by  the  stimulation  of  the  retina  (although  due  to  an  inverted 
image)  with  the  correct  position  of  the  object  as  taught  by  touch. 

(617.  Optic  axis,  optic  angle,  visual  angle — The  principal  optic  axis 
of  an  eye  is  the  axis  of  its  figure  ;  that  is  to  say,  the  straight  line  in  reference 
to  which  it  is  symmetrical.  In  a  well-shaped  eye  it  is  the  straight  line  passing 
through  the  centre  of  the  pupil  and  of  the  crystalline.  The  lines  A<z,  B£, 
are  secondary  axes.  The  eye  sees  objects  most  distinctly  in  the  direction 
of  the  principal  optic  axis. 


Fig.  549- 

The  optic  angle  is  the  angle  BAG  (fig.  549),  formed  between  the  principal 
optic  axes  of  the  two  eyes  when  they  are  directed  towards  the  same  point. 
This  angle  is  smaller  in  proportion  as  the  objects  are  more  distant. 

The  visual  angle  is  the  angle  AOB  (fig.  5  50),  under  which  an  object  is  seen  ; 
that  is  to  say,  the  angle  formed  by  the  secondary  axes  drawn  from  the  optic 
centre  of  the  crystalline  to  the  opposite  extremities  of  the  object.  For  the 
same  distance,  this  angle  increases  with  the  magnitude  of  the  object,  and  for 
the  same  object  it  decreases  as  the  distance  increases,  as  is  the  case  when 


the  object  passes  from  AB  to  A'B'.  It  follows,  therefore,  that  objects  appear 
smaller  in  proportion  as  they  are  more  distant  ;  for  as  the  secondary  axes,  AO, 
BO,  cross  in  the  centre  of  the  crystalline,  the  size  of  the  image  projected  on 
the  retina  depends  on  the  size'  of  the  visual  angle  AOB. 

\  6 1 8.  Estimation  of  the  distance  and  size  of  objects. — The  estimation 
of  distance  and  of  size  depends  on  numerous  circumstances  ;  these  are — the 
visual  angle,  the  optic  angle,  the  comparison  with  objects  whose  size  is 
familiar  to  us  ;  to  these  must  be  added  the  effect  of  what  is  called  aerial 
perspective;  that  is,  a  more  or  less  vaporous  medium  which  enshrouds  the 
distant  objects,  and  thereby  diminishes  not  -only  the  sharpness  of  the  out- 
lines, but  also  softens  the  contrast  between  light  and  shade,  which  close  at 
hand  are  marked. 

When  the  size  of  an  object  is  known,  as  the  figure  of  a  man,  the  height 


5/0  On  Light.  [618- 

of  a  tree  or  of  a  house,  the  distance  is  estimated  by  the  magnitude  of  the 
visual  angle  under  which  it  is  seen.  If  its  size  is  unknown,  it  is  judged 
relatively  to  that  of  objects  which  surround  it. 

A  colonnade,  an  avenue  of  trees,  the  gas-lights  on  the  side  of  a  road, 
appear  to  diminish  in  size  in  proportion  as  their  distance  increases,  because 
the  visual  angle  decreases  ;  but  the  habit  of  seeing  the  columns,  trees,  &c., 
in  their  proper  height,  leads  our  judgment  to  rectify  the  impression  produced 
by  vision.  Similarly,  although  distant  mountains  are  seen  under  a  very 
small  angle,  and  occupy  but  a  small  space  in  the  field  of  view,  our  familiarity 
with  the  effects  of  aerial  perspective  enables  us  to  form  a  correct  idea  of 
their  real  magnitude. 

The  optic  angle  is  also  an  essential  element  in  appreciating  distance. 
Since  this  angle  increases  or  diminishes  according  as  objects  approach  or 
recede,  we  move  our  eyes  so  as  to  make  their  optic  axes  converge  towards 
the  object  which  we  are  looking  at,  and  thus  obtain  an  idea  of  its  distance. 
Nevertheless,  it  is  only  by  long  custom  that  we  can  establish  a  relation 
between  our  distance  from  the  objects,  and  the  corresponding  motion  of  the 
eyes.  It  is  a  curious  fact  that  persons  born  blind,  and  whose  sight  has  been 
restored  by  the  operation  for  cataract,  imagine  at  first  that  all  objects  are  at 
the  same  distance. 

Vertical  distances  are  estimated  too  low  compared  with  horizontal  ones ; 
on  high  mountains  and  over  large  surfaces  of  water,  distances  are  estimated 
too  low  owing  to  the  want  of  intervening  objects.  A  room  filled  with  furni- 
ture appears  larger  than  an  empty  room  of  the  same  size. 

We  cannot  recognise  the  true  form  of  an  object  if,  with  moderate  illu- 
mination, the  visual  angle  is  less  than  half  a  minute.  A  white  square,  a 
metre  in  the  side,  appears  at  a  distance  of  about  5  miles  under  this  angle  as 
a  bright  spot  which  can  scarcely  be  distinguished  from  a  circle  of  the  same 
size. 

A  very  bright  object,  however,  such  as  an  incandescent  platinum  wire, 
is  seen  in  a  dark  ground  under  an  angle  of  2  seconds.  So  too  a  small  dark 
object  is  seen  against  a  bright  ground  ;  thus  a  hair  held  against  the  sky  can 
bg  seen  at  a  distance  of  i  or  2  metres. 

Y  619.  Distance  of  distinct  vision. — The  distance  of  distinct  vision,  as 
already  stated  (587),  is  the  distance  at  which  objects  must  be  placed  so  as  to 
be  seen  with  the  greatest  distinctness.  It  varies  in  different  individuals,  and 
in  the  same  individual  it  is  often  different  in  the  two  eyes.  For  small  objects, 
such  as  print,  it  is  from  10  to  12  inches  in  normal  cases. 

In  order  to  obtain  an  approximate  measurement  of  the  least  distance  of 
distinct  vision,  two  small  parallel  slits  are  made  in  a  card  at  a  distance  of 
O'O3  of  an  inch.  These  apertures  are  held  close  before  the  eye,  and  when 
a  fine  slit  in  another  card  is  held  very  near  them,  the  slit  is  seen  double,  be- 
cause the  rays  of  light  which  have  traversed  both  apertures  do  not  intersect 
each  other  on  the  retina,  but  behind  it.  But,  if  the  latter  card  is  gradually 
removed,  the  distance  is  ultimately  reached  at  which  both  images  coincide 
and  form  one  distinct  image.  This  is  the  distance  of  distinct  vision. 
Stampfer  constructed  an  optomctcr  on  the  principle  of  this  experiment,  which 
is  known  as  Schemer's  experiment. 

Persons   who   see   distinctly  only  at  a  very  short   distance   are   called 


—620]  Accommodation.  571 

myoptic,  or  short-sighted^  and  those  who  see  only  at  a  long  distance  are 
presbyoptic,  or  long-sighted  (629). 

Sharpness  of  sight  may  be  compared  by  reference  to  that  of  a  normal 
eye  taken  as  a  unit.  Such  a  standard  eye,  according  to  Snellen,  recog- 
nises quadrangular  letters  when  they  are  seen  under  an  angle  of  5' ;  if,  for 
instance,  such  letters  are  15  mm.  high  at  a  distance  of  10  metres.  The  sharp- 
ness of  vision  of  one  who  recognises  these  letters  at  a  distance  of  3  metres 

is  then  A. 

/if        I0 

'    620.  Accommodation. — By  this  term  is  meant  the  changes  which  occur 
in  the  eye  to  fit  it  for  seeing  distinctly  objects  at  different  distances  from  it. 

If  the  eye  be  supposed  fixed  and  its  parts  immovable,  it  is  evident  that 
there  could  only  be  one  surface  whose  image  would  fall  exactly  upon  the 
retina ;  the  distance  of  this  surface  from  the  eye  being  dependent  on  the 
refractive  indices  of  the  media  and  the  curvatures  of  the  refracting  surfaces 
of  the  eye.  The  image  of  any  point  nearer  the  eye  than  this  distinctly  seen 
surface  would  fall  behind  the  retina  ;  the  image  of  any  more  distant  point 
would  be  formed  in  front  of  it ;  in  each  case  the  section  of  a  luminous  cone 
would  be  perceived  instead  of  the  image  of  the  point,  and  the  latter  would 
appear  diffused  and  indistinct. 

Experience,  however,  shows  us  that  a  normal  eye  can  see  distinct  images 
of  objects  at  very  different  distances.  We  can,  for  example,  see  a  distant 
tree  through  a  window,  and  also  a  scratch  on  the  pane,  though  not  both  dis- 
tinctly at  the  same  moment ;  for  when  the  eye  is  arranged  to  see  one  clearly, 
the  image  of  the  other  does  not  fall  accurately  upon  the  retina.  An  eye 
completely  at  rest  seems  adapted  for  seeing  distant  objects  ;  the  sense  of 
effort  is  greater  in  a  normal  eye  when  a  near  object  is  looked  at,  after  a 
distant  one,  than  in  the  reverse  case  ;  and  in  paralysis  of  the  nerves  govern- 
ing the  accommodating  apparatus,  the  eye  is  persistently  adapted  for  distant 
sight.  There  must,  therefore,  be  some  mechanism  in  the  eye  by  which  it 
can  be  voluntarily  altered,  so  that  the  more  divergent  rays  proceeding  from 
near  objects  shall  come  to  a  focus  upon  the  retina.  There  are  several  con- 
ceivable methods  by  which  this  might  be  effected  ;  it  is  actually  brought 
about  by  a  drawing  forwards  of  the  crystalline  lens  and  a  greater  convexity 
.  of  its  front  surface. 

NLX^This  is  shown  by  the  following  experiment  : — If  a  candle  be  placed  on  one 
•^  "side  of  the  eye  of  a  person  looking  at  a  distant  object,  and  his  eye  be  observed 
from  tfre  other  side,  three  distinct  images  of  the  flame  will  be  seen ;  the  first 
virtual  and  erect,  is  reflected  from  the  anterior  surface  of  the  cornea  ;  the 
next,  erect  and  less  bright,  is  reflected  from  the  anterior  surface  of  the  lens  ; 
the  third,  inverted  and  brilliant,  is  formed  on  the  posterior  surface  of  the  lens. 
If  now  the  person  look  at  a  near  object,  no  change  is  observed  in  the  first 
and  third  images,  but  the  second  image  becomes  smaller  and  approaches  the 
first ;  which  shows  that  the  anterior  surface  of  the  crystalline  lens  becomes 
more  convex  and  approaches  the  cornea.  In  place  of  the  candle,  Helmholtz 
throws  light  through  two  holes  in  the  screen  upon  the  eye,  and  observes  the 
distance  on  the  eye  between  the  two  shining  points,  instead  of  the  size  of  the 
flame  of  the  candle. 

This  change  in  the  lens  is  effected  chiefly  by  means  of  a  circular  muscle 


572  On  Light.  [620- 

(ciliary  muscle),  the  contraction  of  which  relaxes  the  suspensory  ligament, 
and  so  allows  the  front  surface  of  the  lens  to  assume  more  or  less  of  that 
greater  convexity  which  it  would  normally  exhibit  were  it  not  for  the  drag 
exercised  upon  it  by  the  ligament.  Certain  other  less  important  changes 
occur,  tending  to  make  the  lens  more  convex  and  to  push  it  forwards,  which 
cannot,  however,  be  explained  without  entering  into  minute  anatomical 
details.  When  the  eye  is  accommodated  for  near  vision,  the  pupil  contracts 
and  so  partially  remedies  the  greater  spherical  aberration. 

The  range  of  accommodation^  called  by  Bonders  — ,  is  measured  by 

A 

first  of  all  determining  the  greatest  distance,  R,  at  which  a  person  can 
read  without  spectacles,  and  then  the  smallest,  P,  at  which  he  can  so  read  ; 

X-P-* 

621.  Binocular  vision. — A  single  eye  sees  most  distinctly  any  point 
situated  on  its  optical  axis,  and  less  distinctly  other  points  also,  towards 
which  it  is  not  directly  looking,  but  which  are  still  within  its  circle  of  vision. 

It  is  able  to  judge  of  the  direction  of  any  such  point,  but  unable  by  itself 
to  estimate  its  distance.  Of  the  distance  of  an  object  it  may,  indeed,  learn 
to  judge  by  such  criteria  as  loss  of  colour,  indistinctness  of  outline,  decrease 
in  magnitude,  &c. ;  but  if  the  object  is  near,  the  single  eye  is  not  infallible, 
even  with  these  aids. 

When  the  two  eyes  are  directed  upon  a  single  point,  we  then  gain  the 
power  of  judging  of  its  distance  as  compared  with  that  of  any  other  point, 
and  this  we  seem  to  gain  by  the  sense  of  greater  or  less  effort  required  in 
causing  the  optical  axis  to  converge  upon  the  one  point  or  upon  the  other. 
Now  a  solid  object  may  be  regarded  as  composed  of  points  which  are  at  dif- 
ferent distances  from  the  eye.  Hence,  in  looking  at  such  an  object,  the  axes 
of  the  two  eyes  are  rapidly  and  insensibly  varying  their  angle  of  converg- 
ence, and  we  as  rapidly  are  gaining  experience  of  the  difference  in  distance 
of  the  various  points  of  which  the  object  is  composed,  or,  in  other  words,  an 
assurance  of  its  solidity.  Such  kind  of  assurance  is  necessarily  unattainable 
in  monocular  vision. 

622.  The  principle  of  the  stereoscope. — Let  any  solid  object,  such  as 
a  small  box,  be  supposed  to  be  held  at  some  short  distance  in  front  of  the 
two  eyes.     On  whatever  point  of  it  they  are  fixed,  they  will  see  that  point 
the  most  distinctly,  and  other  points  more  or  less  clearly.     But  it  is  evident 
that,  as  the  two  eyes  see  from  different  points  of  view,  there  will  be  formed 
in  the  right  eye  a  picture  of  the  object  different  from  that  formed  in  the  left ; 
and  it  is  by  the  apparent  union  of  these  two  dissimilar  pictures  that  we  see 
the  object  in  relief.     If,  therefore,  we  delineate  the  object,  first  as  seen  by 
the  right  eye,  and  then  as  seen  by  the  left,  and  afterwards  present  these  dis- 
similar pictures  again  to  the  eyes,  taking  care  to  present  to  each  eye  that 
picture  which  was  drawn  from  its  point  of  view,  there  would  seem  to  be  no 
reason  why  we  should  not  see  a  representation  of  the  object,  as  we  saw  the 
object  itself,  in  relief.     Experiment  confirms  the  supposition.     If  the  object 
held  before  the  eyes  were  a  truncated  pyramid,  r,  and  /,  fig.  551,  would  re- 
present its  principal  lines,  as  seen  by  the  right  and  left  eyes  respectively.     If 
a  card  be  held  between  the  figures,  and  they  are  steadily  looked  at,  r  by  the 


-623] 


The  Reflecting  Stereoscope. 


573 

right  eye,  and  /  simultaneously  by  the  left,  for  a  few  seconds,  there  will  be 
seen  a  single  picture  having  the  unmistakable  appearance  of  relief.     Even 


Fig.  SSL 

without  a  card  interposed,  the  eye,  by  a  little  practice,  may  soon  be  taught 

so  to  combine  the  two  as  to  form  this  solid  picture.     Three  pictures  will  in 

that  case  be  seen,  the  central  being  solid,  and  the  two  outside  ones  plane. 

Fig.  552  will  explain  this.     Let  r  and  /  be  any  two  corresponding  points, 

say  the  points  marked  by  a  large  dot  in  the  figures  drawn  above  ;  R  and  L 

the  positions  of  the  right  and  left  eyes  ;  then  the 

right  eye  sees  the  point  r  in  the  direction  R<?,  and 

the  left  eye  the  point  /  in  the  direction  L<?,  and 

accordingly  each  by  itself  judging  only  by  the 

direction,  they  together  see  these  two  points  as 

one,  and  imagine  it  to  be  situated  at  o.     But  the 

right  eye,  though  looking  in  the  direction  Rr,  also 

receives  an  image  of  /  on  another  part  of  the 

retina,  and  the  left  eye  in  the  same  way  an  image 

of  r,  and  thus  three  images   are  seen.     A  card, 

however,  placed  in  the  position  marked  by  the 

dotted  line  will,  of  course,  cut  off  the  two  side 

pictures.     To  assist  the  eye  in  combining  such 

pairs  of  dissimilar  pictures,  both  mirrors  and  lenses 

have  been  made  use  of,  and  the  instruments  in 

which  either  of  these  are  adapted  to  this  end  are 

called  stereoscopes. 

623.  The  reflecting:  stereoscope. — In  the  reflecting  stereoscope  plane 
mirrors  are  used  to  change  the  apparent  position  of  the  pictures,  so  that  they 
are  both  seen  in  the  same  direction,  and  their  combination  by  the  eye  is 
thus  rendered  easy  and  almost  inevitable.  If  ab,  ab  (fig.  553)  are  two  plane 
mirrors  inclined  to  one  another  at  an  angle  of  90°,  the  two  arrows,  ;r,  y,  would 
both  be  seen  by  the  eyes  situated  at  R  and  L  in  the  position  marked  by  the 
dotted  arrow.  If,  instead  of  the  arrows,  we  now  substitute  such  a  pair  of 
dissimilar  pictures  as  we  have  spoken  of  above,  of  the  same  solid  object,  it 
is  evident  that,  if  the  margins  of  the  pictures  coincide,  other  corresponding 
points  of  the  pictures  will  not.  The  eyes,  however,  almost  without  effort, 
soon  bring  such  points  into  coincidence,  and  in  so  doing  make  them  appear 
to  recede  or  advance,  as  they  are  farther  apart  or  nearer  together  than  any 
two  corresponding  points  (the  right-hand  corner,  for  instance)  of  the  margins 


Fig.  552. 


574 


On  Light. 


[623- 


when  the  pictures  are  placed  side  by  side,  as  in  the  diagram,  fig.  553.  It  will 
be  plain,  also,  on  considering  the  position  for  the  arrows  in  fig.  553,  that  to 


x 


Fig.  553- 


Fig.  554- 


adapt  such  figures  as  those  in  fig.  552  for  use  in  a  reflecting  stereoscope  one 
of  them  must  be  reversed,  or  drawn  as  it  would  be  seen  through  the  paper 
if  held  up  to  the  light. 

624.  The  refracting-  stereoscope. — Since  the  rays  passing  through  a 
convex  lens  are  bent  always  towards  the  thicker  part  of  the  lens,  any  seg- 
ment of  such  a  lens  may  be  readily  adapted  to  change  the  apparent  position 
of  any  object  seen  through  it.  Thus,  if  (fig.  554)  two  segments  be  cut  from 
a  double  convex  lens,  and  placed  with  their  edges  together,  the  arrows,  x,  y, 
would  both  be  seen  in  the  position  of  the  dotted  arrow  by  the  eyes  at  R  and  L. 
If  we  substitute  for  the  arrows  two  dissimilar  pictures  of  the  same  solid 
object,  or  the  same  landscape,  we  shall  then,  if  a  diaphragm,  ab,  be  placed 
between  the  lenses  to  prevent  the  pictures  being  seen  crosswise  by  the  eyes, 
see  but  one  picture,  and  that  apparently  in  the  centre,  and  magnified.  As 
before,  if  the  margins  are  brought  by  the  power  of  the  lenses  to  coincide^ 
other  corresponding  points  will  not  be  coincident 
until  combined  by  an  almost  insensible  effort  of  the 
eyes.  Any  pair  of  corresponding  points  which  are 
farther  apart  than  any  other  pair  will  then  be  seen 
farther  back  in  the  picture,  just  as  any  point  in  the 
background  of  a  landscape  would  be  found  (if  we 
came  to  compare  two  pictures  of  the  landscape,  one 
drawn  by  the  right  eye,  and  the  other  by  the  left)  to 
be  represented  by  two  points  farther  apart  from  one 
another  than  two  others  which  represented  a  point  in 
the  foreground. 

It  will  be  instructive  to  notice  that  there  is  also  a 
second  point  on  this  side  of  the  paper,  at  which,  if  a 
person  look  steadily,  the  diagrams  in  fig.  555  will 
combine,  and  form  quite  a  different  stereoscopic  picture.  Instead  of  a  solid 
pyramid,  a  hollow  pyramidal  box  will  then  be  seen.  The  point  may 
easily  be  found  by  experiment.  Here  again  two  external  images  will  also 
be  seen.  If  we  wish  to  shut  these  out,  and  see  only  their  central  stereo- 
scopic combination,  we  must  use  a  diaphragm  of  paper  held  parallel  to  the 


Fig.  555- 


-625]  Persistence  of  Impressions  on  the  Retina.  575 

plane  of  the  picture  with  a  square  hole  in  it.  This  paper  screen  must  be  so 
adjusted  that  it  may  conceal  the  right-hand  figure  from  the  left  eye,  and  the 
left-hand  figure  from  the  right  eye,  while  the  central  stereoscopic  picture 
may  be  seen  through  the  hole.  It  will  be  plain  from  the  diagram  that  o 
is  the  point  to  which  the  eyes  must  be  directed,  and  at  which  they  will 
imagine  the  point  to  be  situated,  which  is  formed  by  the  combination  of  the 
two  points  r  and  /.  The  dotted  line  shows  the  position  of  the  screen.  A 
stereoscope  with  or  without  lenses  may  easily  be  constructed,  which  will 
thus  give  us,  with  the  ordinary  stereoscopic  slides,  a  reversed  picture ;  for 
instance,  if  the  subject  be  a  landscape,  the  foreground  will  retire  and  the 
background  come  forward. 

When  the  two  retinas  view  simultaneously  two  different  colours,  the  im- 
pression produced  is  that  of  a  single  mixed  tint.  The  power,  however,  of 
combining  the  two  tints  into  a  single  one  varies  in  different  individuals, 
and  in  some  is  extremely  weak.  If  two  white  discs  at  the  base  of  the  stereo- 
scope be  illuminated  by  two  pencils  of  complementary  colours,  and  if  each 
coloured  disc  be  looked  at  with  one  eye,  a  single  white  one  is  seen,  showing 
that  the  sensation  of  white  light  may  arise  from  two  complementary  and 
simultaneous  chromatic  impressions  on  each  of  the  two  retinas. 

Dove  states  that  if  a  piece  of  printing  and  a  copy  are  viewed  in  the  stereo- 
scope, a  difference  in  the  distance  of  the  words,  which  is  not  apparent  to  the 
naked  eye,  causes  them  to  stand  out  from  the  plane  of  the  paper. 

625.  Persistence  of  impressions  on  the  retina. — When  an  ignited 
piece  of  charcoal  is  rapidly  rotated,  we  cannot  distinguish  it  ;  the  appearance 
of  a  circle  of  fire  is  produced  ;  similarly,  rain,  in  falling  drops,  appears  in 
the  air  like  a  series  of  liquid  threads.  In  a  rapidly  rotating  toothed  wheel 
the  individual  teeth  cannot  be  seen.  But  if,  during  darkness,  the  wheel  be 
suddenly  illuminated,  as  by  the  electric  spark,  the  individual  parts  may  be 
clearly  made  out.  The  following  experiment  is  a  further  illustration  of  this 
property : — A  series  of  equal  sectors  are  traced  on  a  disc  of  glass,  and  they 
are  alternately  blackened  ;  in  the  centre  there  is  a  pivot,  on  which  a  second 
disc  is  fixed  of  the  same  dimensions  as  the  first,  but  completely  blackened 
with  the  exception  of  a  single  sector  ;  then  placing  the  apparatus  between  a 
window  and  the  eye,  the  second  disc  is  made  to  rotate.  If  the  movement 
is  slow,  all  the  transparent  sectors  are  seen,  but  only  one  at  a  time  ;  by  a 
more  rapid  rotation  we  see  simultaneously  two,  three,  or  a  greater  number. 
These  various  appearances  are  due  to  the  fact  that  the  impression  of  these 
images  on  the  retina  remains  for  some  time  after  the  object  which  has  pro- 
duced them  has  disappeared  or  become  displaced.  The  duration  of  the  per- 
sistence varies  with  the  sensitiveness  of  the  retina  and  the  intensity  of  light. 

Plateau  investigated  the  duration  of  the  impression  by  numerous  similar 
methods,  and  has  found  that  it  is,  on  the  average,  half  a  second.  Among 
many  curious  instances  of  these  phenomena,  the  following  is  one  of  the  most 
remarkable.  If,  after  having  looked  at  a  brightly  illuminated  window,  the 
eyes  are  suddenly  closed,  the  image  remains  for  a  few  instants— that  is,  a 
sashwork  is  seen  consisting  of  luminous  panes  surrounded  by  dark  frames  ; 
after  a  few  seconds  the  colours  become  interchanged,  the  same  framework  is 
now  seen,  but  the  frames  are  now  bright,  and  the  glasses  are  perfectly  black  ; 
this  new  appearance  may  again  revert  to  its  original  appearance. 


576  -.^  On  Light.  [625- 

The  impression  of  colours  remains  as  well  as  that  of  the  form  of  objects  ; 
for  if  circles  divided  into  sectors  are  painted  in  different  colours,  they  be- 
come confounded,  and  give  the  sensation  of  the  colour  which  would  result 
from  their  mixture.  Yellow  and  red  give  orange  ;  blue  and  red  violet ;  the 
seven  colours  of  the  spectrum  give  white,  as  shown  in  Newton's  disc  (fig.  493). 
This  is  a  convenient  method  of  studying  the  tints  produced  by  mixed  colours. 

A  great  number  of  pieces  of  apparatus  are  founded  on  the  persistence 
of  sensation  on  the  retina ;  such  are  the  thaumatrope,  the  phenakistoscope, 
Faraday 's  wheel,  the  kaleidophone,  and  the  zoetrope. 

The  zoetrope,  or  wheel  of  life,  is  very  convenient  for  representing  a  number 
of  optical,  acoustical,  and  other  vibratory  motions.  It  consists  of  an  open 
cylinder  which  can  be  rotated  about  its  vertical  axis.  At  the  top  are  a 
number  of  vertical  slits.  If  now  the  various  positions  of  a  vibrating  pendu- 
lum, for  instance,  are  drawn  on  a  narrow  strip  of  paper,  the  length  of  which 
is  equal  to  the  circumference,  and  this  is  placed  inside  the  cylinder,  when 
the  wheel  is  rapidly  rotated,  on  looking  through  the  slit  the  pendulum  seems 
as  if  it  were  steadily  vibrating. 

626.  Accidental  images. — When  a  coloured  object  placed  upon  a  black 
ground  is  steadily  looked  at  for  some  time,  the  eye  is  soon  tired,  and  the 
intensity  of  the  colour  enfeebled;  if  now  the  eyes  are  directed  towards 
a  white  sheet,  or  to  the  ceiling,  an  image  will  be  seen  of  the  same  shape  as 
the  object,  but  of  the  complementary  colour  (570)  ;  that  is,  such  a  one  as 
united  to  that  of  the  object  would  form  white      For  a  green  object  the  image 
will  be  red  ;  if  the  object  is  yellow,  the  image  will  be  violet. 

Accidental  colours  are  of  longer  duration  in  proportion  as  the  object  has 
been  more  brilliantly  illuminated,  and  the  object  has  been  longer  looked  at. 
When  a  lighted  candle  has  been  looked  at  for  some  time,  and  the  eyes  are 
turned  towards  a  dark  part  of  the  room,  the  appearance  of  the  flame  remains, 
but  it  gradually  changes  colour  ;  it  is  first  yellow,  then  it  passes  through 
orange  to  red,  from  red  through  violet  to  greenish  blue,  which  is  gradually 
feebler  until  it  disappears.  If  the  eye  which  has  been  looking  at  the  light  be 
turned  towards  a  white  wall,  the  colours  follow  almost  the  opposite  direction  : 
there  is  first  a  dark  picture  on  a  white  ground,  which  gradually  changes  into 
blue,  is  then  successively  green  and  yellow,  and  ultimately  cannot  be  distin- 
guished from  a  white  ground. 

The  reason  of  this  phenomenon  is,  doubtless,  to  be  sought  in  the  fact 
that  the  subsequent  action  of  light  on  the  retina  is  not  of  equal  duration  for 
all  colours,  and  that  the  decrease  in  the  intensity  of  the  subsequent  action 
does  not  follow  the  same  law  for  all  colours.  According  to  Kiilp,  the  dura- 
tions of  the  after-image  with  moderate  illumination  are  for  white,  yellow, 
red,  and  blue,  cri,  0-09,  0-08,  and  0-066  of  a  second  respectively. 

627.  Irradiation. — This  is  a  phenomenon  in  virtue  of  which  white  objects, 
or  those  of  a  very  bright  colour,  when  seen  on  a  dark  ground,  appear  larger 
than  they  really  are.     Thus  a  white  square  upon  a  black  ground  seems 
larger  than  an  exactly  equal  black  square  upon  a  white  ground  (fig.  556). 
Irradiation  arises  from  the  fact  that  the  impression  produced  on  the  retina 
extends  beyond  the  outline  of  the  image. ,    It  bears  the  same  relation  to  the 
space  occupied  by  the  image,  that  the  duration  of  the  impression  does  to  the 
time  during  which  the  image  is  seen. 


627] 


Irradiation. 


577 


Fig.  556. 


The  effect  of  irradiation  is  very  perceptible  in  the  apparent  magnitude  of 
stars,  which  may  thus  appear  much  larger  than  they  really  are  ;  also  in  the 
appearance  of  the  moon  when  two  or  three  days  old,  the 
brightly  illuminated  crescent  seeming  to  extend  beyond 
the  darker  portion  of  the  disc,  and  hold  it  in  its  grasp. 

Plateau  found  that  irradiation  differs  very  much  in 
different  people,  and  even  in  the  same  person  it  differs 
on  different  days.  He  also  found  that  irradiation  in- 
creases with  the  lustre  of  the  object,  and  the  length  of 
time  during  which  it  is  viewed.  It  manifests  itself  at 
all  distances  ;  diverging  lenses  increase  and  condensing 
lenses  diminish  it. 

Accidental  haloes  are  the  colours  which,  instead  of 
succeeding  the  impression  of  an  object  like  accidental 
colours,  appear  round  the  object  itself  when  it  is  looked 
at  fixedly.  The  impression  of  the  halo  is  the  opposite  to  that  of  the  object : 
if  the  object  is  bright  the  halo  is  dark,  and  vice  versa.  These  appearances 
are  best  produced  in  the  following  manner  : — A  white  surface,  such  as  a 
sheet  of  paper,  is  illuminated  by  coloured  light,  and  a  narrow  opaque  body 
held  so  as  to  cut  off  some  of  the  coloured  rays.  In  this  manner  a  narrow 
shadow  is  obtained  which  is  illuminated  by  the  surrounding  white  daylight, 
and  appears  complementary  to  the  coloured  ground.  If  red  glass  is  used, 
the  shadow  appears  green,  and  blue  when  a  yellow  glass  is  used. 

The  contrast  of  colours  is  a  reciprocal  action  exerted  between  two  adja- 
cent colours,  and  in  virtue  of  which  to  each  one  is  added  the  complementary 
colour  of  the  other.  Chevreul  found  that  when  red  and  yellow  colours  are 
adjacent,  red  acquires  a  violet  and  yellow  an  orange  tint.  If  the  experiment 
is  made  with  red  and  blue,  the  former  acquires  a  yellow,  and  the  latter  a 
green  tint ;  with  yellow  and  blue,  yellow  passes  to  orange,  and  blue  towards 
indigo  ;  if  a  narrow  strip  of  grey  paper  be  laid  on  a  sheet  of  light  green 
paper,  it  appears  reddish,  if  laid  on  blue  paper  it  seems  yellow,  and  so  on  for 
a  vast  number  of  combinations  ;  in  all  cases  the  colour  is  complementary 
to  the  colour  of  the  base.  The  importance  of  this  phenomenon  in  its  ap- 
plication to  the  manufacture  of  coloured 
cloths,  carpets,  curtains,  &c.,  may  be 
readily  conceived. 

The  contrast  may  be  conveniently  ex- 
amined by  means  of  the  apparatus  shown 
in  fig.  557  in  about  £  scale.  It  consists 
of  a  thin  vertical  board,  AB,  painted 
white,  and  the  base,  DC,  painted  black,  on 
which  are  painted  circles  about  f  of  an 
inch  in  diameter,  black  and  white  re- 
spectively. A  sheet  of  coloured  glass  is  in- 
clined at  an  angle  of  45° ;  if  now  the  eye  be 
so  held  that  the  image  of  the  white  circle 
•on  DC  reflected  from  the  under  surface  of  the  glass  plate  is  looked  at  in  front 
of  the  circle  on  AB,  the  image  appears  of  a  colour  complementary  to  that  of 
the  glass.  Thus  with  a  green  plate  a  red  spot  is  seen  on  a  green  ground. 

P  P 


Fig.  557- 


5/8  On  Light.  [628- 

628.  The  eye  is  not  achromatic. — It  had  long  been  supposed  that  the 
human  eye  was  perfectly  achromatic  ;  but  this  is  clearly  impossible,  as  all 
the  refractions  are  made  the  same  way,  viz.  towards  the  axis  ;  moreover,  the 
experiments  of  Wollaston,  of  Young,  of  Fraunhofer,  and  of  Miiller  have 
shown  that  it  was  not  true  in  any  absolute  sense. 

Fraunhofer  showed  that  in  a  telescope  with  two  lenses,  a  very  fine  wire 
placed  inside  the  instrument  in  the  focus  of  the  object-glass  is  seen  distinctly 
through  the  eyepiece,  when  the  telescope  is  illuminated  with  red  light ;  but 
it  is  invisible  by  violet  light  even  when  the  eyepiece  is  in  the  same  position. 
In  order  to  see  the  wire  again,  the  distance  of  the.  lensesrmust  be  diminished 
to  a  far  greater  extent  than  would  correspond  to  the  degree  of  refrangibility 
of  violet  light  in  glass.  In  this  case,  therefore,  the  effect  must  be  due  to  a 
chromatic  aberration  in  the  eye. 

Miiller,  on  looking  at  a  white  disc  on  a  dark  ground,  found  that  the  image 
is  sharp  when  the  eye  is  accommodated  to  the  distance  of  the  disc — that  is, 
when  the  image  forms  on  the  retina  ;  but  he  found  that,  if  the  image  is 
formed  in  front  of  or  behind  the  retina,  the  disc  appears  surrounded  by  a 
very  narrow  blue  edge.  If  a  finger  be  held  up  in  front  of  one  eye  (the  other 
being  closed)  in  such  a  manner  as  to  allow  the  light  to  enter  only  one-half 
of  the  pupil,  and,  of  course,  obliquely,  and  the  eye  be  then  directed  to  any 
well-defined  line  of  light,  such  as  a  slit  in  the  shutter  of  a  darkened  room, 
or  a  strip  of  white  paper  on  a  black  ground,  this  line  of  light  will  appear  as  a 
complete  spectrum. 

Miiller  concluded  from  these  experiments  that  the  eye  is  sensibly  achro- 
matic as  long  as  the  image  is  received  at  the  focal  distance,  or  when  it  is 
accommodated  to  the  distance  of  the  object.  The  cause  of  this  apparent 
achromatism  cannot  be  exactly  stated.  It  has  generally  been  attributed  to 
the  tenuity  of  the  luminous  beams  which  pass  through  the  pupillary  aperture, 
and  that  these  unequally  refrangible  rays,  meeting  the  surfaces  of  the  media 
of  the  eye  almost  at  the  normal  incidence,  are  very  little  refracted,  from 
which  it  follows  that  the  chromatic  aberration  is  irhperceptible  (584). 

Spherical  aberration,  as  we  have  already  seen,  is  corrected  by  the  iris 
(612).  The  iris  is,  in  point  of  fact,  a  diaphragm,  which  stops  the  marginal 
rays  and  only  allows  those  to  pass  which  are  near  the  axis. 

629.  Short  sight  and  long  sight;  myopy  and  presbytism. — The  most 
usual  affections  of  the  eye  are  myopy  and  presbytism,  or  short  sight  and  long 
sight.     Short  sight  is  the  habitual  accommodation  of  the  eyes  for  a  distance 
less  than  that  of  ordinary  vision,  so  that  persons  affected  in  this  way  only 
see  very  near  objects  distinctly.     The  usual  cause  of  short  sight  is  a  too 
great  convexity  of  the  cornea  or  of  the  crystalline  ;  the  eye  being  then  too 
convergent,  the  focus,  in  place  of  forming  on  the  retina,  is  formed  in  front, 
so  that  the  image  is  indistinct.     It  may  be  remedied  by  means  of  diverging 
glasses,  which  in  making  the  rays  deviate  from  their  common  axis  throw  the 
focus  farther  back,  and  cause  the  image  to  be  formed  on  the  retina-. 

The  habitual  contemplation  of  small  objects — as  when  children  are  too 
much  accustomed,  in  reading  and  writing,  to  place  the  paper  close  to  their 
eyes,  or  working  with  a  microscope — may  produce  short  sight.  It  is  common 
in  the  case  of  young  people,  but  diminishes  with  age. 

Long  sight  is  the  contrary  of  short  sight :  the  eye  can  see  distant  objects 


-630]  Eye-Glasses.     Spectacles.  579 

very  well,  but  cannot  distinguish  those  which  are  very  near.  It  is  common 
with  advancing  years.  The  cause  of  long  sight  is  that  the  eye  is  not  suffi- 
ciently convergent,  and  hence  the  image  of  objects  is  formed  beyond  the 
retina  ;  but  if  the  objects  are  removed  farther  off,  the  image  approaches  the 
retina,  and  when  they  are  at  a  suitable  distance  is  formed  exactly  upon  it, 
so  that  the  object  is  clearly  seen.  *Long  sight  is  corrected  by  means  of  con- 
verging lenses.  These  glasses  bring  the  rays  together  before  their  entrance 
into  the  eye,  and,  therefore,  if  the  converging  power  is  properly  chosen,  the 
image  will  be  formed  exactly  on  the  retina. 

Double  convex  lenses  were  formerly  alone  used  for  long-sighted  persons, 
and  double  concave  for  short-sighted  persons.  Wollaston  first  proposed  to 
replace  these  glasses  by  concavo-convex  lenses,  C  and  F  (fig.  468),  so  placed 
that  their  curvature  is  in  the  same  direction  as  that  of  the  eye.  By  means 
of  these  glasses  a  much  wider  range  is  attained,  and  hence  they  have  been 
called  periscopic  glasses.  They  have  the  disadvantage  of  reflecting  too  much. 

630.  Eye-glasses.  Spectacles.  —  The  glasses  commonly  used  by  short  - 
or  long-sighted  persons  are  known  under  the  general  name  of  eye-glasses  or 
spectacles.  Generally  speaking,  numbers  are  engraved  on  these  glasses 
which  express  their  focal  length  in  inches.  The  spectacles  must  be  so  chosen 
that  they  are  close  to  -the  eye,  and  that  they  make  the  distance  of  distinct 
vision  10  or  12  inches. 

The  number  which  a  short-  or  long-sighted  person  ought  to  use  may  be 
calculated,  knowing  the  distance  of  distinct  vision.  The  formula 

£M\M  (i) 

J   d-p 

serves  for  long-sighted  persons,  where/being  the  '  number'  of  the  spectacles 
which  ought  to  be  taken  —  that  is,  the  number  expressing  the  focal 
lei<gth  -p  is  the  distance  of  distinct  vision  in  ordinary  cases  (about  12 
inches),  and  d  the  distance  of  distinct  vision  for  the  person  affected  by  long 
sight. 

The  above  formula  is  obtained  from  the  equation  I  —  I  -=  -  by  substitut- 

P    P     J 

ing  d  for  p'.  In  this  case  the  formula  (6)  of  article  559  is  used,  and  not 
formula  (5),  because  the  image  seen  by  spectacles  being  on  the  same  side 
of  the  object  in  reference  to  the  lens,  the  sign  p'  ought  to  be  the  opposite 
of  that  of  /,  as  in  the  case  of  virtual  images  from  the  paragraph  already 
cited. 

For  short-sighted  persons,/  is  calculated  by  the  formula    I  —  I.    =    -1 

P    P  f 

(559)5  which  refers  to  concave  lenses,  and  which,  replacing/'  by  d  °ives 


To  calculate,  for  instance,  the  number  of  a  glass  which  a  person  ought 
to  use  in  whom  the  distance  of  distinct  vision  is  36,  knowing  that  the  dis- 
tance of  ordinary  distinct  yision  is  12  inches  ;  making  p—12.  and  ^=36  in 

the  above  formula  (i),  we  get/  =  ^       [-=  18. 

p  p  2 


58o  On  Light.  [631- 

631.  Diplopy. — Diplopy  is  an  affection  of  the  eye  which  causes  objects 
to  be  seen  double  ;  that  is,  that  two  images  are  seen  instead  of  one.    Usually 
the  two  images  are  almost  entirely  superposed,  and  one  of  them  is  much 
more  distinct  than  the  other.     Diplopy  may  be  caused  by  the  co-operation 
of  two  unequal  eyes,  but  it  may  also  affect  a  single  eye.     The  latter  case  is, 
doubtless,  due  to  some  defect  of  conformation  in  the  crystalline  or  other 
parts  of  the  eye  which  produces  a  bifurcation  of  the  luminous  ray,  and  thus 
two  images  are  formed  on  the  retina  instead  of  one.     A  single  eye  may  also 
be  affected  with  triplopy,  but  in  this  case  the  third  image  is  exceedingly 
weak. 

632.  Achromatopsy. — Achromatopsy,  or  colour  disease  or  blindness,  is  a 
curious  affection  which  renders  us  incapable  of  distinguishing  colours,  or  at 
any  rate  certain  colours.    Persons  affected  in  this  manner  can  distinguish  the 
outlines  of  bodies  without  difficulty,  and  they  can  also  discriminate  between 
light  and  shade,  but  they  are  unable  to  distinguish  the  different  colours. 

The  commonest  case  is  that  of  red  blindness  ;  Dalton  had  it  in  a  pre- 
eminent degree,  and  from  the  fact  that  he  very  carefully  described  it,  the 
disease  has  been  sometimes  called  Daltonism.  To  a  person  so  affected  red 
appears  like  black,  and  the  brighter  shades  bluish-green  ;  bluish-green 
and  white  seem  the  same,  or  at  all  events  only  different  in  shade.  Yellow 
appears  like  green  ;  but  he  distinguishes  between  them,  for  the  yellow  appears 
brighter. 

He  who  is  blind  for  green,  sees  that  colour  as  black,  and  its  lighter  shades 
red.  He  only  sees  red  and  blue  with  their  intermediate  stages  ;  yellow  ap- 
pears bright  red ;  white  and  pink  arc  alike,  the  spectrum  is  only  red  and  blue  ; 
in  the  green  there  is  a  grey  band.  Violet  blindness  is  very  infrequent  and 
not  well  known  ;  it  can  be  artificially  produced  by  taking  santonine.  Colour- 
disease  is  usually  congenital ;  it  has,  however,  been  produced  by  straining  the 
eyes  in  dim  light.  It  is  far  more  frequent  with  males  than  with  females. 

Owing  to  the  difference  in  even  healthy  individuals  as  regards  their  per- 
ception of  different  shades  of  colour,  the  only  certain  means  of  discerning 
any  particular  tint  is  to  define  its  position  by  means  of  the  nearest  Fraun- 
hofer's  line  (574).  The  best  test  for  ordinary  use  is  to  give  the  patient  a 
skein  of  wool  of  a  particular  tint — green,  rose,  or  red—  and  to  require  him  to 
match  it,  with  others  which  appear  to  him  of  the  same  tint,  among  a  large 
bundle  of  skeins  of  many  colours. 

633.  ophthalmoscope. — This  instrument,  as  its  name  indicates,  is  de- 
signed for  the  examination  of  the  eye,  and  was  invented  in  1851  by  Professor 
Helmholtz.  It  consists  : — I.  Of  a  concave  spherical  reflector  of  glass  or 
metal,  M  (figs.  558,  559),  in  the  ^middle  of  which  is  a  small  hole  about  a 
sixth  of  an  inch  in  diameter.  The  focal  length  of  the  reflector  is  from  8  to 
10  inches.  2.  Of  a  converging  achromatic  lens,  <?,  which  is  held  in  front  of 
the  eye  of  the  patient.  3.  Of  several  lenses,  some  convergent,  others  diver- 
gent, any  one  'of  which  can  be  fixed  in  a  frame  behind  the  mirror  so  as  to 
correct  any  given  imperfection  in  the  observer's  sight.  If  the  mirror  is  of 
silvered  glass,  it  is  not  necessary  that  it  be  pierced  at  the  centre ;  it  is  suf- 
ficient that  the  silvering  at  the  centre  be  removed. 

To  make  use  of  the  ophthalmoscope,  the  patient  is  placed  in  a  darkened 
room,  and  a  lamp  furnished  with  a  screen  put  beside  him,  E.  The  screen 


-633] 


Ophthalmoscope. 


serves  to  shade  the  light  from  his  head,  and  keep  it  in  darkness.  The  ob- 
server, A,  holding  in  one  hand  the  reflector,  employs  it  to  concentrate  the 
light  of  the  lamp  near  the  eye,  B,  of  the  patient,  and  with  his  other  hand 
holds  the  achromatic  lens,  o,  in  front  of  the  eye.  By  this  arrangement  the 
back  of  the  eye  is  lighted  up,  and  its  structure  can  be  clearly  discerned. 

Fig-  559  shows  how  the  image  of  the  back  of  the  eye  is  produced,  which 
the  observer,  A,  sees  on  looking  through  the  hole  in  the  reflector.     Let  ab 


Fig.  558. 

be  the  part  of  the  retina  on  which  the  light  is  concentrated,  pencils  of  rays 
proceeding  from  ab  would  form  an  inverted  and  aerial  image  of  ab  at  a'b\ 
These  pencils,  however,  on  leaving  the  eye,  pass  through  the  lens  0,  and 
thus  the  image  a"b"  is  in  fact  formed,  inverted,  but  distinct,  and  in  a  position 


Fig.  559- 

fit  for  vision.  The  great  quantity  of  light  concentrated  by  the  ophthalmoscope 
is  apt  to  irritate  painfully  the  eye  of  the  patient.  There  are,  therefore,  inter- 
posed between  the  lamp  and  the  reflector  coloured  glasses,  to  cut  off  the 
irritating  rays,  viz.  the  red,  yellow,  and  violet  rays.  The  glasses  generally 
employed  are  stained  green  or  cobalt  blue. 

By  means  of  the  ophthalmoscope  Helmholtz  has  found  that,  in  an  optical 
point  of  view,  no  eye  is  free  from  defects. 


582  On  Light.  [634- 


CHAPTER   VII. 

SOURCES   OF   LIGHT.      PHOSPHORESCENCE. 

634.  Various  sources  of  light. — The  various  sources  of  light  are  the 
sun,  the  stars,  heat,  chemical  combination,  phosphorescence,  electricity,  and 
meteoric  phenomena.     The  last  two  sources  will  be  treated  under  the  articles 
Electricity  and  Meteorology. 

The  origin  of  the  light  emitted  by  the  sun  and  by  the  stars  is  unknown  ; 
it  is  assumed  that  the  ignited  envelope  by  which  the  sun  is  surrounded  is 
gaseous,  because  the  light  of  the  sun,  like  that  emitted  from  all  gaseous 
bodies,  gives  no  trace  of  polarisation  in  the  polarising  telescope  (Chapter 
VIII.) 

As  regards  the  light  developed  by  heat,  Pouillet  has  observed  that  bodies 
begin  to  be  luminous  in  the  dark  at  a  temperature  of  500°  to  600° ;  above 
that  the  light  is  brighter  in  proportion  as  the  temperature  is  higher. 

The  luminous  effects  witnessed  in  many  chemical  combinations  are  due  to 
the  high  temperatures  produced.  This  is  the  case  with  the  artificial  lights 
used  for  illuminations,  for  ordinary  luminous  flames  are  nothing  more  than 
gaseous  matters  containing  solids  heated  to  incandescence. 

635.  Phosphorescence  :  its  sources. — Phosphorescence  is  the  property 
which  a  large  number  of  substances  possess  of  emitting  a  feeble  luminosity 
when  placed  under  certain  conditions. 

The  various  phenomena  may  be  referred  to  five  causes  : — 

i.  Spontaneous  phosphorescence  in  certain  vegetables  and  animals  ;  for 
instance,  it  is  very  intense  in  the  glow-worm,  and  the  brightness  of  its  light 
appears  to  depend  on  its  will.  Its  light  consists  of  a  continuous  spectrum 
from  C  to  near  £,  and  is  particularly  rich  in  blue  and  green  rays.  In  tropical 
climates  the  sea  is  often  covered  with  a  bright  phosphorescent  light  due  to 
some  extremely  small  zoophytes.  These  animalcules  emit  a  luminous  matter 
so  subtle  that  Quoy  and  Gaimard,  during  a  voyage  under  the  equator, 
having  placed  two  in  a  tumbler  of  water,  the  liquid  immediately  became 
luminous  throughout  its  entire  mass. 

ii.  Phosphorescence  by  elevation  of  temperature.  This  is  best  seen  in 
certain  species  of  diamonds,  and  particularly  in  chlorophane,  a  variety  of 
fluorspar,  which,  when  heated  to  300°  or  400°,  suddenly  becomes  luminous, 
emitting  a  greenish-blue  light. 

Hagenbach  examined  the  spectrum  of  phosphorescent  fluorspar,  and  found 
that  it  consisted  of  only  nine  bands :  four  blue,  two  green,  two  yellow,  and 
one  orange.  As  the  relative  intensities  of  these  bands  are  continual!^ 
changing,  it  is  easy  to  understand  the  different  colours  presented  by  different 
specimens  of  this  mineral. 


-636]  Phosphorescence  by  Insolation.  583 

iii.  Phosphorescence  by  mechanical  effects,  such  as  friction,  percussion, 
cleavage,  &c.  ;  for  example,  when  two  crystals  of  quartz  are  rubbed  against 
each  other  in  darkness,  when  a  lump  of  sugar  is  broken,  or  when  a  plate  of 
mica  is  cleft. 

iv.  Phosphorescence  by  electricity,  like  that  which  results  from  the  fric- 
tion of  mercury  against  the  glass  in  a  barometric  tube,  and  especially  from 
the  electric  sparks  proceeding  either  from  an  ordinary  electrical  machine,  or 
from  a  RuhmkorfFs  coil. 

v.  Phosphorescence  by  insolation  or  exposure  to  the  sun.  A  large  number 
of  substances,  after  having  been  exposed  to  the  action  of  sunlight,  or  of 
the  diffused  light  of  the  atmosphere,  emit  in  darkness  a  phosphorescence 
the  colour  and  intensity  of  which  depend  on  the  nature  and  physical  condi- 
tion of  these  substances. 

636.  Phosphorescence  by  insolation. — This  was  first  observed  in  1604 
in  Bolognese  phosphorus  (sulphide  of  barium),  but  it  also  exists  in  a  great 
number  of  substances.  The  sulphides  of  calcium  and  strontium  are  those 
which  present  it  in  the  highest  degree.  When  well  prepared,  after  being 
exposed  to  the  light,  they  are  luminous  for  several  hours  in  darkness.  But 
as  this  phosphorescence  takes  place  in  a  vacuum  as  well  as  in  a  gaseous 
medium,  it  cannot  be  attributed  to  a  chemical  action,  but  rather  to  a  tempo- 
rary modification  which  the  body  undergoes  from  the  action  of  light.  A 
phosphorescent  sulphide  of  calcium  is  prepared  for  industrial  purposes,  and 
is  known  as  Balmain's  luminous  paint. 

After  the  substances  above  named,  the  best  phosphorescents  are  the 
following,  in  the  order  in  which  they  are  placed  :  a  large  number  of  diamonds 
(especially  yellow  ones),  and  most  specimens  of  fluorspar  ;  then  arragonite, 
calcareous  concretions,  chalk,  apatite,  heavy  spar,  dried  nitrate  of  calcium 
and  dried  chloride  of  calcium,  cyanide  of  calcium,  a  large  number  of 
strontium  or  barium  compounds,  magnesium  and  its  carbonate,  &c.  Besides 
these  a  large  number  of  organic  substances  also  become  phosphorescent  by 
insolation  ;  for  instance,  dry  paper,  silk,  cane-sugar,  milk-sugar,  amber,  the 
teeth,  &c. 

The  different  spectral  rays  are  not  equally  well  fitted  to  render  substances 
phosphorescent.  The  maximum  effect  takes  place  in  the  violet  rays,  or  even 
a  little  beyond  ;  while  the  light  emitted  by  phosphorescent  bodies  generally 
corresponds  to  rays  of  a  smaller  refrangibility  than  those  of  the  light  received 
by  them  and  giving  rise  to  the  action. 

The  tint  which  phosphorescent  bodies  assumes  is  very  variable,  and  even 
in  the  same  body  it  changes  with  the  manner  in  which  it  is  prepared.  In 
strontium  compounds  green  and  blue  tints  predominate  ;  and  orange,  yellow, 
and  green  tints  in  the  sulphides  of  barium. 

The  duration  of  phosphorescence  varies  also  in  different  bodies.  In  the 
sulphides  of  calcium  and  strontium,  phosphorescence  lasts  as  long  as  thirty 
hours  ;  with  other  substances  it  does  not  exceed  a  few  seconds,  or  even  a 
fraction  of  a  second. 

The  colour  emitted  by  an  artificial  phosphorescent  alters  with  the 
temperature  during  insolation.  Thus  with  sulphide  of  strontium  the  light  is 
dark  violet  at  -20°  C.,  bright  blue  at  +40°,  bluish-green  at  70°,  greenish- 
yellow  at  1 00°,  and  reddish-yellow  of  feeble  luminosity  at  200°  C. 


584 


On  Light. 


[636 


Phosphoroscope.  In  experimenting  with  bodies  whose  phosphorescence 
lasts  a  few  minutes  or  even  a  few  seconds,  it  is  simply  necessary  to  expose 
them  to  solar  or  diffused  light  for  a  short  time,  and  then  place  them  in  dark- 
ness :  their  luminosity  is  very  apparent,  especially  if  care  has  been  taken  to 
close  the  eyes  previously  for  a  few  moments.  But  in  the  case  of  bodies  whose 
phosphorescence  lasts  only  a  very  short  time,  this  method  is  inadequate. 
Becquerel  invented  an  ingenious  apparatus,  the  phosphoroscope,  by  which 
bodies  can  be  viewed  immediately  after  being  exposed  to  light :  the  interval 
which  separates  the  insolation  and  observation  can  be  made  as  small  as 
possible,  and  measured  with  great  precision. 


Fig.  560 

This  apparatus,  which  is  constructed  by  Duboscq,  consists  of  a  closed 
cylindrical  box,  AB  (fig.  560),  of  blackened  metal ;  on  the  ends  are  two 
apertures  opposite  each  other  which  have  the  form  of  a  circular  sector.  One 
only  of  these,  0,  is  seen  in  the  figure.  The  box  is  fixed,  but  it  is  traversed  in 
the  centre  by  a  movable  axis,  to  which  are  fixed  two  circular  screens,  MM 
and  PP,  of  blackened  metal  (fig.  561).  Each  of  these  screens  is  perforated 
by  four  apertures  of  the  same  shape  as  those  in  the  box  ;  but  while  the  latter 


Phosphoroscope.  585 

correspond  to  each  other,  the  apertures  of  the  screens  alternate,  so  that  the 
open  parts  of  the  one  correspond  to  the  closed  parts  of  the  other.  The  two 
screens,  as  already  mentioned,  are  placed  in  the  box,  and  fixed  to  the  axis, 
which  by  means  of  a  train  of  wheels,  worked  by  a  handle,  can  be  made  to 
turn  with  any  velocity. 

In  order  to  investigate  the  phosphorescence  of  any  body  by  means  of 
this  instrument,  the  body  is  placed  on  a  stirrup  interposed  between  the  two 
rotating  screens.  The  light  cannot  pass  at  the  same  time  through  the 
opposite  apertures  of  the  sides  A  and  B,  because  one  of  the  closed  parts  of 
the  screen  MM,  or  of  the  screen  PP,  is  always  between  them.  So  that  when 
a  body,  #,  is  illuminated  by  light  from  the  other  side  of  the  apparatus,  it 
could  not  be  seen  by  an  observer  looking  at  the  aperture,  <?,  for  then  it  would 
be  masked  by  the  screen  PP.  Accordingly,  when  an  observer  saw  the  body 
a,  it  would  not  be  illuminated,  as  the  light  would  be  intercepted  by  the  closed 
parts  of  a  screen  MM.  The  body  a  would  alternately  appear  and  dis- 
appear ;  it  would  disappear  during  the  time  of  its  being  illuminated,  and 
appear  when  it  was  no  longer  so.  The  time  which  elapses  between  the 
appearance  and  disappearance  depends  on  the  velocity  of  rotation  of  the 
screens.  Suppose,  for  instance,  that  they  made  1 50  turns  in  a  second ;  as 
one  revolution  of  the  screens  is  effected  in  T^  of  a  second,  there  would  be 
four  appearances  and  four  disappearances  during  that  time.  Hence  the 
length  of  time  elapsing  between  the  time  of  illumination  and  of  observation 
would  be  |  of  T|5  of  a  second  or  croooS  of  a  second. 

Observations  with  the  phosphoroscope  are  made  in  a  dark  chamber,  the 
observer  being  on  that  side  on  which  is  the  wheelwork.  A  ray  of  solar  or 
electric  light  is  allowed  to  fall  upon  the  substance  #,  and,  the  screens 
being  made  to  rotate  more  or  less  rapidly,  the  body  a  appears  luminous  by 
transparence  in  a  continuous  manner,  when  the  interval  between  insolation 
and  observation  is  less  than  the  duration  of  the  phosphorescence  of  the  body. 
By  experiments  of  this  kind,  Becquerel  has  found  that  substances  which 
usually  are  not  phosphorescent  become  so  in  the  phosphoroscope  ;  such,  for 
instance,  is  Iceland  spar.  Uranium  compounds  present  the  most  brilliant 
appearance  in  this  apparatus  ;  they  emit  a  very  bright  luminosity  when  the 
observer  can  see  them  0-03  or  0-04  of  a  second  after  insolation.  But  a  large 
number  of  bodies  produce  no  effect  in  the  phosphoroscope  ;  for  instance, 
quartz,  sulphur,  phosphorus,  metals,  and  liquids. 


586  On  Light.  .          [637- 


CHAPTER   VIII. 

DOUBLE   REFRACTION.      INTERFERENCE.      POLARISATION. 

637.  The  undulatory  theory  of  light. — It  has  been  already  stated  (499) 
'that  the  phenomenon  of  light  is  ascribed  to  undulations  propagated  through 
an  exceedingly  rare  medium  called  the  luminiferous  ether,  which  is  supposed 
to  pervade  all  space,  and  to  exist  between  the  molecules  of  the  ordinary 
forms  of  matter.  In  short,  it  is  held  that  light  is  due  to  the  undulations  of 
the  ether,  just  as  sound  is  due  to  undulations  propagated  through  the  air. 
In  the  latter  case  the  undulations  cause  the  drum  of  the  ear  to  vibrate 
and  produce  the  sensation  of  sound.  In  the  former  case,  the  undulations 
cause  points  of  the  retina  to  vibrate  and  produce  the  sensation  of  light. 
The  two  cases  differ  in  this,  that  in  the  case  of  sound  there  is  independent 
evidence  of  the  existence  and  vibration  of  the  medium  (air)  which  propagates 
the  undulation  ;  whereas  in  the  case  of  light  the  existence  of  the  medium 
and  its  vibrations  is  assumed,  because  that  supposition  connects  and  explains 
in  the  most  complete  manner  a  long  series  of  very  various  phenomena. 
There  is,  however,  no  independent  evidence  of  the  existence  of  the  lumini- 
ferous ether. 

The  analogy  between  the  phenomena  of  sound  and  light  is  very  close  ; 
thus,  the  intensity  of  a  sound  is  greater  as  the  amplitude  of  the  vibration  of 
each  particle  of  the  air  is  greater,  and  the  intensity  of  light  is  greater  as  the 
amplitude  of  the  vibration  of  each  particle  of  the  ether  is  greater.  Again,  a 
sound  is  more  acute  as  the  length  of  each  undulation  producing  the  sound  is 
less,  or,  what  comes  to  the  same  thing,  according  as  the  number  of  vibrations 
per  second  is  greater.  In  like  manner,  the  colour  of  light  is  different  ac- 
cording to  the  length  of  the  undulation  producing  the  light :  a  red  light  is 
due  to  a  comparatively  long  undulation,  and  corresponds  to  a  deep  sound, 
while  a  violet  light  is  due  to  a  short  undulation,  and  corresponds  to  an  acute 
sound. 

Although  the  length  of  the  undulations  cannot  be  observed  directly,  yet 
they  can  be  inferred  from  certain  phenomena  with  great  exactness.  The 
following  table  gives  the  lengths,  in  inches  and  millimetres,  of  the  undulations 
corresponding  to  the  light  at  the  principal  dark  lines  of  the  spectrum  : — 

Length  of  Length  of 

Undulation  Undulation 

Dark  line  in  in:hes  in  millimetres 

B 0-0000271  0-0006874 

C 0-0000258  0-0006562 

Dx 0-0000232  0-0005897 

E 0-0000207  0-0005271 

F  .......  0-0000191  0-0004862 

G 0-0000169  0-0004311 

H 0-0000159  0-0003969 


-638]  Physical  Explanation  of  Single  Refraction.  587 

It  will  be  remarked  that  the  limits  are  very  narrow  within  which  the 
lengths  of  the  undulations  of  the  ether  must  be  comprised,  if  they  are  to 
be  capable  of  producing  the  sensation  of  light.  In  this  respect  light  is  in 
marked  contrast  to  sound.  For  the  limits  are  very  wide  within  which  the 
lengths  of  the  undulations  of  the  air  may  be  comprised  when  they  produce 
the  sensation  of  sound  (244). 

The  undulatory  theory  readily  explains  the  colours  of  different  bodies. 
According  to  that  theory,  certain  bodies  have  the  property  of  exciting  undula- 
tions of  different  lengths,  and  thus  producing  light  of  given  colours.  White 
light  or  daylight  results  from  the  coexistence  of  undulations  of  all  possible 
lengths. 

The  colour  of  a  body  is  due  to  the  power  it  has  of  extinguishing  certain 
vibrations,  and  of  reflecting  others  ;  and  the  body  appears  of  the  colour  pro- 
duced by  the  coexistence  of  the  reflected  vibrations.  A  body  appears  white 
when  it  reflects  all  different  vibrations  in  the  proportion  in  which  they  are 
present  in  the  spectrum  ;  it  appears  black  when  it  reflects  light  in  such 
small  quantities  as  not  to  affect  the  eye.  A  red  body  is  one  which  has  the 
property  of  reflecting  in  predominant  strength  those  vibrations  which  pro- 
duce the  sensation  of  red.  This  is  seen  in  the  fact  that,  when  a  piece  of  red 
paper  is  held  against  the  daylight,  and  the  reflected  light  is  caught  on  a 
white  wall,  this  also  appears  red.  A  piece  of  red  paper  in  the  red  part  of 
the  spectrum  appears  of  a  brighter  red,  and  a  piece  of  blue  paper  held  in 
the  blue  part  appears  a  brighter  blue ;  while  a  piece  of  red  paper  placed  in 
the  violet  or  blue  part  appears  almost  black.  In  the  last  case  the  red  paper 
can  only  reflect  red  rays,  while  it  extinguishes  the  blue  rays,  and  as  the  blue 
of  the  spectrum  is  almost  free  from  red,  so  little  is  reflected  that  the  paper 
appears  black. 

The  undulatory  theory  likewise  explains  the  colours  of  transparent  bodies. 
Thus,  a  vibrating  motion  on  reaching  a  body  sets  it  in  vibration.  So  also  the 
vibrations  of  the  lumiriiferous  ether  are  communicated  to  the  ether  in  a  body, 
and  setting  it  in  motion,  produce  light  of  different  colours.  When  this  motion 
is  transmitted  through  any  body,  it  is  said  to  be  transparent  or  translucent, 
according  to  the  different  degrees  of  strength  with  which  this  transmission  is 
effected.  In  the  opposite  case  it  is  said  to  be  opaqtie. 

When  light  falls  upon  a  transparent  body,  the  body  appears  colourless  if 
all  the  vibrations  are  transmitted  in  the  proportion  in  which  they  exist  in  the 
spectrum.  But  if  some  of  the  vibrations  are  checked  or  extinguished,  the 
emergent  light  will  be  of  the  colour  produced  by  the  coexistence  of  the  un- 
checked vibrations.  Thus,  when  a  piece  of  blue  glass  is  held  before  the  eye, 
the  vibrations  producing  red  and  yellow  are  extinguished,  and  the  colour  is 
due  to  the  emergent  vibrations  which  produce  blue  light. 

The  undulatory  theory  also  accounts  for  the  reflection  and  refraction  of 
light,  as  well  as  other  phenomena  which  are  yet  to  be  described.  The  ex- 
planation of  the  refraction  of  light  is  of  so  much  importance  that  we  shall 
devote  to  it  the  following  article. 

Y~o~3S.  Physical  explanation  of  single  refraction. — The  explanation  of 
this  phenomenon  by  means  of  the  undulatory  theory  of  light  presupposes 
that  of  the  mode  of  propagation  of  a  plane  wave.  Now,  if  a  disturbance 
originated  at  any/#z>z/  of  the  ether,  it  would  be  propagated  as  a  spherical 


588 


On  Light. 


[638- 


wave  in  all  directions  round  that  point  with  a  uniform  velocity.  If,  instead 
of  a  single  point,  we  consider  the  front  of  a  plane  wave,  it  is  evident  that 
disturbances  originate  simultaneously  at  all  points  of  the  front,  and  that 
spherical  waves  proceed  from  each  point  with  the  same  uniform  velocity. 
Consequently  all  these  spheres  will  at  any  subsequent  instant  be  touched  by 
a  plane  parallel  to  the  original  plane.  The  disturbances  propagated  from 
the  points  in  the  first  position  of  the  wave  will  mutually  destroy  each  other, 
except  in  the  tangent  plane  ;  consequently  the  wave  advances  as  a  plane 
wave,  its  successive  positions  being  the  successive  positions  of  the  tangent 
plane.  If  the  wave  moves  in  any  medium  with  a  velocity  v,  it  will  describe 
a  space  vt  in  a  time  /,  in  a  direction  at  right  angles  to  the  wave-front. 

In  any  given  moment  let  mn  (fig.  562)  be  the  position  of  the  wave-front  of 
a  ray  of  light,  which,  moving  through  any  medium,  meets  the  plane  surface 

AB  of  any  denser  refract- 
ing medium.  In  the  same 
moment  in  which  the 
wave-front  reaches  «,  m 
becomes  the  centre  of  a 
spherical  wave  system 
which  moves  in  the  se- 
cond medium  ;  and  as 
the  elasticity  of  the  second 
medium  is  different  from 
that  of  the  first,  the  ve- 
locity of  propagation  of 
the  wave  in  the  two  media  will  be  different.  While  the  plane  wave  moves 
from  n  to  K,  the  corresponding  wave  starting  from  m  reaches  the  surface 
of  a  sphere  the  radius  of  which  is  less  than  #K,  if  the  second  medium  is 
more  strongly  refracting  than  the  first.  The  incident  wave  in  like  manner 
reaches  m'  and  n'  simultaneously,  and  while  n  moves  to  K,  m'  moves  to  o'y 
the  surface  of  a  sphere  the  radius  of  which,  m'o\  is  to  mo  as  n'  is  to  nK. 
All  the  elementary  waves  proceeding  from  points  intermediate  to  n  and  K 
which  arise  from  the  same  incident  wave,  touch  one  and  the  same  plane 
K0'0,  and  the  refracted  ray  proceeds  in  the  new  medium  perpendicular  to  this 
tangent  plane. 

Now  nK  and  mo  represent  the  velocities  of  light  in  the  unit  of  time  in  the 
two  media  respectively  :  let  mK  be  taken  as  unit  of  length,  then 

nK  =  sin  nmK  and  mo  =  sin  mKo. 

Now  mnK  is  the  angle  of  incidence  of  the  ray,  and  mKo  is  the  angle  of 
refraction,  and  nK  and  mo  are  the  velocities  of  light  in  the  two  media 
respectively ;  hence  we  see  that  these  velocities  are  to  each  other  in  the 
same  ratio  as  the  sines  of  the  angles  of  incidence  and  refraction ;  a  conclu- 
sion which  agrees  with  the  results  of  direct  observation  (506)  and  forms  a 
beautiful  confirmation  of  the  truth  of  the  undulatory  theory. 


Fig.  562. 


DOUBLE    REFRACTION. 


639.  Double  refraction. — It  has  been  already  stated  (536)  that  a  large 
number  of  crystals  possess  the  property  of  double  refraction,  in  virtue  of 


-640]  Uniaxial  Crystals.  589 

which  a  single  incident  ray  in  passing  through  any  one  of  them  is  divided 
into  two,  or  undergoes  bifurcation,  whence  it  follows  that,  when  an  object 
is  seen  through  one  of  these  crystals,  it  appears  double.  The  fact  of  the 
existence  of  double  refraction  in  Iceland  spar  was  first  stated  by  Bartholin 
in  1669,  but  the  law  of  double  refraction  was  first  enunciated  exactly  by 
Huyghens,  in  his  treatise  on  light,  written  in  1678  and  published  in  1690. 

Crystals  which  possess  this  peculiarity  are  said  to  be  double-refracting. 
It  is  found  to  a  greater  or  less  extent  in  all  crystals  which  do  not  belong  to 
the  cubical  system.  Bodies  which  crystallise  in  this  system,  and  those 
which,  like  glass,  are  destitute  of  crystallisation,  have  no  double  refraction. 
The  property  can,  however,  be  imparted  to  them  when  they  are  unequally 
compressed,  or  when  they  are  cooled  quickly  after  having  been  heated,  in 
which  state  glass  is  said  to  be  unannealed.  Of  all  substances,  that  which 
possesses  it  most  remarkably  is  Iceland  spar  or  carbonate  of  calcium.  In 
many  substances,  the  power  of  double  refraction  can  hardly  be  proved  to 
exist  directly  by  the  bifurcation  of  an  incident  ray  ;  but  its  existence  is  shown 
indirectly  by  their  being  able  to  depolarise  light  (665). 

Fresnel  explained  double  refraction  by  assuming  that  the  ether  in  double- 
refracting  bodies  is  not  equally  elastic  in  all  directions  ;  from  which  it 
follows  that  the  vibrations,  in  certain  directions  at  right  angles  to  each 
other,  are  transmitted  with  unequal  velocities ;  these  directions  being  depen- 
dent on  the  constitution  of  the  crystal.  This  hypothesis  is  confirmed  by 
the  property  which  glass  acquires  of  becoming  double-refracting  by  being 
unannealed  and  by  pressure. 

Y  640.  Uniaxial  crystals. — In  all  double-refracting  crystals  there  is  one 
direction,  and  in  some  a  second  direction,  possessing  the  following  property  : — 
When  a  point  is  looked  at  through  the  crystal  in  this  particular  direction,  it 
does  not  appear  double.  The  lines  fixing  these  directions  are  called  optic 
axes ;  and  sometimes,  though  not  very  properly,  axes  of  double  refraction. 
A  crystal  is  called  uniaxial  when  it  has  one  optic  axis  ;  that  is  to  say,  when 
there  is  one  direction  within  the  crystal  along 
which  a  ray  of  light  can  proceed  without 
bifurcation.  When  a  crystal  has  two  such 
axes,  it  is  called  a  biaxial  crystal. 

The  uniaxial  crystals  most  frequently 
used  in  optical  instruments  are  Iceland  spar, 
quartz,  and  tourmaline.  Iceland  spar  crystal- 
lises in  rhombohedra,  whose  faces  form  with 
each  other  angles  of  105°  5'  or  74°  55'.  It 
has  eight  solid  angles  (see  fig.  563).  Of  these,  two,  situated  at  the  extremities 
of  one  of  the  diagonals,  are  severally  contained  by  three  obtuse  angles.  A 
line  drawn  within  one  of  these  two  angles  in  such  a  manner  as  to  be  equally 
inclined  to  the  three  edges  containing  the  angle  is  called  the  axis  of  the 
crystal.  If  all  the  edges  of  the  crystal  were  equal,  the  axis  of  the  crystal 
would  coincide  with  the  diagonal,  ab. 

Brewster  showed  that  in  all  uniaxial  crystals  the  optic  axis  coincides  with 
the  axis  of  crystallisation. 

The  principal  plane  with  reference  to  a  point  of  any  face  of  a  crystal, 
whether  natural  or  artificial,  is  a  plane  drawn  through  that  point  at  right 


590  On  Light.  [640- 

angles  to  the  face  and  parallel  to  the  optic  axis.  If  in  fig.  563  we  suppose 
the  edges  of  the  rhombohedron  to  be  equal,  the  diagonal  plane  abed  contains 
the  optic  axis  (ab\  and  is  at  right  angles  to  the  faces  aedfand  c/ibg ;  conse- 
quently it  is  parallel  to  the  principal  plane  at  any  point  of  either  of  those 
two  faces.  For  this  reason  abed  is  often  called  the  principal  plane  with 
respect  to  those  faces. 

X64I.  Ordinary  and  extraordinary  ray. —  Of  the  two  rays  into  which 
n  incident  ray  is  divided  on  entering  a  uniaxial  crystal  one  is  called  the 
ordinary  and  the  other  the  extraordinary  ray.  The  ordinary  ray  follows 
the  laws  of  single  refraction  ;  that  is,  with  respect  to  that  ray  the  sine  of  the 
angle  of  incidence  bears  a  constant  ratio  to  the  sine  of  the  angle  of  refraction, 
and  the  plane  of  incidence  coincides  with  the  plane  of  refraction.  Except 
in  particular  positions,  the  extraordinary  ray  follows  neither  of  these  laws. 
The  images  corresponding  to  the  ordinary  and  extraordinary  rays  are  called 
the  ordinary  and  extraordinary  images  respectively. 

If  a  transparent  specimen  of  Iceland  spar  be  placed  over  a  dot  of  ink, 
on  a  sheet  of  white  paper,  two  images  will  be  seen.  One  of  them,  the 
ordinary  image,  will  seem  slightly  nearer  to  the  eye  than  the  other,  the  extra- 
ordinary image.  Suppose  the  spectator  to  view  the  dot  in  a  direction  at 
right  angles  to  the  paper,  then,  if  the  crystal,  with  the  face  still  on  the  paper, 
be  turned  round,  the  ordinary  image  will  continue  fixed,  and  the  extraordinary 
image  will  describe  a  circle  round  it,  the  line  joining  them  being  always  in 
the  direction  of  the  shorter  diagonal  of  the  face  of  the  crystal,  supposing  its 
edges  to  be  of  equal  length.  In  this  case  it  is  found  that  the  angle  between 
the  ordinary  and  extraordinary  ray  is  6°  12'. 

642.  The  laws  of  double  refraction  in  a  uniaxial  crystal. — These 
phenomena  are  found  to  obey  the  following  laws  : — 

i.  Whatever  be  the  plane  of  incidence,  the  ordinary  ray  always  obeys 
the  two  general  laws  of  single  refraction  (537).  The  refractive  index  for  the 
ordinary  ray  is  called  the  ordinary  refractive  index. 

ii.  In  every  section  perpendicular  to  the  optic  axis  the  extraordinaiy  ray 
also  follows  the  laws  of  single  refraction.  Consequently  in  this  plane  the 
extraordinary  ray  has  a  constant  refractive  index,  which  is  called  the  ordinary 
refractive  index. 

iii.  In  every  principal  section  the  extraordinary  ray  follows  the  second 
law  only  of  single  refraction  ;  that  is,  the  planes  of  incidence  and  refraction 
coincide,  but  the  ratio  of  the  sines  of  the  angles  of  incidence  and  refraction 
is  not  constant. 

iv.  The  velocities  of  light  along  the  rays  are  unequal.  It  can  be  shown 
that  the  difference  between  the  squares  of  the  reciprocals  of  the  velocities 
along  the  ordinary  and  extraordinary  rays  is  proportional  to  the  square  of  the 
sine  of  the  angle  between  the  latter  ray  and  the  axis  of  the  crystal. 

There  is  an  important  difference  between  the  velocity  of  the  ray  and  the 
velocity  of  the  corresponding  plane  wave.  If  the  velocities  of  the  plane 
waves  corresponding  to  the  ordinary  and  extraordinary  rays  are  considered, 
the  difference  between  the  squares  of  these  velocities  is  proportional  to  the 
square  of  the  sine  of  the  angle  between  the  axis  of  the  crystal,  and  the  normal 
to  that  plane  wave  which  corresponds  to  the  extraordinary  ray.  The  normal 
and  the  ray  do  not  generally  coincide. 


-644]  Double  Refraction  in  Biaxial  Crystals.  591 

Huyghens  gave  a  very  remarkable  geometrical  construction,  by  means  of 
which  the  directions  of  the  refracted  rays  can  be  determined  when  the  direc- 
tions of  the  incident  ray  and  of  the  axis  are  known  relatively  to  the  face  of 
the  crystal.  This  construction  was  not  generally  accepted  by  physicists  un- 
til Wollaston,  and  subsequently  Malus,  showed  its  truth  by  numerous  exact 
measurements. 

643.  Positive  and  negative  uniaxial  crystal. — The  term  extraordinary 
refractive  index  has  been  defined  in  the  last  article.     For  the  same  crystal 
its  magnitude  always  differs  from  that  of  the  ordinary  refractive  index  ;  for 
example,  in  Iceland  spar  the  ordinary  refractive  index  is   1*654,  while  the 
extraordinary  refractive  index  is  1*483.     In  this   case   the   ordinary  index 
exceeds  the  extraordinary  index.    When  this  is  the  case,  the  crystal  is  said  to 
be  negative.     On  the  other  hand,  when  the  extraordinary  index  exceeds  the 
ordinary  index,  the  crystal  is  said  to  be  positive.    The  following  list  gives  the 
names  of  some  of  the  principal  uniaxial  crystals  : — 

Negative  Uniaxial  Crystals. 

Iceland  spar  Ruby  Pyromorphite 

Tourmaline  Emerald  Ferrocyanide  of  potassium 

Sapphire  Apatite  Nitrate  of  sodium 

Positive  Uniaxial  Crystals. 

Zircon  Apophyllite  Titanite 

Quartz  Ice  Boracite 

644.  Double  refraction  in  biaxial  crystals.— A  large  number  of  crystals, 
including  all  those  belonging  to  the  trimetric^  the  monoclinic,  and  the  triclinic 
systems,  possess  two  optic  axes  ;  in  other  words,  in  each  of  these  crystals 
there  are  two  directions  along  which  a  ray  of  light  passes  without  bifurcation. 
A  line  bisecting  the  acute  angle  between  the  optic  axes  is  called  the  medial 
line  ;   one  that  bisects  the  obtuse  angle  is  called  the  supplementary  line. 
It  has  been  found  that  the  medial  and  supplementary  lines  and  a  third  line 
at  right  angles  to  both  are  closely  related  to  the  fundamental  form  of  the 
crystal  to  which  the  optic  axes  belong.     The  acute  angle  between  the  optic 
axes  is  different  in  different  crystals.     The  following  table  gives  the  magnitude 
of  this  angle  in  the  case  of  certain  crystals  : — 

Nitre  .         .  .  •  .       5°  20'  Mica    .         .  .  .  45  o 

Strontianite  '.,;.  .       6    56  Sugar  .      •..'  .  .  50  o 

Arragonite  .  .  .1818  Selenite        .  .  .  60  o 

Anhydrite    .  .  .     28°    7'  Epidote        .  .  .  84  19 

Heavy  spar  .  ,  .     37  42  Sulphate  of  iron  .  .  90  o 

When  a  ray  of  light  enters  a  biaxial  crystal,  and  passes  in  any  direction 
not  coinciding  with  an  optic  axis,  it  bifurcates  ;  in  this  case,  however, 
neither  ray  conforms  to  the  laws  of  single  refraction,  but  both  are  extra- 
ordinary rays.  To  this  general  statement  the  following  exception  must  be 
made  : — In  a  section  of  a  crystal  at  right  angles  to  the  medial  line  one  ray 
follows  the  laws  of  ordinary  refraction,  and  in  a  section  at  right  angles  to- 
the  supplementary  line  the  other  ray  follows  the  laws  of  ordinary  refraction. 


592 


On  Light. 


[645- 


INTERFERENCE  AND   DIFFRACTION. 


645.  Interference  of  ligrht. — The  name  interference  is  given  to  the  re- 
ciprocal action  which  two  rays  of  light  exert  upon  each  other  when  they  are 
emitted  from  two  neighbouring  sources,  and  meet  each  other  under  a  very 
small  angle.  This  action  may  be  observed  by  means  of  the  following  ex- 
periment : — In  the  shutter  of  a  dark  room  two  very  small  apertures  of  the 
same  diameter  are  made  close  to  each  other.  The  apertures  are  closed 
by  pieces  of  coloured  glass — red,  for  example — by  which  two  pencils  of 
homogeneous  light  are  introduced.  These  two  pencils  form  two  divergent 
luminous  cones,  which  meet  at  a  certain  distance  ;  they  are  received  on  a 
white  screen  a  little  beyond  the  place  at  which  they  meet,  and  in  the  segment 
common  to  the  two  discs  which  form  upon  this  screen  some  very  well-defined 
alternations  of  red  and  black  bands  are  seen.  If  one  of  the  two  apertures 
be  closed,  the  fringes  disappear,  and  are  replaced  by  an  almost  uniform  red 
tint.  From  the  fact  that  the  dark  fringes  disappear  when  one  of  the  beams 
is  intercepted,  it  is  concluded  that  they  arise  from  the  interference  of  the  two 
pencils  which  cross  obliquely. 

This  experiment  was  first  made  by  Grimaldi,  but  was  modified  by 
Young.  Grimaldi  had  drawn  from  it  the  conclusion  that  light  added  to  light 


Fig.  564- 


produced  darkness.  The  full  importance  of  this  principle  remained  for 
a  long  time  unrecognised,  until  these  inquiries  were  resumed  by  Young 
and  Fresnel,  of  whom  the  latter,  by  a  modification .  of  Grimaldi's  experi- 
ment, rendered  it  an  experimentum  crucis  of  the  truth  of  the  undulatory 
hypothesis. 

In  Grimaldi's  experiment  diffraction  (646)  takes  place,  for  the  luminous 
rays  pass  by  the  edge  of  the  aperture.  In  the  following  experiment,  which 
is  due  to  Fresnel,  the  two  pencils  interfere  without  the  possibility  of  diffraction. 

Two  plane  mirrors,  AB  and  BC  (fig.  564),  of  metal,  are  arranged  close  to 


-645]  Interference  of  Light.  593 

each  other,  so  as  to  form  a  very  obtuse  angle,  ABC,  which  must  be  very 
little  less  than  180°.  A  pencil  of  red  light,  which  passes  into  the  dark 
chamber,  is  brought  to  a  focus,  F,  by  means  of  a  lens,  L.  On  diverging  from 
F  the  rays  fall  partly  on  AB,  and  partly  on  BC.  If  BA  is  produced  to  P  and 
FPFj  is  drawn  at  right  angles  to  AP,  and  if  PFj  is  made  equal  to  PF,  then 
the  rays  which  fall  on  AB  will,  after  reflection,  proceed  as  if  they  diverged 
from  Fr  If  a  similar  construction  is  made  for  the  rays  falling  on  BC,  they 
will  proceed  after  reflection  as  if  they  diverged  from  F2.  A  little  considera- 
tion will  show  that  F7  and  F2  are  very  near  each  other.  Suppose  the  re- 
flected rays  to  fall  on  a  screen  SSj  placed  nearly  at  right  angles  to  their 
directions.  Every  point  of  the  screen  which  receives  light  from  both  pencils 
is  illuminated  by  both  rays,  viz.  one  from  F15  the  other  from  F2  :  thus  the 
point  H  is  illuminated  by  two  rays,  as  also  are  K  and  I.  Now  the  combined 
action  of  these  two  pencils  is  to  form  a  series  of  parallel  bands  alternately 
light  and  dark  on  the  screen  at  right  angles  to  the  plane  of  the  paper.  This 
is  the  fundamental  phenomenon  of  interference  ;  and  that  it  results  from  the 
joint  action  of  the  two  pencils  is  plain,  for  if  the  light  which  falls  upon  either 
of  the  mirrors  is  cut  off,  the  dark  bands  disappear. 

This  remarkable  experiment  is  explained  in  the  most  satisfactory  manner 
by  the  undulatory  theory  of  light.  The  explanation  exactly  resembles  that 
already  given  of  the  formation  of  nodes  and  loops  by  the  combined  action  of 
two  aerial  waves  (262) ;  the  only  difference  being  that  in  that  case  the  vibrat- 
ing particles  were  supposed  to  be  particles  of  air,  whereas,  in  the  present 
case,  the  vibrating  particles  are  supposed  to  be  those  of  the  luminiferous 
ether.  Consider  any  point  K  on  the  screen,  and  first  let  us  suppose  the  dis- 
tance of  K  from  Fl  and  F2  to  be  equal.  Then  the  undulations  which  reach 
K  will  always  be  in  the  same/to^,  and  the  particle  of  ether  at  K  will  vibrate 
as  if  the  light  came  from  one  source  :  the  amplitude  of  the  vibration,  how- 
ever, will  be  increased  in  exactly  the  same  manner  as  happens  at  a  loop  or 
ventral  point ;  consequently  at  K  the  intensity  of  the  light  will  be  increased. 
And  the  same  will  be  true  for  all  parts  on  the  screen,  such  that  the  difference 
between  their  distances  from  the  two  images  equals  the  length  of  one,  two, 
three,  &c.,  undulations.  If,  on  the  other  hand,  the  distances  of  K  from  Fl 
and  F2  differ  by  the  length  of  half  an  undulation,  then  the  two  waves  would 
reach  K  in  exactly  opposite  phases.  Consequently,  whatever  velocity  would 
be  communicated  at  any  instant  to  a  particle  of  ether  by  the  one  undulation, 
an  exactly  equal  and  opposite  velocity  would  be  communicated  by  the  other 
undulation,  and  the  particle  would  be  permanently  at  rest,  or  there  would  be 
darkness  at  that  point  ;  this  result  being  produced  in  a  manner  precisely  re- 
sembling the  formation  of  a  nodal  point  already  explained.  The  same  will 
be  true  for  all  positions  of  K,  such  that  the  differences  between  its  distances 
from  Fj  and  F2  is  equal  to  three  halves,  or  five  halves,  or  seven  halves,  &c., 
of  an  undulation.  Accordingly,  there  will  be  on  the  screen  a  succession  of 
alternations  of  light  and  dark  points,  or  rather  lines — for  what  is  true  of  points 
in  the  plane  of  the  paper  (fig.  564)  will  be  equally  true  of  other  points  on  the 
screen,  which  is  supposed  to  be  at  right  angles  to  the  plane  of  the  paper. 
Between  the  light  and  dark  lines  the  intensity  of  the  light  will  vary,  increas- 
ing gradually  from  darkness  to  its  greatest  intensity,  and  then  decreasing 
to  the  second  dark  line,  and  so  on. 

QQ 


594  On  Light.  [645- 

If  instead  of  red  light  any  other  coloured  light  were  used — for  example, 
violet  light — an  exactly  similar  phenomenon  would  be  produced,  but  the  dis- 
tance from  one  dark  line  to  another  would  be  different.  If  white  light  were 
used,  each  separate  colour  tends  to  produce  a  different  set  of  dark  lines. 
Now  these  sets  being  superimposed  on  each  other,  and  not  coinciding,  the 
dark  lines  due  to  one  colour  are  illuminated  by  other  colours,  and  instead  of 
dark  lines  a  succession  of  coloured  bands  is  produced.  The  number  of 
coloured  bands  produced  by  white  light  is  much  smaller  than  the  number  of 
dark  lines  produced  by  a  homogeneous  light ;  since  at  a  small  distance  from 
the  middle  band  the  various  colours  are  completely  blended,  and  a  uniform 
white  light  produced. 

Y^646.  Diffraction  and  fringes. — Diffraction  is  a  modification  which  light 
undergoes  when  it  passes  the  edge  of  a  body,  or  when  it  traverses  a  small 
aperture — a  modification  in  virtue  of  which  the  luminous  rays  appear  to 
become  bent,  and  to  penetrate  into  the  shadow. 

This  phenomenon  may  be  observed  in  the  following  manner : — A  beam  of 
solar  light  is  allowed  to  pass  through  a  very  small  aperture  in  the  shutter  of 
a  dark  room,  where  it  is  received  on  a  condensing  lens,  L  (fig.  565),  with  a 


Fig.  565- 

short  focal  length.  A  red  glass  is  placed  in  the  aperture  so  as  to  allow  only 
red  light  to  pass.  An  opaque  screen,  e,  with  a  sharp  edge  a — a  razor,  for 
instance — is  placed  behind  the  lens  beyond  its  focus,  and  intercepts  one  por- 
tion of  the  luminous  cone,  while  the  other  is  projected  on  the  screen  b,  of 
which  B  represents  a  front  view.  The  following  phenomena  are  now  seen  : — 
Within  the  geometrical  shadow,  the  limit  of  which  is  represented  by  the  line 
ab,  a  faint  light  is  seen,  which  gradually  fades  in  proportion  as  it  is  farther 
from  the  limits  of  the  shadow.  In  this  part  of  the  screen — which,  being  above 
the  line  ab,  might  be  expected  to  be  uniformly  illuminated — a  series  of 
alternate  dark  and  light  bands  or  fringes  is  seen  parallel  to  the  line  of  shadow 
which  gradually  become  more  indistinct  and  ultimately -disappear.  The  limits 
between  the  light  and  dark  fringes  are  not  quite  sharp  lines :  there  are  parts 
of  maximum  and  minimum  intensity  which  gradually  fade  off  into  each  other. 

All  the  colours  of  the  spectrum  give  rise  to  the  same  phenomenon,  but 
the  fringes  are  broader  in  proportion  as  the  light  is  less  refrangible.  Thus, 
with  red  light  they  are  broader  than  with  green,  and  with  green  than  with 
violet.  Hence,  with  white  light,  which  is  composed  of  different  colours,  the 
dark  spaces  of  one  tint  overlap  the  light  spaces  of  another,  and  thus  a  series 
of  prismatic  colours  will  be  produced. 

If,  instead  of  placing  the  edge  of  an  opaque  body  between  the  light  and 
the  screen,  a  very  narrow  body  be  interposed,  such  as  a  hair  or  a  fine  metallic 
wire,  the  phenomena  will  be  different.  Outside  the  space  corresponding  to- 
the  geometrical  shadow,  there  is  a  series  of  fringes,  as  in  the  former  case. 
But  within  the  shadow  also  there  is  a  series  of  alternate  light  and  dark  bands. 


-647]  Gratings.  595 

They  are  called  interior  fringes,  and  are  much  narrower  and  more  numerous 
than  the  external  fringes. 

When  a  small  opaque  circular  disc  is  interposed,  white  light  being  used, 
its  shadow  on  the  screen  shows  in  the  middle  a  bright  spot  surrounded  by  a 
series  of  coloured  concentric  rings  ;  the  bright  spot  is  of  various  colours 
according  to  the  relative  positions  of  the  disc  and  screen.  The  haloes  some- 
times seen  round  the  sun  and  moon  belong  to  this  class  of  phenomena.  They 
are  due,  as  Fraunhofer  showed,  to  the  diffraction  of  light  by  small  globules 
of  fog  in  the  atmosphere.  Fraunhofer  even  gave  a  method  of  estimating 
the  mean  diameter  of  these  globules  from  the  dimensions  of  the  haloes. 

1647.  Grating-s. — Phenomena  of  diffraction  of  another  class  are  produced 
by  allowing  the  pencil  of  light  from  the  luminous  point  to  traverse  an  aper- 
ture in  the  form  of  a  narrow  slit  in  an  opaque  screen.     The  diffracted  light 
may  be  received  on  a  sheet  of 
white  paper,  but  the  images 
are  much  better  seen  through 
a  small  telescope  placed  be- 
hind   the    aperture.     If   the 
aperture   is   very  small,  the 
telescope  may  be  dispensed 
with,  and  the  figure  may  be 
viewed  by  placing  the  aper-  Fig  s66 

ture  before  the  eye.     If  now 

monochromatic  light,  red  for  instance  (572),  be  allowed  to  fall  through  such 
a  narrow  slit,  a  bright  band  of  red  light  is  seen,  and  right  and  left  of  it  a 
series  of  similar  bands  gradually  diminishing  in  brightness  and  separated  by 
dark  bands. 

The  breadth  of  these  bands  differs  with  the  nature  of  the  light,  being 
narrower  and  nearer  together  in  violet  than  in  green,  and  these  again  nar- 
rower and  nearer  than  in  red,  as  shown  in  fig.  566.  If  ordinary  white  light 
be  used,  then  the  colours  are  not  exactly  superposed,  but  a  series  of  equi- 
distant spectra  is  formed  on  each  side  of  the  bright  line,  with  their  violet 
side  turned  inwards. 

In  order  to  explain  this,  let  us  refer  to  fig.  567,  which  represents  the 
formation  of  the  first  dark  band.  When  light  is  incident  on  the  slit,  AB,  the 
particles  of  ether  there,  which  we  will  represent  by  the  dotted  lines,  will  be 
set  in  vibration,  and  each  point  will  become  the  centre  of  a  new  series  of 
oscillations.  Consider  now  the  undulations  which  constitute  a  ray  proceed- 
ing at  right  angles  to  the  plane  of  the  slit :  all  such  undulations  will  form  a 
band  of  light  on  the  screen  MN.  Those  which  are  not  parallel  but  proceed 
at  equal  inclinations,  and  meet  at  the  point  r,  will  be  in  the  same  phase  and 
will  reinforce  each  other,  and  the  line  of  maximum  brightness  will  be  at  r, 
Consider,  however,  a  pencil  of  rays  which  proceeds  from  the  slit  in  an 
oblique  direction  and  which  meets  the  screen,  or  the  retina,  in  the  point  s, 
and  let  us  suppose  that  the  difference  between  the  lengths  of  the  paths  of 
the  undulations  proceeding  from  the  edges  b  and  a — that  is,  bs  and  as — is 
equal  to  the  length  of  an  undulation.  Make  sc  =  sb  and  join  be  \  then  ac  is 
the  length  of  the  undulation. 

Let  us  suppose  that  the  whole  set  of  undulations  which  proceeds  from 

Q  Q  2 


On  Light. 


[647- 


Fig.  567. 


the  slit  ab  is  divided  at  d  into  two  equal  groups  of  undulations.  Then  a 
little  consideration  will  show  that  at  any  part  of  the  path  there  will  be  a  dif- 
ference of  phase  of  half  an  undulation  between  the  ray  from  the  margin  «, 

and  that  from  the  centre  d\  and  to  each 
undulation  constituting  the  group  on  the 
left  there  will  be  a  corresponding  one 
among  the  groups  on  the  right,  which  just 
differs  from  it  by  half  an  undulation  ;  the 
general  effect  will  be  that  the  group  on 
the  left  will  be  half  an  undulation  behind 
the  group  on  the  right,  and  both  arriving 
at  the  screen  in  opposite  phases  neutralise 
each  other  and  produce  darkness. 

When  the  difference  between  the  paths 
of  the  marginal  undulations  is  equal  to 
half  a  wave-length,  a  partial  destruction 
of  light  takes  place  ;  the  luminous  inten- 
sity corresponding  to  this  obliquity  is  a 
little  less  than  half  that  of  the  undiffracted 
—  B  light.  If  the  marginal  distance  is  one 
and  a  half  undulations,  we  can,  as  before, 
conceive  the  whole  pencil  divided  into 
three  parts,  of  which  two  will  neutralise  each  other,  and  the  third  only  will 
be  effective.  There  will  be  a  luminous  band,  but  one  of  less  intensity.  In 
like  manner  where  the  marginal  undulations  differ  by  two  whole  wave- 
lengths, they  will  again  extinguish  each  other,  and  a  dark  band  will  be  the 
result.  Thus  there  will  be  formed  a  series  of  alternate  dark  and  bright 
bands  of  rapidly  diminishing  intensity.  In  general,  when  the  difference  of 
path  of  the  rays  proceeding  from  the  margin  of  the  slit  amounts  to  n  wave- 
lengths, n  being  any  whole  number,  we  have  a  dark  band,  and  when  it 
amounts  to  n  +  £  wave-lengths,  a  bright  band. 

The  phenomena  of  diffraction  produced  when  other  than  straight  lines  are 
used  are  often  of  great  beauty.  They  have  been  more  particularly  examined 
by  Schwerdt,  and  the  whole  of  the  phenomena  are  in  exact  accordance  with 
the  undulatory  theory,  though  the  explanation  is  in  many  cases  somewhat 
intricate.  The  theory  renders  it  possible  to  predict  the  appearance  which 
any  particular  aperture  will  produce,  just  as  astronomy  enables  us  to  foretell 
the  motions  of  the  heavenly  bodies.  Some  of  the  simpler  forms — such  as 
straight  lines,  triangles,  squares — may  be  cut  out  of  tinfoil  pasted  on  glass, 
and  apertures  of  any  form  may  be  produced  with  great  accuracy  by  taking 
on  glass  a  collodion  photograph  of  a  sheet  of  paper,  on  which  the  required 
shapes  are  drawn  in  black. 

Looking  through  any  of  these  apertures  at  a  luminous  point,  we  see  it  sur- 
rounded with  coloured  spectra  of  very  various  forms,  and  of  great  beauty. 
The  beautiful  colours  seen  on  looking  through  a  bird's  feather  at  a  distant 
source  of  light,  and  the  colours  of  striated  surfaces,  such  as  mother-of-pearl, 
are  due  to  a  similar  cause.  A  beautiful  phenomenon  of  the  same  kind  is  the 
aureole  observed  on  looking  at  a  candle  flame  through  lycopodium  powder 
strewn  on  glass. 


-648]  Diffraction  Spectra.  597 

648.  Diffraction  Spectra.— The  most  important  of  these  figures  are  the 
gratings  proper,  which  may  be  produced  by  arranging  a  series  of  fine  wires 
parallel  to  each  other,  or  by  careful  ruling  on  a  piece  of  smoked  glass,  or  by 
photographic  reduction.  Nobert  has  made  such  gratings  by  ruling  lines  on 
glass  with  a  diamond,  in  which  there  are  no  less  than  12,000  lines  in  an  inch 
in  breadth.  Dr.  Stone  has  constructed  such  gratings  for  reflection,  by  ruling 
lines  on  plates  of  nickel ;  this  metal  has  the  advantage  of  hardness,  non- 
liability to  tarnish,  and  great  reflecting  power. 

If  a  grating  be  used  instead  of  a  single  slit,  as  above  described,  the 
phenomena  are  in  general  the  same,  though  of  greater  brilliancy.  With 
homogeneous  light  and  such  a  grating,  there  is  seen,  on  each  side  of  the 
central  bright  line,  a  series  of  sharply  defined  narrow  bands  and  lines  of 
light,  gradually  increasing  in  breadth  and  diminishing  in  intensity  as  their 
distance  from  the  central  line  increases.  If  white  light  be  used  the  white 


Fig.  566. 

band  is  seen  in  [the  centre,  and  on  each  side  of  it  a  sharply  defined  iso- 
lated spectrum  with  the  violet  edges  inwards.  Next  to  this,  and  separated 
by  a  dark  interval,  is  on  each  side  a  somewhat  broader  but  similar  spectrum, 
and  then  follow  others  which  become  fainter  and  broader  and  overlap 
each  other.  The  brightness  and  sharpness  of  these  spectra  depend  on  the 
closeness  of  the  lines,  and  on  the  opacity  of  the  intermediate  space.  In 
those  which  are  ruled  by  diamond  on  glass,  the  parts  scratched  represent 
the  opaque  parts. 

For  objective  representation  the  image  of  a  slit  in  a  dark  shutter, 
through  which  the  sunlight  enters,  is  focussed  by  means  of  a  convex  lens  on 
a  screen  at  a  distance,  and  then  a  grating  is  placed  in  the  path  of  the  rays. 

The  spectra  produced  by  means  of  a  grating  are  known  as  interference  or 
diffraction  spectra.  Very  accurate  gratings  can  now  be  easily  and  cheaply 
prepared  by  means  of  photography,  and  their  use  for  scientific  purposes  is 
extending. 

There  are  many  points  of  difference  between  these  spectra  and  those 
produced  by  the  prism,  and  for  scientific  work  the  former  are  preferable. 

A  diffraction  spectrum  is  the  purer  the  greater  the  number  of  lines  in  the 
grating,  provided  they  are  equidistant.  The  spectra  are,  however,  not  more 
than  i  as  bright  as  prismatic  spectra ;  and,  to  obtain  the  maximum  bright- 
ness, the  opaque  intervals  should  be  as  opaque  and  the  transparent  ones 
as  transparent  as  possible. 


598  On  Light.  [648- 

On  the  other  hand,  in  diffraction  spectra,  the  colours  are  uniformly  dis- 
tributed in  their  true  order  and  extent  according  to  the  difference  in  their 
wave-lengths,  and  according  therefore  to  a  property  which  is  inherent  in  the 
light  itself ;  while  in  prismatic  spectra  the  red  rays  are  concentrated,  and  the 
violet  ones  dispersed.  In  diffraction  spectra  the  centre  is  the  brightest  part. 

Fig.  568  represents  a  grating  spectrum,  together  with  an  equally  long 
spectrum  produced  by  a  flint-glass  prism  ;  the  upper  being  that  produced  by 
the  grating.  It  will  be  seen  that  D  in  the  one  spectrum  is  in  almost  exactly 
the  same  position  as  F  in  the  other. 

Diffraction  spectra  have,  moreover,  the  advantage  of  giving  a  far  larger 
number  of  dark  lines,  and  of  giving  them  in  their  exact  relative  positions. 
Thus,  in  a  particular  region  in  which  Angstrom  had  mapped  118  lines, 
Draper,  by  means  of  a  diffraction  spectrum,  was  able  to  photograph  at  least 
293.  Diffraction  spectra  also  extend  farther  in  the  direction  of  the  ultra- 
violet, and  give  more  dark  lines  in  that  region. 

The  most  perfect  gratings  have  quite  recently  been  constructed  by 
Professor  Rowland,  of  Baltimore,  by  means  of  a  machine  specially  planned 
and  constructed  for  the  purpose,  and  the  chief  feature  in  which  is  a  practi- 
cally perfect  screw.  Using  this  machine,  he  has  been  able  to  rule  gratings 
with  as  many  as  43,000  lines  to  the  inch,  nor  does  this  represent  the  limit  of 
the  power  of  the  machine.  Gratings  with  14,000  or  28,000  lines  give,  however, 
the  best  definition.  Another  great  improvement  is  to  rule  the  gratings  on 
spherical  instead  of  on  flat  surfaces  ;  in  this  way  the  spectrum  can  be  formed 
without  a  telescope,  which  is  a  matter  of  great  importance,  as  telescopes 
interfere  with  a  great  many  experiments.  The  spectroscope  is  thus  reduced 
to  its  simplest  form,  so  that  an  instrument  of  very  high  power  may  be  con- 
structed at  a  small  cost. 

By  means  of  his  gratings  Professor  Rowland  has  been  able  to  resolve 
lines  in  the  spectrum  which  had  never  hitherto  been  separated. 

649.  Determination  of  wave-length. — The  relative  positions  of  these 
bright  and  dark  lines  furnish  a  means  of  calculating  the  wave-length  or 
length  of  undulation  of  any  particular  colour.  We  must  first  of  all  know 
the  distance  rs  of  the  first  dark  band  from  the  bright  one.  The  bands  are 
not  uniform  in  brightness,  or  darkness,  but  there  is  in  each  case  a  position  of 
maximum  intensity,  and  it  is  from  these  that  the  distances  are  measured. 
If  the  bands  are  viewed  through  a  telescope,  the  angle  is  observed  through 
which  the  axis  must  be  turned  from  the  position  in  which  the  cross  wire 
coincides  with  the  centre  of  the  bright  band  to  that  in  which  it  coincides 
with  the  centre  of  the  dark  band.  From  this  angle,  which  can  be  very'  ac- 
curately measured,  the  distance  is  easily  calculated.  When  the  diffraction 
bands  are  received  on  a  screen,  the  distance  may  be  directly  measured,  and 
most  accurately  by  taking  half  the  distance  between  the  centres  of  the  first 
pair  of  dark  bands. 

We  have  thus  the  similar  triangles  abc,  and  rds,  in  which  ac\bc  =  rs\  rd 
(fig.  567).  Now  be  may  be  taken  equal  to  ab,  the  width  of  the  slit,  which  can 
be  measured  directly  with  great  accuracy  by  means  of  a  micrometric  screw 
(n),  and  rd\s  the  distance  of  the  screen.  Hence 

rjx  ab 

ac=  -    - — . 
rd 


-650]  Colours  of  Thin  Plates.     Newton's  Rings.  599 

Now  aC)  the  difference  between  as  and  sc,  equal  to  the  length  of  an  undu- 
lation of  this  particular  colour.  In  one  experiment  with  red  light  the  width 
of  the  slit  ab  was  0-015  in.,  the  distance  rs  0-15  in.,  and  the  distance  of  the 


screen  93  in.,  which  gave  ^=°--X_     -     0-000024  in.  as  the  wave-length 

of  red  light.  Using  blue  light  the  distance  of  rs  was  found  to  be  cri,  which 
gives  0-000016. 

Knowing  the  length  of  the  undulations,  we  can  easily  calculate  their 

number  in  a  second,  n,  from  the  formula  n  =  ^  (232),  where  v  is  the  velocity 

of  light.  Taking  this  at  186,000  miles,  we  get  for  the  red  corresponding  to 
the  dark  line  B  434,420,000,000,000  as  the  number  of  oscillations  in  a  second, 
and  for  the  H  in  the  violet  758,840,000,000,000  undulations. 

If,  instead  of  a  single  slit,  gratings  be  used,  we  have  the  possibility  of 
more  accurate  results,  for  the  contrast  is  greater,  and  thus  the  distance  is 
more  easily  determined.  The  width  of  the  slit  is  then  easily  calculated  if  we 
know  the  number  of  lines  in  a  given  space. 

Y*t5'5o.  Colours  of  thin  plates.  Newton's  rings.  —  All  transparent  bodies, 
solids,  liquids,  or  gases,  when  in  sufficiently  fine  laminae,  appear  coloured 
with  very  bright  tints,  especially  by  reflection.  Crystals  which  cleave  easily, 
and  can  be  obtained  in  very  thin  plates,  such  as  mica  and  selenite,  show  this 
phenomenon,  which  is  also  well  seen  in  soap-bubbles  and  in  the  layers  of  air 
in  cracks  in  glass  and  in  crystals.  A  drop  of  oil  spread  rapidly  over  a  large 
sheet  of  water  exhibits  all  the  colours  of  the  spectrum  in  a  constant  order. 
A  soap-bubble  appears  white  at  first,  but,  in  proportion  as  it  is  blown  out, 
brilliant  iridescent  colours  appear,  especially  at  the  top,  where  it  is  thinnest. 
These  colours  are  arranged  in  horizontal  zones  around  the  summit,  which 
appears  black  when  there  is  not  thickness  enough  to  reflect  light,  and  the 
bubble  then  suddenly  bursts. 

Newton,  who  first  studied  the  phenomena  of  the  coloured  rings  in  soap- 
bubbles,  wishing  to  investigate  the  relation  between  the  thickness  of  the 
thin  plate,  the  colour  of 
the  rings,  and  their  extent, 
produced  them  by  means 
of  a  layer  of  air  interposed       .__________tpi__________^ 

between  two  glasses,  one 

plane  and  the  other  con- 

vex, and  with  a  very  long  Flg-  s69< 

focus  (fig.  569).     The  two  surfaces  being  cleaned  and  exposed  to  ordinary 

light  in  front  of  a  window,  so  as  to  reflect  light,  there  is  seen  at  the  point  of 

contact  a  black  spot  surrounded  by  six  or  seven  coloured  rings,  the  tints  of 

which  become  gradually  less  strong.    If  the  glasses  are  viewed  by  transmitted 

light,  the  centre  of  the  rings  is  white,  and  each  of  the  colours  is  exactly  com- 

plementary of  that  of  the  rings  by  reflection.     The  lens  and  the  glass  plate 

are  usually  arranged  in  a  brass  mount  which  by  means  of  three  screws  allows 

the  pressure  to.be  regulated. 

With  homogeneous  light,  red  for  example,  the  rings  are  successively 
black  and  red  ;  the  diameters  of  corresponding  rings  are  less  as  the  colour 
is  more  refrangible,  but  with  white  light  the  rings  are  of  the  different  colours 


6oo  On  Light.  [650- 

of  the  spectrum,  which  arises  from  the  fact  that,  as  the  rings  of  the  different 
simple  colours  have  different  diameters,  they  are  not  exactly  superposed,  but 
are  more^or  less  separated. 

It  is  usual  to  speak  of  the  successive  rings  as  the  first,  second,  third,  &c. 
By  the  first  ring  is  understood  that  of  least  diameter.  Knowing  the  radius 
of  any  particular  ring,  p,  and  the  radius  of  curvature,  R,  of  the  lens,  the  thick- 
ness, d,  of  the  corresponding  layer  of  air  is  given  approximately  by  the 
formula 

*.£L 

2R 

Newton  found   that  the  thicknesses  corresponding  to  the  successive  dark 

rings  are  proportional  to  the  numbers  o,  2,  4,  6 ,  while  for  the 

bright  rings  the  thicknesses  were  proportional  to  i,  3,  5 He  found 

that  for  the  first  bright  ring  the  thickness  was  ^-—QQ  of  an  inch,  when  the 
light  used  was  the  brightest  part  of  the  spectrum  ;  that  is,  the  part  on  the 
confines  of  the  orange  and  yellow  rays. 

If  the  focal  length  of  the  lens  is  from  three  to  four 
yards,  the  rings  can  be  seen  with  the  naked  eye ;  but 
if  the  length  is  less,  the  rings  must  be  looked  at  with 
a  lens. 

651.  Explanation  of  Newton's  rings. — Newton's 
rings,  and  all  phenomena  of  thin  plates,  are  simple 
cases  of  interference. 

In  fig.  570,  let  MNOP  represent  a  thin  plate  of  a 
transparent  body,  on  which  a  pencil  of  parallel  rays 
\j  L  of  homogeneous  light,   ab,    impinges:    this  will   be 

partially  reflected  in  the  direction  <fc,  and  partially  re- 
fracted towards  d.  But  the  refracted  ray  will  under- 
go a  second  reflection  at  the  surface,  OP  ;  the  reflected  ray  will  emerge  at  e  in 
the  same  direction  as  the  pencil  of  light  reflected  at  the  first  surface  ;  and 
consequently  the  two  pencils  be  and  ef  will  destroy  or  augment  each  other's 
effect  according  as  they  are  in  the  same  or  different  phases.  We  shall  thus 
have  an  effect  produced  similar  to  that  of  the  fringes. 


POLARISATION   OF  LIGHT. 

652.  Polarisation  by  double  refraction. — It  has  been  already  seen  that 
when  a  ray  of  light  passes  through  a  crystal  of  Iceland  spar  (641),  it  becomes 
divided  into  two  rays  of  equal  intensity  \  viz.  the  ordinary  ray,  and  the  ex- 
traordinary ray.  These  rays  are  found  to  possess  other  peculiarities,  which 
are  expressed  by  saying  they  are  polarised ';  namely,  the  ordinary  ray  in  a 
principal  plane,  and  the  extraordinary  ray  in  a  plane  at  right  angles  to  a 
principal  plane.  The  phenomena  which  are  thus  designated  may  be  de- 
scribed as  follows  : — Suppose  a  ray  of  light  which  has  undergone  ordinary 
refraction  in  a  crystal  of  Iceland  spar,  to  be  allowed  to  pass  through  a  second 
crystal,  it  will  generally  be  divided  into  two  rays  ;  namely,  one  ordinary,  and 
the  other  extraordinary,  but  of  unequal  intensities.  If  the  second  crystal 
be  turned  round  until  the  two  principal  planes  coincide — that  is,  until  the 


-653] 


Polarisation  by  Reflection. 


60 1 


crystals  are  in  similar  or  in  opposite  positions — then  the  extraordinary  ray 
disappears,  and  the  ordinary  ray  is  at  its  greatest  intensity  ;  if  the  second 
crystal  is  turned  farther  round,  the  extraordinary  ray  reappears,  and-increases 
in  intensity  as  the  angle  increases,  while  the  ordinary  ray  diminishes  in  in- 
tensity until  the  principal  planes  are  at  right  angles  to  each  other,  when  the 
extraordinary  ray  is  at  its  greatest  intensity  and  the  ordinary  ray  vanishes. 
These  are  the  phenomena  produced  when  the  ray  which  experienced  ordi- 
nary refraction  in  the  first  crystal  passes  through  the  second.  If  the  ray 
which  has  experienced  extraordinary  refraction  in  the  first  crystal  is  allowed 
to  pass  through  the  second  crystal  the  phenomena  are  similar  to  those  above 
described  ;  but  when  the  principal  planes  coincide,  an  extraordinary  ray  alone 
emerges  from  the  second  crystal,  and  when  the  planes  are  at  right  angles,  an 
ordinary  ray  alone  emerges. 

These  phenomena  may  also  be  thus  described  : — Let  O  and  E  denote 
the  ordinary  and  extraordinary  rays  produced  by  the  first  crystal.  When 
O  enters  the  second  crystal,  it  generally  gives  rise  to  two  rays,  an  ordinary 
(O0),  and  an  extraordinary  (O^),  of  unequal  intensities.  When  E  enters  the 
second  crystal,  it  likewise  gives  rise  to  two  rays,  viz.  an  ordinary  (E0)  and 
an  extraordinary  (E*),  of  unequal  intensities,  the  intensities  varying  with 
the  angle  between  the  principal  planes  of  the  crystals.  When  the  principal 
planes  coincide,  only  two  rays,  viz.  O0  and  E<?,  emerge  from  the  second 
crystal,  and  when  the  planes  are  at  right  angles,  only  two  rays,  viz.  O<?  and 
E0,  emerge  from  the  second  crystal.  Since  O  gives  rise  to  an  ordinary  ray 
when  the  principal  planes  are  parallel,  and  E  gives  rise  to  an  ordinary  ray 
when  they  are  at  right  angles,  it  is  manifest  that  O  is  related  to  the  principal 
plane  in  the  same  manner  that  E  is  related  to  a  plane  at  right  angles  to  a 
principal  plane. 

This  phenomenon,  which  is  produced  by  all  double-refracting  crystals, 
was  observed   by   Huyghens   in    Iceland   spar,   and   in   consequence  of  a. 
suggestion  of  Newton's  was  afterwards  called 
polarisation.    It  remained,  however,  an  isolated 
fact  until  the  discovery  of  polarisation  by  re- 
flection recalled  the  attention  of  physicists  to 
the  subject.   The  latter  discovery  was  made  by 
Malus  in  1808. 

\  653.  Polarisation  by  reflection.— When 
a  ray  of  light,  ab  (fig.  571),  falls  on  a  polarised 
unsilvered  glass  surface,  fghi,  inclined  to  it  at 
an  angle  of  35°  25',  it  is  reflected,  and  the 
reflected  ray  is  polarised  in  the  plane  of  re- 
flection. If  it  were  transmitted  through  a 
crystal  of  Iceland  spar,  it  would  pass  through 
without  bifurcation,  and  undergo  an  ordinary  ^ 
refraction,  when  the  principal  plane  coincides 
with  the  plane  of  reflection  ;  it  would  also  be 
transmitted  without  bifurcation,  but  undergo 
extraordinary  refraction,  when  the  principal  plane  is  at  right  angles  to  the 
plane  of  reflection  ;  in  other  positions  of  the  crystal  it  would  give  rise  to  an 
ordinary  and  an  extraordinary  ray  of  different  intensities,  according  to  the 


Fig.  571- 


€02  On  Light.  [653- 

angle  between  the  plane  of  reflection  and  the  principal  plane  of  the  crystal. 
The  peculiar  property  which  the  light  has  acquired  by  reflection  at  the  sur- 
face fghi  can  also  be  exhibited  as  follows  : — Let  the  polarised  ray  be  be 
received  at  c,  on  a  second  surface  of  unsilvered  glass,  at  the  same  angle,  viz. 
35°  25'.  If  the  surfaces  are  parallel,  the  ray  is  reflected  ;  but  if  the  second 
plate  is  caused  to  turn  round  cb^  the  intensity  of  the  reflected  ray  continually 
diminishes,  and  when  the  glass  surfaces  are  at  right  angles  to  each  other,  no 
light  is  reflected.  By  continuing  to  turn  the  upper  mirror  the  intensity  of 
the  reflected  ray  gradually  increases,  and  attains  a  maximum  value  when  the 
surfaces  are  again  parallel. 

The  above  statement  will  serve  to  describe  the  phenomenon  of  polarisa- 
tion by  reflection  so  far  as  the  principles  are  concerned  ;  the  apparatus  best 
adapted  for  exhibiting  the  phenomenon  will  be  described  farther  on. 

654.  Angle  of  polarisation. — The  polarising  angle  of  a  substance  is  the 
angle  which  the  incident  ray  must  make  with  the  perpendicular  to  a  plane 
polished  surface  of  that  substance  in  order  that  the  polarisation  be  complete. 
For  glass  this  angle  is  54°  35',  and  if  in  the  preceding  experiment  the  lower 
mirror  were  inclined  at  any  other  angle  than  this,  the  light  would  not  be 
•completely  polarised  in  any  position  ;  this  would  be  shown  by  its  being 
partially  reflected  from  the  upper  surface  in  all  positions.  Such  light  is 
said  to  be  partially  polarised.  The  polarising  angle  for  water  is  52°  45' ; 
for  quartz,  57°  32' ;  for  diamond,  68°  ;  and  it  is  56°  30'  for  obsidian,  a  kind  01 
volcanic  glass  which  is  often  used  in  these  experiments. 

Light  which  is  reflected  from  the  surface  of  water,  from  a  slate  roof,  from 
a  polished  table,  or  from  oil  paintings,  is  all  more  or  less  polarised.  The 
ordinary  light  of  the  atmosphere  is  frequently  polarised,  especially  in  the 
earlier  and  later  periods  of  the  day,  when  the  solar  rays  fall  obliquely  on 
the  atmosphere.  Almost  all  reflecting  surfaces  may  be  used  as  polarising 
mirrors.  Metallic  surfaces  form,  however,  an  important  exception. 

Brewster  has  discovered  the  following  remarkably  simple  law  in  reference 
to  the  polarising  angle  : — 

The  polarising  angle  of  a  substance  is  that  angle  of  incidence  for  which 
the  reflected  polarised  ray  is  at  right  angles  to  the  refracted  ray. 

Thus,  in  fig.  572,  if  si  is  the  incident,  ir 
the  refracted,  and  if  the  reflected  ray,  the 
polarisation  is  most  complete  when  fi  is  at 
right  angles  to  ir. 

Thefl/ane  of  polarisation  is  the  plane  of 
reflection  in  which  the  light  becomes  polar- 
ised ;  it  coincides  with  the  plane  of  inci- 
dence, and  therefore  contains  the  polarising 
angle. 

A  simple  geometrical  consideration  will 
show  that  the  above  law  may  be   thus   ex- 
Flg-  572'  pressed  -.—The  tangent  of  the  angle  of  polari- 

sation of  a  substance  is  equal  to  its  refractive  index.  As  the  refractive  index 
differs  with  the  different  colours,  it  follows  that  the  angle  of  polarisation  can- 
not be  the  same  for  all  colours.  This  explains  why  a  ray  of  white  light  is 
never  completely  polarised. 


— 657J  Norrembergs  Apparatus.  603 

K  655.  Polarisation  by  single  refraction. — When  an  unpolarised  lu- 
minous ray  falls  upon  a  glass  plate  placed  at  the  polarising  angle,  one  part 
is  reflected  ;  the  other  part  becomes  refracted  in  passing  through  the  glass, 
-and  the  transmitted  light  is  now  found  to  be  partially  polarised.  If  the  light 
which  has  passed  through  one  plate,  and  whose  polarisation  is  very  feeble, 
be  transmitted  through  a  second  plate  parallel  to  the  first,  the  effects  become 
more  marked,  and  by  ten  or  twelve  plates  are  tolerably  complete.  A  bundle 
of  such  plates,  for  which  the  best  material  is  the  glass  used  for  covering 
microscopic  objects,  fitted  in  a  tube  at  the  polarising  angle,  is  frequently 
used  for  examining  or  producing  polarised  light. 

If  a  ray  of  light  fall .  at  any  angle  on  a  transparent  medium,  the  same 
holds  good  with  a  slight  modification.  In  fact,  part  of  the  light  is  reflected 
and  part  refracted,  and  both  are  found  to  be  partially  polarised,  equal  quan- 
tities in  each  being  polarised,  and  their  planes  of  polarisation  being  at  right 
angles  to  each  other.  It  is,  of  course,  to  be  understood  that  the  polarised 
portion  of  the  reflected  light  is  polarised  in  the  plane  of  reflection,  which  is 
likewise  the  plane  of  refraction. 

\f^6$6.  Polarising-  instruments. — Every  instrument  for  investigating  the 
properties  of  polarised  light  consists  essentially  of  two  parts — one  for  polaris- 
ing the  light,  the  other  for  ascertaining  or  exhibiting  the  fact  of  light  having 
undergone  polarisation.  The  former  part  is  called  the  polariser,  the  latter 
the  analyser.  Thus  in  art.  652  the  crystal  producing  the  first  refraction  is 
the  polariser,  that  producing  the  second  refraction  is  the  analyser.  In  art. 
653  the  mirror  at  which  the  first  reflection  takes  place  is  the  polariser,  that 
.at  which  the  second  reflection  takes  place  is  the  analyser.  Some  of  the 
most  convenient  means  of  producing  polarised  light  will  now  be  described, 
and  it  will  be  remarked  tbat  any  instrument  that  can  be  used  as  a  polariser 
•can  also  be  used  as  an  analyser.  The  experimenter  has  therefore  consider- 
able^ liberty  of  selection. 

("""657.  Worremtoerg's  apparatus. — The  most  simple  but  complete  instru- 
ment for  polarising  light  is  that  invented  by  Norremberg.  It  maybe  used 
for  repeating  most  of  the  experiments  on  polarised  light. 

It  consists  of  two  brass  rods,  b  and  d  (fig.  573),  which  support  an  unsil- 
vered  mirror,  n,  of  ordinary  glass,  movable  about  a  horizontal  axis.  A  small 
graduated  circle  indicates  the  angle  of  inclination  of  the  mirror.  Between 
the  feet  of  the  two  columns  there  is  a  silvered  glass,  p,  which  is  fixed  and 
horizontal.  At  the  upper  end  of  the  columns  there  is  a  graduated  plate,  /, 
in  which  a  circular  disc,  o,  rotates.  This  disc,  in  which  there  is  a  square 
.aperture,  supports  a  mirror  of  black  glass,  m,  which  is  inclined  to  the  vertical 
at  the  polarising  angle.  An  annular  disc,  k,  can  be  fixed  at  different  heights 
•on  the  columns  by  means  of  a  screw.  A  second  ring,  a,  may  be  moved 
around  the  axis.  It  supports  a  black  screen,  in  the  centre  of  which  there  is 
a  circular  aperture. 

When  the  mirror  n  makes  with  the  vertical  an  angle  of  35°  25',  which  is 
the  complement  of  the  polarising  angle  for  glass,  the  luminous  rays,  S/z, 
which  meet  the  mirror  at  this  angle,  become  polarised,  and  are  reflected  in 
the  direction  np  to  wards  the  mirror/,  which  sends  them  in  the  direction  pnr. 
After  having  passed  through  the  glass,  n,  the  polarised  ray  falls  upon  the 
blackened  glass  m  under  an  angle  of  35°  25',  because  the  mirror  makes 


604 


On  Light. 


[657- 


exactly  the  same  angle  with  the  vertical.     But  if  the  disc,  0,  to  which  the 
mirror,  ?/z,  is  fixed,  be  turned  horizontally,  the  intensity  of  the  light  reflected 

from  the  upper  mirror  gradually 
diminishes,  and  totally  disap- 
pears when  it  has  been  moved 
through  90°.  The  position  is 
that  represented  in  the  diagram  : 
the  plane  of  incidence  on  the 
upper  mirror  is  then  perpendi- 
cular to  the  plane  of  incidence, 
Snfl,  on  the  mirror  n.  When  the 
upper  mirror  is  again  turned,  the 
intensity  of  the  light  increases 
uutil  it  has  passed  through  180°, 
when  it  again  reaches  a  maxi- 
mum. The  mirrors  m  and  n 
are  then  parallel.  The  same 
phenomena  are  repeated  as  the 
mirror  m  continues  to  be  turned 
in  the  same  direction,  until  it 
again  comes  into  its  original 
position  ;  the  intensity  of  the 
reflected  light  being  greatest 
when  the  mirrors  are  parallel, 
and  being  reduced  to  zero  when 
they  are  at  right  angles.  If  the 
mirror  m  is  at  a  greater  or  less 
angle  than  35°  25',  a  certain, 
quantity  of  light  is  reflected  in. 
all  positions  of  the  plane  of  in- 
cidence. 

658.  Tourmaline. — The  primary  form  of  this  crystal  is  a  regular  hex- 
agonal prism.  Tourmaline,  as  already  stated,  is  a  negative  uniaxial  crystal^ 
and  its  optic  axis  coincides  with  the  axis  of  the  prism.  For  optical  purposes 
a  plate  is  cut  from  it  parallel  to  the  axis.  When  a  ray  of  light  passes 
through  such  a  plate,  an  ordinary  ray  and  an  extraordinary  ray  are  produced 
polarised  in  planes  at  right  angles  to  each  other  ;  viz.  the  former  in  a  plane 
at  right  angles  to  the  plate  parallel  to  the  axis,  and  the  latter  in  a  plane  at 
right  angles  to  the  axis.  The  crystal  possesses,  however,  the  remarkable 
property  of  rapidly  absorbing  the  ordinary  ray  ;  consequently,  when  a  plate 
of  a  certain  thickness  is  used,  the  extraordinary  ray  alone  emerges — in 
other  words,  a  beam  of  common  light  emerges  from  the  plate  of  tourmaline 
polarised  in  a  plane  at  right  angles  to  the  axis  of  the  crystal.  If  the  light 
thus  transmitted  be  viewed  through  another  similar  plate  held  in  a  parallel 
position,  little  change  will  be  observed  excepting  that  the  intensity  of  the 
transmitted  light  will  be  about  equal  to  that  which  passes  through  a  plate  of 
double  the  thickness  ;  but  if  the  second  tourmaline  be  slowly  turned,  the 
light  will  become  feebler,  and  will  ultimately  disappear  when  the  axes  of  the 
two  plates  are  at  right  angles. 


-660]  Nicer s  Prism.  605 

The  objections  to  the  use  of  the  tourmaline  are  that  it  is  not  very  trans- 
parent, and  that  plates  of  considerable  thickness  must  be  used  if  the  polarisa- 
tion is  to  be  complete.  For  unless  the  ordinary  ray  is  completely  absorbed 
the  emergent  light  will  be  only  partially  polarised. 

Herapath  discovered  that  sulphate  of  iodoquinine  has  the  property  of 
polarising  light  in  a  remarkable  degree.  Unfortunately,  it  is  a  very  fragile 
salt,  and  difficult  to  obtain  in  large  crystals. 

659.  l>oul>le-refracting:  prism  of  Iceland  spar. — When  a  ray  of  light 
passes  through  an  ordinary  rhombohedron  of  Iceland  spar,  the  ordinary  and 
extraordinary  rays  emerge   parallel   to   the   original  ray,  consequently  the 
separation  of  the  rays  is  proportional  to  the  thickness  of  the  prism.     But  if 
the  crystal  is  cut  so  that  its  faces  are  inclined  to  each  other,  the  deviations 
of  the  ordinary  and  extraordinary  rays  will  be  different,  they  will  not  emerge 
parallel,  and  their  separation  will   be   greater   as   their   distance  from  the 
prism  increases.     The  light,  however,  in  passing  through  the  prism  becomes 
decomposed,  and  the  rays  will  be  coloured.      It  is  therefore  necessary  to 
achromatise   the   prism,  which  is  done  by  combining  it  with  .a   prism   of 
glass  with  its  refracting  angle  turned  in  the  contrary  direction  (fig.  575).     In 
order  to  obtain  the  greatest  amount  of  divergence,  the  refracting  edges  of 
the  prism  should  be  cut  parallel  to  the  optic  axis,  and  this  is  always  done. 

Let  us  suppose  that  a  ray  of  polarised  light  passes  along 
the  axis  of  the  cylinder  (fig.  575),  and  let  us  suppose  that  the 
•cylinder  is  caused  to  turn  slowly  about  its  axis  ;   then  the 
resulting  phenomena  are  exactly  like  those  already  described 
(643).    Generally  there  will  be  an  ordinary  and  extraordinary 
ray  produced,  whose  relative  intensities  will  vary  as  the  tube 
is  turned.     But  in  two  opposite  positions  the  ordinary  ray 
alone  will  emerge,  and  in  two  others  at  right  angles  to  the          *$'ig.  575. 
former  the  extraordinary  ray  will  alone  emerge.     When  the 
ordinary  ray  alone  emerges,  the  principal  plane  of  the  crystal— that  is,  a 
plane  at  right  angles  to  its  face,  and  parallel  to  its  refracting  edge — coincides 
with  the  original  plane  of  polarisation  of  the  ray.     Consequently,  by  means 
of  the  prism,  it  can  be  ascertained  both  that  the  ray  is  polarised,  and  like- 
wise the  plane  in  which  it  is  polarised. 

660.  Nicol's   prism. — The    Nicol's  prism  is  one  of  the  most  valuable 
means  of  polarising  light,  for  it  is  perfectly  colourless,  it  polarises  light  com- 
pletely, and  it  transmits  only  one  beam  of  polarised  light,  the  other  being 
entirely  suppressed. 

It  is  constructed  out  of  a  rhombohedron  of  Iceland  spar,  about  an  inch 
in  height  and  ^  of  an  inch  in  breadth.  This  is  bisected  in  the  plane  which 
passes  through  the  obtuse  angles  as  shown  in  fig.  577  ;  that  is,  along  the 
plane  acbd  (fig.  563).  The  two  halves  are  then  again  joined  in  the  same 
order  by  means  of  Canada  balsam. 

The  principle  of  the  Nicol's  prism  is  this  : — The  refractive  index  of  Canada 
balsam,  i'549,  is  less  than  the  ordinary  index  of  Iceland  spar  1*654,  but  greater 
than  its  extraordinary  index  i'483-  Hence,  when  a  luminous  ray  SC  (fig. 
577)  enters  the  prism,  the  ordinary  ray  is  totally  reflected  on  the  surface,  ab, 
and  takes  the  direction!  Q/O,  by  which  it  is  refracted  out  of  the  crystal, 
while  the  extraordinary  ray,  C<?,  emerges  alone.  Since  the  Nicol's  prism 


606  On  Light.  [660- 

allows  only  the  extraordinary  ray  to  pass,  it  may  be  used,  like  a  tourmaline, 
as  an  analyser  or  as  a  polariser. 

Foucault  replaced  the  layer  of  Canada  balsam  by  one  of  air,  the  two- 
prisms  being  kept  together  by  the  mounting.  The  advantage  of  this  is  that 
the  section  ab  (fig.  577)  need  not  be  so  acute,  so  that  the  prism  becomes 
shorter,  and  therefore  cheaper. 


Fig.  576.  Fig,  577. 

Nicol's  prism  is  the  most  important  feature  of  most  polarising  apparatus. 
It  is  better  than  the  polarising  mirror  on  account  of  its  more  complete  polar- 
isation, and  has  the  advantage  over  tourmaline  of  giving  a  colourless  field 
of  view. 

\  661.  Physical  theory  of  polarised  light. — The  explanation  of  the  dark 
bands  produced  by  the  interference  of  light  is  stated  in  art.  650  to  resemble 
exactly  that  of  the  formation  of  nodes  and  loops  given  in  art.  276. 

It  might  hence  be  supposed  that  the  vibrations  producing  light  are  quite 
similar  to  those  producing  sound.  But  this  is  by  no  means  the  case.  In 
fact,  no  assumption  is  made  in  art.  652  as  to  the  direction  in  which  the 
vibrating  particles  move,  and  accordingly  the  explanation  is  equally  true 
whether  the  particles  vibrate  in  the  direction  AB,  BA,  or  at  right  angles  to 
AB.  As  a  matter  of  fact,  the  former  is  the  case  with  the  vibrations  produc- 
ing sound,  the  latter  with  the  vibrations  producing  light.  In  other  words, 
the  vibrations  producing  sound  take  place  in  the  direction  of  propagation,  the 
vibrations  producing  light  are  transversal  to  the  direction  of  propagation. 

This  assumption  as  to  the  direction  of  the  vibration  of  the  particles  of 
ether  producing  light  is  rendered  necessary,  and  is  justified,  by  the  pheno- 
mena of  polarisation. 

When  a  ray  of  light  is  polarised,  all  the  particles  of  ether  in  that  ray 
vibrate  in  straight  lines  parallel  to  a  certain  direction  in  the  front  of  the 
wave  corresponding  to  the  ray. 

When  a  ray  of  light  enters  a  double-refracting  medium,  such  as  Iceland 
spar,  it  becomes  divided  into  two,  as  we  have  already  seen.  Now  it  can  be 
shown  to  be  in  strict  accordance  with  mechanical  principles  that,  if  a  medium 
possesses  unequal  elasticity  in  different  directions,  a  plane  wave  produced 
by  transversal  vibrations  entering  that  medium  will  give  rise  to  two  plane 
waves  moving  with  different  velocities  within  the  medium,  and  the  vibrations 
of  the  particles  in  front  of  these  waves  will  be  in  directions  parallel  respect- 
ively to  two  lines  at  right  angles  to  each  other.  If,  as  is  assumed  in  the 
undulatory  theory  of  light,  the  ether  exists  in  a  double-refracting  crystal  in 
such  a  state  of  unequal  elasticity,  then  the  two  plane  waves  will  be  formed 
as  above  described,  and  these,  having  different  velocities,  will  give  rise  to 
two  rays  of  unequal  refrangibility  (638).  This  is  the  physical  account 
of  the  phenomenon  of  double  refraction.  It  will  be  remarked  that  the 


-663]          Laws  of  the  Interference  of  Polarised  Rays.  607 

vibrations  corresponding  to  the  two  rays  are  transversal,  rectilinear,  and 
in  directions  perpendicular  to  each  other  in  the  rays  respectively.  Accord- 
ingly the  same  theory  accounts  for  the  fact  that  the  two  rays  are  both 
polarised,  and  in  planes  at  right  angles  to  each  other. 

It  is  a  point  still  unsettled  whether,  when  a  ray  of  light  is  polarised  with 
respect  to  a  given  plane,  the  vibrations  take  place  in  directions  within  or 
perpendicular  to  that  plane.  Fresnel  was  of  the  latter  opinion.  It  is,  how- 
ever, convenient  in  some  cases  to  regard  the  plane  of  polarisation  as  that 
plane  in  which  the  vibrations  take  place. 


COLOURS   PRODUCED   BY  THE   INTERFERENCE   OF   POLARISED   LIGHT. 

^662.  laws  of  the  interference  of  polarised  rays. — After  the  discovery 
of  polarisation,  Fresnel  and  Arago  tried  whether  polarised  rays  presented 
the  same  phenomena  of  interference  as  ordinary  rays.  They  were  thus  led 
to  the  discovery  of  the  following  laws  in  reference  to  the  interference  of 
polarised  light,  and,  at  the  same  time,  of  the  brilliant  phenomena  of  colora- 
tion, which  will  be  presently  described  : — 

I.  When  two  rays  polarised  in  the  same  plane  interfere  with  each  other, 
they  produce,  by  their  interference,  fringes  of  the  very  same  kind  as  if  they 
were  common  light. 

II.  When  two  rays  of  light  are  polarised  at  right  angles  to  each  other,, 
they  produce  no  coloured  fringes  in  the  same  circumstances  under  which 
two  rays  of  common  light  would  produce  them.     When  the  rays  are  po- 
larised in  planes  inclined  to  each  other  at  any  other  angles,  they  produce 
fringes  of  intermediate  brightness  ;  and,  if  the  angle  is  made  to  change,  the 
fringes  gradually  decrease  in  brightness   from  o°  to   90°,  and  are  totally 
obliterated  at  the  latter  angle. 

III.  Two  rays  originally  polarised  in  planes  at  right  angles  to  each  other 
may  be  subsequently  brought  into  the  same  plane  of  polarisation  without 
acquiring  the  power  of  forming  fringes  by  their  interference. 

IV.  Two  rays  polarised  at  right  angles  to  each  other,  and  afterwards- 
brought  into  the  same  plane  of  polarisation,  produce  fringes  by  their  inter- 
ference like  rays  of  common  light,  provided  they  originated  in  a  pencil  the- 
whole  of  which  was  originally  polarised  in  any  one  plane. 

V.  In  the  phenomena  of  interference  produced  by  rays  that  have  suffered 
double  refraction,  a  difference  of  half  an  undulation  must  be  allowed,  as  one 
of  the  pencils  is  retarded  by  that  quantity,  from  some  unknown  cause. 

663.  Effect  produced  by  causing-  a  pencil  of  polarised  rays  to  tra- 
verse a  double-refractingr  crystal. — The  following  important  experiment 
may  be  made  most  conveniently  by  Norremberg's  apparatus  (fig.  573).     At 
g  (fig.  574)  there  is  a  Nicol's  prism.     A  plate  of  a  double-refracting  crystal' 
cut  parallel  to  its  axis  is  placed  on  the  disc  at  e.     In  the  first  place,  however, 
suppose  the  plate  of  the  crystal  to  be  removed.     Then,  since  the  Nicol's; 
prism  allows  only  the  extraordinary  ray  to  pass  when  it  is  turned  so  that  its . 
principal  plane  coincides  with  the  plane  of  reflection,  no  light  will  be  trans- 
mitted (660).     Place  the  plate  of  doubly  refracting  crystal,  which  is  supposed 
to  be  of  moderate  thickness,  in  the  path  of  the  reflected  ray  at  e.     Light  is : 


608  On  Light.  [663- 

now  transmitted  through  the  Nicol's  prism.  On  turning  the  plate,  the 
intensity  of  the  transmitted  light  varies  ;  it  reaches  its  maximum  when  the 
principal  plane  of  the  plate  is  inclined  at  an  angle  of  45°  to  the  plane  of 
reflection,  and  disappears  when  these  planes  either  coincide  with  or  are  at 
right  angles  to  each  other.  The  light  in  this  case  is  white.  The  interposed 
plate  may  be  called  the  depolarising  plate.  The  same  or  equivalent  phe- 
nomena are  produced  when  any  other  analyser  is  used.  Thus,  assume  the 
double-refracting  prism  to  be  used.  Suppose  the  depolarising  plate  to  be 
removed.  Then,  generally,  two  rays  are  transmitted ;  but  if  the  principal 
plane  of  the  analyser  is  turned  in  the  plane  of  primitive  polarisation,  the 
ordinary  ray  only  is  transmitted,  and  then,  when  turned  through  90°,  the 
extraordinary  ray  only  is  transmitted.  Let  the  analyser  be  turned  into 
the  former  position,  then,  when  the  depolarising  plate  is  interposed,  both 
ordinary  and  extraordinary  rays  are  seen,  and  when  the  depolarising  plate 
is  slowly  turned  round,  the  ordinary  and  extraordinary  rays  are  seen  to  vary 
in  intensity,  the  latter  vanishing  when  the  principal  plane  of  the  polarising 
plate  either  coincides  with,  or  is  at  right  angles  to,  the  plane  of  primitive 
polarisation. 

664.  Effect  produced  when  the  plate  of  crystal  is  very  thin. — In 
order  to  exhibit  this,  take  a  thin  film  of  selenite  or  mica  between  the  twen- 
tieth and  sixtieth  of  an  inch  thick,  and  interpose  it  as  in  the  last  article.  If 
the  thickness  of  the  film  is  uniform,  the  light  now  transmitted  through  the 
analyser  will  be  no  longer  white,  but  of  a  uniform  tint ;  the  colour  of  the 
tint  being  different  for  different  thicknesses — for  instance,  red,  or  green,  or 
blue,  or  yellow,  according  to  the  thickness  ;  the  intensity  of  the  colour  de- 
pending on  the  inclination  of  the  principal  plane  of  the  film  to  the  plane  of 
reflection,  being  greatest  when  the  angle  of  inclination  is  45°.  Let  us  now 
suppose  the  crystalline  film  to  be  fixed  in  that  position  in  which  the  light  is 
brightest,  and  suppose  its  colour  to  be  red.  Let  the  analyser  (the  Nicol's 
prism)  be  turned  round,  the  colour  will  grow  fainter,  and  when  it  has  been 
turned  through  45°,  the  colour  disappears,  and  no  light  is  transmitted ;  on 
turning  it  further,  the  complementary  colour,  green^  makes  its  appearance, 
and  increases  in  intensity  -until  the  analyser  has  been  turned  through  90° ; 
after  which  the  intensity  diminishes  until  an  angle  of  135°  is  attained,  when 
the  light  again  vanishes,  and,  on  increasing  the  angle,  it  changes  again  into 
red.  Whatever  be  the  colour  proper  to  the  plate,  the  same  series  of  pheno- 
mena will  be  observed,  the  colour  passing  into  its  complementary  when  the 
analyser  is  turned.  That  the  colours  are  really  complementary  is  proved 
by  using  a  double-refracting  prism  as  analyser.  In  this  case  two  rays  are 
transmitted,  each  of  which  goes  through  the  same  changes  of  colour  and  in- 
tensity as  the  single  ray  described  above  ;  but  whatever  be  the  colour  and 
intensity  of  the  one  ray  in  a  given  position,  the  other  ray  will  have  the  same 
when  the  analyser  has  been  turned  through  an  angle  of  90°.  Consequently, 
these  two  rays  give  simultaneously  the  appearances  which  are  successively 
presented  in  the  above  case  by  the  same  ray  at  an  interval  of  90°.  If  now 
the  two  rays  are  allowed  to  overlap,  they  produce  white  light ;  thereby 
proving  their  colours  to  be  complementary. 

Instead  of  using  plates  of  different  thicknesses  to  produce  different  tints, 
the  same  plate  may  be  employed  inclined  at  different  angles  to  the  polarised 


-665]  Theory  of  the  Phenomena  of  Depolarisation.  609 

ray.     This  causes  the  ray  to  traverse  the  film  obliquely,  and,  in  fact,  amounts 
to  an  alteration  in  its  thickness. 

With  the  same  substance,  but  with  plates  of  increasing  thickness,  the 
tints  follow  the  laws  of  the  colours  of  Newton's  rings  (650).  The  thickness 
of  the  depolarising  plate  must,  however,  be  different  from  that  of  the  layer  of 
air  in  the  case  of  Newton's  rings  to  produce  corresponding  colours.  Thus 
corresponding  colours  are  produced  by  a  plate  of  mica  and  a  layer  of  air 
when  the  thickness  of  the  former  is  about  400  times  that  of  the  latter.  In 
the  case  of  selenite  the  thickness  is  about  230  times,  and  in  the  case  of  Ice- 
land spar  about  13  times,  that  of  the  corresponding  layer  of  air. 

665.  Theory  of  the  phenomena  of  depolarisation. — The  phenomena 
described  in  the  last  articles  admit  of  complete  explanation  by  the  undulatory 
theory,  but  not  without  the  aid  of  abstruse  mathematical  calculations.  What 
follows  will  show  the  nature  of  the  explanation.  Let  us  suppose,  for  con- 
venience, that  in  the  case  of  a  polarised  ray  the  particles  of  ether  vibrate 
in  the  plain  of  polarisation  (66 1),  and  that  the  analyser  is  a  double  refract- 
ing prism,  with  its  principal  plane  in  the  plane  of  primitive  polarisation  ; 
then  the  vibrations,  being  wholly  in  that  plane,  have  no  resolved  part  in 
a  plane  at  right  angles  to  it,  and,  consequently,  no  extraordinary  ray  passes 
through  the  analyser  ;  in  other  words,  only  an  ordinary  ray  passes.  Now 
take  the  depolarising  plane  cut  parallel  to  the  axis,  and  let  it  be  interposed 
in  such  a  manner  that  its  principal  plane  makes  any  angle  (6}  with  the  plane 
of  primitive  polarisation.  The  effect  of  this  will  be  to  cause  the  vibrations 
of  the  primitive  ray  to  be  resolved  in  the  principal  plane  and  at  right  angles 
to  the  principal  plane,  thereby  giving  rise  to  an  ordinary  ray  (O),  and  an  ex- 
traordinary ray  (£),  which,  however,  do  not  become  separated  on  account  of 
the  thinness  of  the  depolarising  plate.  They  will  not  form  a  single  plane 
polarised  ray  on  leaving  the  plate,  since  they  are  unequally  retarded  in  pass- 
ing through  it,  and  consequently  leave  it  in  different  phases.  Since  neither 
of  the  planes  of  polarisation  of  O  and  E  coincides  with  the  principal  plane 
of  the  analyser,  the  vibrations  composing  them  will  again  be  resolved — viz. 
O  gives  rise  to  O<9  and  Oe  and  E  gives  rise  to  E<?  and  E<?.  But  the  vibra- 
tions composing  Qo  and  E0,  being  in  the  same  phase,  give  rise  to  a  single 
ordinary  ray,  \o,  and  in  like  manner  Oe  and  E.e  give  rise  to  a  single  extra- 
ordinary ray,  \e.  Thus  the  interposition  of  the  depolarising  plate  restores 
the  extraordinary  ray. 

Suppose  the  angle  6  to  be  either  o°  or  90°.  In  either  case  the  vibrations 
are  transmitted  through  the  depolarising  plate  without  resolution,  conse- 
quently they  remain  wholly  in  the  plane  of  primitive  polarisation,  and  on 
entering  the  analyser  cannot  give  rise  to  an  extraordinary  ray. 

If  the  Nicol's  prism  is  used  as  an  analyser,  the  ordinary  ray  is  suppressed 
by  mechanical  means.  Consequently  only  \e  will  pass  through  the  prism, 
and  that  for  all  values  of  6  except  o°  and  90°. 

A  little  consideration  will  show  that  the  joint  intensities  of  all  the  rays 
existing  at  any  stage  of  the  above  transformations  must  continue  constant, 
but  that  the  intensities  of  the  individual  rays  will  depend  on  the  magnitude 
of  6  ;  and  when  this  circumstance  is  examined  in  detail,  it  explains  the  fact 
that  \e  increases  in  intensity  as  0  increases  from  o°  to  45°,  and  then  decreases 
in  intensity  as  6  increases  from  45°  to  90°. 

R  R 


6 io  On  Light.  [665- 

In  regard  to  the  colour  of  the  rays,  it  is  to  be  observed  that  the  formulae 
for  the  intensities  of  \o  and  le  contain  a  term  depending  on  the  length  of  the 
wave  and  the  thickness  of  the  plate.  Consequently,  when  white  light  is  used 
the  relative  intensities  of  its  component  colours  are  changed,  and,  therefore, 
\o  and  le  will  each  have  a  prevailing  tint,  which  will  be  different  for  different 
thicknesses  of  the  plate.  The  tints  will,  however,  be  complementary,  since 
the  joint  intensities  of  \o  and  le  being  the  same  as  that  of  the  original  ray 
they  will,  when  superimposed,  restore  all  the  components  of  that  ray  in  their 
original  intensities,  and  therefore  produce  white  light. 

666.  Coloured  rings  produced  by  polarised  light  in  traversing 
double  refracting  films. — In  the  experiments  with  Norremberg's  apparatus 
which  have  just  been  described  (663),  a  pencil  of  parallel  rays  traverses  the 
film  of  crystal  perpendicularly  to  its  faces,  and  as  all  parts  of  the  film  act  in 
the  same  manner,  there  is  everywhere  the  same  tint.  But  when  the  incident 
rays  traverse  the  plate  under  different  obliquities,  which  comes  to  the  same 
thing  as  if  they  traversed  plates  differing  in  thickness,  coloured  rings  are 
formed  similar  to  Newton's  rings. 

The  best  method  of  observing  these  new  phenomena  is  by  means  of  the 
tourmaline  pincette  (fig.  578).  This  is  a  small  instrument  consisting  of  two 
tourmalines,  cut  parallel  to  the  axis,  each  of  them  being  fitted  in  a  copper 


Fig.  578. 

disc.  These  two  discs,  which  are  perforated  in  the  centre,  and  blackened,, 
are  mounted  in  two  rings  of  silvered  copper,  which  is  coiled,  as  shown  in 
the  figure,  so  as  to  form  a  spring,  and  press  together  the  tourmalines.  The 
tourmalines  turn  with  the  disc,  and  may  be  so  arranged  that  their  axes  are 
either  perpendicular  or  parallel. 

The  crystal  to  be  experimented  upon,  being  fixed  in  the  centre  of  a  cork 
disc,  is  placed  between  the  two  tourmalines,  and  the  pincette  is  held  before 
the  eye  so  as  to  view  diffused  light.  The  tourmaline  farthest  from  the  eye 
acts  as  polariser  and  the  other  as  analyser.  If  the  crystal  thus  viewed  is 
uniaxial,  and  cut  perpendicularly  to  the  axis,  and  a  homogeneous  light — 
red  for  instance— is  looked  at,  a  series  of  alternately  dark  and  red  rings 
is  seen.  With  another  simple  colour  similar  rings  are  obtained,  but  their 
diameter  decreases  with  the  refrangibility  of  the  colour.  On  the  other 
hand,  the  diameters  of  the  rings  diminish  when  the  thickness  of  the  plates 
increases,  and  beyond  a  certain  {hickness  no  more  rings  are  produced. 
If,  instead  of  illuminating  the  rings  by  homogeneous  light,  white  light  be 
used,  as  the  rings  of  the  different  colours  produced  have  not  the  same  dia- 
meter, they  are  partially  superposed,  and  produce  very  brilliant  variegated 
colours. 

The  position  of  the  crystal  has  no  influence  on  the  rings,  but  this  is  not 
the  case  with  the  r4ative  position  of  the  two  tourmalines.  For  instance, 
in  experimenting  on  Iceland  spar  cut  perpendicular  to  the  axis,  and  from  i 


512 


On  Light. 


[667- 


logical  reasons.  In  this  way  the  optical  investigation  becomes  a  valuable 
aid  in  mineralogy  ;  as,  for  example,  in  the  case  of  mica,  of  which  there  are 
two  mineralogical  species,  the  uniaxial  and  the  biaxial. 

All  the  phenomena  which  have  been  described  are  only  obtained  by 
means  of  polarised  light.  Hence,  a  double  refracting  film,  with  either  a 
Nicol's  prism  or  a  tourmaline  as  analyser,  may  be  used  to  distinguish  between 
polarised  and  unpolarised  light ;  that  is,  as  a  polariscope. 

'y'o68.  Colours  produced  by  compressed  or  by  unannealed  glass. — 
Ordinary  glass  is  not  endowed  with  the  power  of  double  refraction.  It 


Fig.  579- 


Fig.  5 


Fig.  581. 


mm 


Fig.  582. 


Fig.  583- 


Fig.  584. 


acquires  this  property,  however,  if  by  any  cause  its  elasticity  becomes 
more  modified  in  one  direction  than  in  another.  In  order  to  effect  this, 
it  may  be  strongly  compressed  in  a  given  direction,  or  it  may  be  curved, 
or  tempered  ;  that  is  to  say,  cooled  after  having  been  heated.  If  the 
glass  is  then  traversed  by  a  beam  of  polarised  light,  effects  of  colour  are 
obtained  which  are  entirely  analogous  to  those  described  in  the  case  of 
doubly  refracting  crystals.  They  are,  however,  susceptible  of  far  greater 
variety,  according  as  the  plates  of  glass  have  a  circular,  square,  rectangu- 
lar, or  triangular  shape,  and  according  to  the  degree  of  tension  of  their 
particles. 

When  the  polariser  is  a  mirror  of  black  glass,  on  which  the  light  of  the 
sky  is  incident,  and  the  analyser  is  a  Nicol's  prism,  through  which  the 
glass  plates  traversed  by  polarised  light  are  viewed,  figs.  579,  580,  582 
represent  the  appearances  presented  successively,  when  a  square  plate 
of  compressed  glass  is  turned  in  its  own  plane;  figs.  581  and  584  re- 
present the  appearances  produced  by  a  circular  plate  under  the  same 
circumstances  ;  and  fig.  583  that  produced  when  one  rectangular  plate  is 
superposed  on  another.  This  figure  also  varies  when  the  system  of  plates 
is  turned. 


—670]  Elliptical  and  Circular  Polarisation.  6 1 


ELLIPTICAL,   CIRCULAR,   AND   ROTATORY   POLARISATION. 

669.  Definition  of  elliptical  and  circular  polarisation. — In  the  cases 
hitherto  considered,  the  particles  of  ether  composing  a  polarised  ray  vibrate 
in  parallel  straight  lines  ;   to  distinguish  this  case  from  those  we  are  now  to 
consider,  such  light  is  frequently  called  plane  polarised  light.     It  sometimes 
happens  that  the  particles  of  ether  describe  ellipses  about  their  positions  of 
rest,  the  planes  of  the  ellipses  being  perpendicular  to  the  direction  of  the 
ray.    If  the  axes  of  these  ellipses  are  equal  and  parallel,  the  ray  is  said  to  be 
elliptically  polarised.     In  this  case  the  particles  which,  when  at  rest,  occu- 
pied a  straight  line,  are,  when  in  motion,  arranged  in  a  helix  round  the  line 
of  their  original  position  as  an  axis,  the  helix  exchanging  from  instant  to 
instant.     If  the  axes  of  the  ellipses  are  equal,  they  become  circles,  and  the 
light  is  said  to  be  circularly  polarised.     If  the  minor  axes  become  zero,  the 
ellipses  coincide  with  their  major  axes,  and  the  light  becomes,  plane  polarised. 
Consequently,  plane  polarised  light  and  circularly  polarised  light  are  parti- 
cular cases  of  elliptically  polarised  light. 

670.  Theory  of  the  origin  of  elliptical  and  circular  polarisation. — 
Let  us  in  the  first  place  consider  a  simple  pendulum  (55)  vibrating  in  any 
plane,  the  arc  of  vibration  being  small.     Suppose  that,  when  in  its  lowest 
position,  it  received  a  blow  in  a  direction  at  right  angles  to  the  direction  of 
its  motion,  such  as  would  make  it  vibrate  in  an  arc  at  right  angles  to  its 
arc  of  primitive  vibration,  it  follows  from  the  law  of  the  composition   of 
velocities  (52)  that  the  joint  effect  will  be  to  make  it  vibrate  in  an  arc  inclined 
at  a  certain  angle  to  the  arc  of  primitive  vibration,  the  magnitude  of  the 
angle  depending  on  the  magnitude  of  the  blow.     If  the  blow  communicated 
a  velocity  equal  to  that  with  which  the  body  is  already  moving,  the  angle 
would  be  45°.     Next  suppose  the  blow  to  communicate  an  equal  velocity, 
but  to  be  struck  when  the  body  is  at  its  highest  point,  this  will  cause  the 
particle  to  describe  a  circle,  and  to  move  as  a  conical  pendulum.      If  the 
blow  is  struck  under  any  other  circumstances,  the  particle  will  describe  an 
ellipse.     Now  as  the  two  blows  would  produce  separately  two  simple  vibra- 
tions in  directions  at  right  angles  to  each  other,  we   may  state  the  result 
arrived  at  as  follows  : — If  two  rectilinear  vibrations  are   superinduced   on 
the  same  particle  in  directions  at  right  angles  to  each  other,  then:    I.  If 
they  are  in  the  same  or  opposite  phases,  they  make  the  point  describe  a 
rectilinear  vibration  in  a  direction  inclined  at  a  certain  angle  to  either  of 
the  original  vibrations.      2.  But  if  their  phases  differ  by  90°  or  a  quarter 
of  a  vibration,  the  particle  will  describe  a  circle,  provided  the  vibrations  are 
equal.     3.  Under  other  circumstances  the  particle  will  describe  an  ellipse. 

To  apply  this  to  the  case  of  polarised  light.  Suppose  two  rays  of  light 
polarised  in  perpendicular  planes  to  coincide,  each  would  separately  cause 
the  same  particles  to  vibrate  in  perpendicular  directions.  Consequently — 
i.  If  the  vibrations  are  in  the  same  or  opposite  phases,  the  light  resulting  from 
the  two  rays  is  plane  polarised.  2.  If  the  rays  are  of  equal  intensity,  and 
their  phases  differ  by  90°,  the  resulting  light  is  circularly  polarised.  3.  Under 
other  circumstances  the  light  is  elliptically  polarised. 

As  an  example  if  reference  is  made  to  arts.  665  and  666,  it  will  be  seen 


614  On  Light.  [670- 

that  the  rays  denoted  by  O  and  E  are  superimposed  in  the  manner  above 
described.  Consequently,  the  light  which  leaves  the  depolarising  plate  is 
elliptically  polarised.  If,  however,  the  principal  plane  of  the  depolarising 
plate  is  turned  so  as  to  make  an  angle  of  45°  with  the  plane  of  primitive 
polarisation,  O  and  E  have  equal  intensities  ;  and  if,  further,  the  plate  is 
made  of  a  certain  thickness,  so  that  the  phases  of  O  and  E  may  differ  by 
90°,  or  by  a  quarter  of  a  vibration,  the  light  which  emerges  from  the  plate  is 
circularly  polarised.  This  method  may  be  employed  to  produce  circularly 
polarised  light. 

Circular  or  elliptical  polarisation  may  be  either  right-handed  or  left- 
handed,  or  what  is  sometimes  called  dextrogyrate  and  l&vogyrate.  If  the  ob- 
server looks  along  the  ray  in  the  direction  of  propagation,  from  polariser 
to  analyser,  then,  if  the  particles  move  in  the  same  direction  as  the  hands 
of  a  watch  with  its  face  to  the  observer,  the  polarisation  is  right-handed. 

671.  Fresnel's  rhomb. — This  is  a  means  of  obtaining  circularly  polarised 
light.     We  have  just  seen  (670)  that,  to  obtain  a  ray  of  circularly  polarised 
light,  it  is  sufficient  to  decompose  a  ray  of  plane  polarised  light  in  such 
a  manner  as   to   produce  two   rays   of  light   of  equal   intensity  polarised 
in  planes  at  right  angles  to  each  other,  and  differing  in  their  paths  by  a 
quarter  of  an  undulation.     Fresnel  effected  this  by  means  of  a  rhomb  which 
has  received  his  name.     It  is  made  of  glass  ;  its  acute  angle  is  54°,  and  its 
obtuse  126°.     If  a  ray  (a,  fig.  585)  of  plain  polarised  light  falls  perpendicu- 
larly on  the  face  AB,  it  will  undergo  two  total  internal  reflections  at  an  angle 
of  about  54°,  one  at  E,  and  the  other  at  F,  and  will  emerge  perpendicularly. 

If  the  plane  ABCD  be  inclined  at  an  angle  of 
45°  to  the  plane  of  polarisation,  the  polarised  ray 
will  be  divided  into  two  coincident  rays,  with  their 
planes  of  polarisation  at  right  angles  to  each  other, 
and  it  appears  that  one  of  them  loses  exactly  a 
quarter  of  an  undulation,  so  that  on  emerging  from 
the  rhomb  the  ray  is  circularly  polarised.  If  the  ray 
emerging  as  above  from  Fresnel's  rhomb  is  ex- 
amined, it  will  be  found  to  differ  from  plane  polarised 
light  in  this,  that,  when  it  passes  through  a  double 
refracting  prism,  the  ordinary  and  extraordinary 
rays  are  of  equal  intensity  in  all  positions  of  the 
Fig  5gs  prism.  Moreover,  it  differs  from  ordinary  light  in 

this,  that,  if  it  passed  through  a  second  rhomb  placed 

parallel  to  the  first,  a  second  quarter  of  an  undulation  will  be  lost,  so  that 
the  parts  of  the  original  plane  polarised  ray  will  differ  by  half  an  undulation, 
and  the  emergent  ray  will  be  plane  polarised  ;  moreover  the  plane  of  polar- 
isation will  be  inclined  at  an  angle  of  45°  to  ABCD,  but  on  the  other  side 
from  the  plane  of  primitive  polarisation. 

672.  Elliptical  polarisation.— In  addition  to  the  method  already  men- 
tioned (671),  elliptically  polarised  light  is  generally  obtained  whenever  plane 
polarised  light   suffers   reflection.      Polarised   light  reflected  from   metals 
•becomes  elliptically  polarised,  the  degree  of  ellipticity  depending  on  the  direc- 
tion of  the  incident  ray,  and  of  its  plane  of  polarisation,  as  well  as  on  the  nature 
of  the  reflecting  substance.     When  reflected  from  silver,  the  polarisation  is 


-674]         Physical  Explanation  of  Rotatory  Polarisation.          615 

almost  circular,  and  from  galena  almost  plane.  If  elliptically  polarised  light  be 
analysed  by  the  Nicol's  prism,  it  never  vanishes,  though  at  alternate  positions 
it  becomes  fainter  ;  it  is  thus  distinguished  from  plane  and  from  circular 
polarised  light.  If  analysed  by  Iceland  spar  neither  image  disappears,  but 
they  undergo  changes  in  intensity. 

Light  can  also  be  polarised  elliptically  in  Fresnel's  rhomb.  If  the  angle 
between  the  planes  of  primitive  polarisation  and  of  incidence  be  any  other 
than  45°,  the  emergent  ray  is  elliptically  polarised. 

673.  Rotatory  polarisation, — Rock  crystal  or  quartz  possesses  a  re- 
markable property  which  was  long  regarded  as  peculiar  to  itself  among  all 
crystals,  though  it  has  been  since  found  to  be  shared  by  tartaric  acid  and  its 
salts,  together  with  some  other  crystallised  bodies.  This  property  is  called 
rotatory  polarisation,  and  may  be  described  as  follows  :  Let  a  ray  of 
homogeneous  light  be  polarised,  and  let  the  analyser,  say  a  Nicol's  prism,  be 
turned  till  the  light  does  not  pass  through  it.  Take  a  thin  section  of  a  quartz 
crystal  cut  at  right  angles  to  its  axis,  and  place  it  between  the  polariser  and 
the  analyser  with  its  plane  at  right  angles  to  the  rays.  The  light  will  now 
pass  through  the  analyser.  The  phenomenon  is  not  the  same  as  that  pre- 
viously described  (663),  for,  if  the  rock  crystal  is  turned  round  its  axis,  no 
effect  is  produced,  and  if  the  analyser  is  turned,  the  ray  is  found  to  be  plane 
polarised  in  a  plane  inclined  at  a  certain  angle  to  the  plane  of  primitive 
polarisation.  If  the  light  is  red,  and  the  plate  i  millimetre  thick,  this  angle 
is  about  17°.  In  some  specimens  of  quartz  the  plane  of  polarisation  is 
turned  to  the  right  hand,  in  others  to  the  left  hand.  Specimens  of  the 
former  kind  are  said  to  be  right-handed,  those  of  the  latter  kind  left-handed. 
This  difference  corresponds  to  a  difference  in  crystallographic  structure. 
The  property  possessed  by  rock  crystal  of  turning  the  plane  of  polarisation 
through  a  certain  angle  was  thoroughly  investigated  by  Biot,  who,  amongst 
other  results,  arrived  at  this  : — For  a  given  colour  the  angle  through  which 
the  plane  of  polarisation  is  turned  is  proportional  to  the  thickness  of  the 
quartz. 

674.  Physical  explanation  of  rotatory  polarisation. — The  explanation 
of  the  phenomenon  described  in  the  last  article  is  as  follows  :  When  a  ray 
of  polarised  light  passes  along  the  axis  of  the  quartz  crystal,  it  is  divided  into 
two  rays  of  circularly  polarised  light  of  equal  intensity,  which  pass  through 
the  crystal  with  Jifferent  velocities.  In  one  the  circular  polarisation  is  right- 
handed,  in  the  other  left-handed  (670).  The  existence  of  these  rays  was 
proved  by  Fresnel,  who  succeeded  in  separating  them.  On  emerging  from 
the  crystal,  they  are  compounded  into  a  plane  polarised  ray ;  but,  since  they 
move  with  unequal  velocities  within  the  crystal,  they  emerge  in  different 
phases,  and  consequently  the  plane  of  polarisation  will  not  coincide  with  the 
plane  of  primitive  polarisation.  This  can  be  readily  shown  by  reasoning 
similar  to  that  employed  in  art.  670.  The  same  reasoning  will  also  show 
that  the  plane  of  polarisation  will  be  turned  to  the  right  or  left,  according 
as  the  right-handed  or  left-handed  ray  moves  with  the  greater  velocity. 
Moreover,  the  amount  of  the  rotation  will  depend  on  the  amount  of  the 
retardation  of  the  ray  whose  velocity  is  least ;  that  is  to  say,  it  will  depend 
on  the  thickness  of  the  plate  of  quartz.  In  this  manner  the  phenomena  of 
rotatory  polarisation  can  be  completely  accounted  for. 


6i6  On  Light.  [675- 

675.  Coloration  produced  by  rotatory  polarisation. — The  rotation  is 
different  with -'different  colours  ;  its  magnitude  depends  on  the  refrangibility, 
and  is  greatest  with  the  most  refrangible  rays.  In  the  case  of  red  light  a 
plate  i  millimetre  in  thickness  will  rotate  the  plr.ne  17°,  while  a  plate  of  the 
same  thickness  will  rotate  it  44°  in  the  case  of  violet  light.  Hence  with 
white  light  there  will,  in  each  position  of  the  analysing  Nicol's  prism,  be  a 
greater  or  less  quantity  of  each  colour  transmitted.  In  the  case  of  a  right- 
handed  crystal,;. when  the  Nicol's  prism  is  turned  to  the  right,  the  colours 
will  successively  appear  from  the  less  refrangible  to  the  more  so — that  is, 
in  the  order  of  the  spectrum,  from  red  to  violet ;  with 
a  left-handed  crystal  in  the  reverse  order.  Obviously 
in  turning  the  Nicol's  prism  to  the  left,  the  reverse  of 
these  results  will  take  place. 

When  a  quartz  plate  cut  perpendicularly  to  the 
axis  and  traversed  by  a  ray  of  polarised  light  is 
looked  at  through  a  doubly  refracting  prism,  two 

brilliantly  coloured  images  are  seen,  of  which  the  tints  are  complementary  :. 
for  their  images  are  partially  superposed,  and  in  this  position  there  is. 
white  light  (fig.  586).  When  the  prism  is  turned  from  left  to  right,  the  two 
images  change  colour  and  assume  successively  all  the  colours  of  the 
spectrum. 

This  will  be  understood  from  what  has  been  said  about  the  different 
rotation  for  different  colours.  Quartz  rotates  the  plane  of  polarisation  for 
red  17°  for  each  millimetre,  and  for  violet  44°  ;  hence  from  the  great  difference 
of  these  two  angles,  when  the  polarised  light  which  has  traversed  the  quartz 
plate  emerges,  the  various  simple  colours  which  it  contains  are  polarised 
in  different  planes.  Consequently,  when  the  rays  thus  transmitted  by  the 
quartz  pass  through  a  double-refracting  prism,  they  are  each  decomposed 
into  two  others  polarised  at  right  angles  to  each  other  :  the  various  simple 
colours  are  not  divided  in  the  same  proportion  between  the  ordinary  and 
extraordinary  rays  furnished  by  the  prism ;  the  two  images  are,  therefore, 
coloured  ;  but,  since  those  which  are  wanting  in  one  occur  in  the  other,  the 
colours  of  the  images  are  perfectly  complementary. 

These  phenomena  of  coloration  may  be  well  seen  by  means  of  Norrem- 
berg's  apparatus  (fig.  573).  A  quartz  plate,  s,  cut  at  right  angles  to  the  axis 
and  fixed  in  a  cork  disc,  is  placed  on  a  screen  e  ;  the  mirror  n  (fig.  573), 
being  then  so  inclined  that  a  ray  of  polarised  light  passes  through  the  quartz, 
the  latter  is  viewed  through  a  double-refracting  prism,  g ;  when  this  tube  is 
turned  the  complementary  images  furnished  by  the  passage  of  polarised 
light  through  the  quartz  are  seen. 

676.  Rotatory  power  of  liquids. — Biot  found  that  a  great  number  of 
liquids  and  solutions  possess  the  property  of  rotatory  polarisation.  He 
further  observed  that  the  deviation  of  the  plane  of  polarisation  can  reveal 
differences  in  the  composition  of  bodies  where  none  is  exhibited  by  chemical 
analysis.  For  instance,  the  two  sugars  obtained  by  the  action  of  dilute  acids 
on  cane-sugar  deflect  the  plane  of  polarisation,  the  one  to  the  right  and  the 
other  to  the  left,  although  the  chemical  composition  of  the  two  sugars  is  the 
same. 

The  rotatory  power  of  liquids  is  far  less  than  that  of  quartz.     In  con- 


-676] 


Rotatory  Power  of  Liquids. 


6i7 


centrated  syrup  of  cane-sugar,  which  possesses  the  rotatory  power  in  the 
highest  degree,  the  power  is  ^  that  of  quartz,  so  that  it  is  necessary  to 
operate  upon  columns  of  liquids  of  considerable  length — 8  inches,  for 
example. 

Fig.  587  represents  an   apparatus  devised  by  Biot  for  measuring  the 
rotatory  power  of  liquids.     On  a  metal  groove,  g,  fixed  to  a  support,  r,  is  a 


Fig.  587- 

brass  tube  d  20  centimetres  long,  in  which  is  contained  the  liquid  experimented 
upon.  This  tube,  which  is  tinned  inside,  is  closed  at  each  end  by  glass 
plates  fastened  by  screw  collars.  At  m  is  a  mirror  of  black  glass,  inclined 
at  the  polarising  angle  to  the  axis  of  the  tubes  bd  and  <z,  so  that  the  ray  re- 
flected by  the  mirror  m,  in  the  direction  bda,  is  polarised.  In  the  centre  of 
the  graduated  circle  /£,  inside  the  tube  «,  and  at  right  angles  to  the  axis  bda, 
is  a  double-refracting  achromatic  prism,  which  can  be  turned  about  the  axis 
of  the  apparatus  by  means  of  a  button  n.  The  latter  is  fixed  to  a  limb  c,  on 
which  is  a  vernier,  to  indicate  the  number  of  degrees  turned  through.  Lastly, 
from  the  position  of  the  mirror  m,  the  plane  of  polarisation,  Sod,  of  the  re- 
flected ray  is  vertical,  and  the  zero  of  the  graduation  of  the  circle  h  is  on 
this  plane. 

Before  placing  the  tube  d  in  the  groove  g,  the  extraordinary  image  fur- 
nished by  the  double-refracting  prism  disappears  whenever  the  limb  c  corre- 
sponds to  the  zero  of  the  graduation,  because  then  the  double-refracting  prism 
is  so  turned  that  its  principal  section  coincides  with  the  plane  of  polarisation 
(661).  This  is  the  case  also  when  the  tube  d  is  full  of  water  or  any  other 
inactive  liquid,  like  alcohol,  ether,  &c.,  which  shows  that  the  plane  of  polari- 
sation has  not  been  turned.  But  if  the  tube  be  filled  with  a  solution  of  cane- 


On  Light.  [676- 

sugar  or  any  other  active  liquid,  the  extraordinary  image  reappears,  and  to 
•extinguish  it,  the  limb  must  be  turned  to  a  certain  extent  either  to  the  right 
or  to  the  left  of  zero,  according  as  the  liquid  is  right-handed  or  left-handed, 
showing  that  the  polarising  plane  has  been  turned  by  the  same  angle.  With 
solution  of  cane-sugar  the  rotation  takes  place  to  the  right  ;  and  if  with  the 
same  solution  tubes  of  different  lengths  are  taken,  the  rotation  is  found  to 
increase  proportionally  to  the  length,  in  conformity  with  art.  673  ;  further, 
with  the  same  tube,  but  with  solutions  of  various  strengths,  the  rotation 
increases  with  the  quantity  of  sugar  dissolved,  so  that  the  quantitative 
analysis  of  a  solution  may  be  made  by  means  of  its  angle  of  deviation. 

In  this  experiment  homogeneous  light  must  be  used  ;  for,  as  the  various 
tints  of  the  spectra  have  different  rotatory  powers,  white  light  is  decomposed 
in  traversing  an  active  liquid,  and  the  extraordinary  image  does  not  disappear 
completely  in  any  position  of  the  double-refracting  prism — it  simply  changes 
the  tint.  The  transition  tint  (677)  may,  however,  be  observed.  To  avoid 
this  inconvenience,  a  piece  of  red  glass  is  placed  in  the  tube  between  the  eye 
and  the  double-refracting  prism,  which  only  allows  red  light  to  pass.  The 
extraordinary  image  disappears  in  that  case,  whenever  the  principal  section 
of  the  prism  coincides  with  the  plane  of  polarisation  of  the  red  ray. 

677.  Soleil's  saccharimeter. — Soleil  constructed  an  apparatus,  based 
upon  the  rotatory  power  of  liquids,  for  analysing  saccharine  substances, 
to  which  the  name  saccharimeter  is  applied.  Fig.  588  represents  the  sac- 
charimeter fixed  horizontally  on  its  foot,  and  fig.  589  gives  a  longitudinal 
section. 

The  principle  of  this  instrument  is  not  that  of  observing  the  amplitude 
of  the  rotation  of  the  plane  of  polarisation,  as  in  Biot's  apparatus,  but  that 
of  compensation  }  that  is  to  say,  a  second  active  substance  is  used  acting  in  the 
opposite  direction  to  that  analysed,  and  whose  thickness  can  be  altered  until 
the  contrary  actions  of  the  two  substances  completely  neutralise  each  other. 
Instead  of  measuring  the  deviation  of  the  plane  of  polarisation,  the  thick- 
ness is  measured  which  the  plate  of  quartz  must  have  in  order  to  obtain 
perfect  compensation. 

The  apparatus  consists  of  three  parts — a  tube  containing  the  liquid  to  be 
analysed,  a  polariser,  and  an  analyser. 

The  tube  m,  containing  the  liquid,  is  made  of  copper,  tinned  on  the 
inside,  and  closed  at  both  ends  by  two  glass  plates.  It  rests  on  a  support, 
k)  terminated  at  both  ends  by  tubes,  r  and  #,  in  which  are  the  crystals  used 
as  analysers  and  polarisers,  and  which  are  represented  in  section  (fig.  589). 

In  front  of  the  aperture  S  (fig.  589)  is  placed  an  ordinary  lamp. 
The  light  emitted  by  this  lamp  in  the  direction  of  the  axis  first  meets  a 
double-refracting  prism  r,  which  serves  as  polariser  (659).  The  ordinary 
image  alone  meets  the  eye,  the  extraordinary  image  being  projected  out  of 
the  field  of  vision  in  consequence  of  the  amplitude  of  the  angle  which  the 
ordinary  makes  with  the  extraordinary  ray.  The  double-refracting  prism  is 
in  such  a  position  that  the  plane  of  polarisation  is  vertical,  and  passes  through 
the  axis  of  the  apparatus. 

Emerging  from  the  double-refracting  prism,  the  polarised  ray  meets  a 
plate  of  quartz  with  double  rotation  ;  that  is,  this  plate  rotates  the  plane 
both  to  the  right  and  to  the  left.  This  is  effected  by  constructing  the  plate 


-677] 


Saccharimeter. 


619 


of  two  quartz  plates  of  opposite  rotation  placed  one  on  the  other,  as  shown 
in  fig.  590,  so  that  the  line  of  separation  is  vertical  and  in  the  same  plane  as 
the  axis  of  the  apparatus.  These  plates,  cut  perpendicularly  to  the  axis, 
have  a  thickness  of  375  millimetres,  corresponding  to  a  rotation  of  90°,  and 


Fig.  588. 

give  a  rose-violet  tint,  called  the  tint  of  passage^  or  transition  tint.  As  the 
quartz,  whether  right-handed  or  left-handed,  turns  always  to  the  same  extent 
for  the  same  thickness,  it  follows  that  the  two  quartz  plates  a  and  b  turn 
the  plane  of  polarisation  equally,  one  to  the  right  and  the  other  to  the  left. 
Hence,  looked  at  through  a  double-refracting  prism,  they  present  exactly  the 
same  tint. 

Having  traversed  the  quartz  q,  the  polarised  ray  passes  into  the  liquid 
in  the  tube  m,  and  then  meets  a  single  plate  of  quartz  /,  of  any  thickness, 
the  use  of  which  will  be  seen  presently.  The  compensator  «,  which  destroys 
the  rotation  of  the  column  of  liquid  m,  consists  of  two  quartz  plates,  with  the 
•same  rotation  either  to  the  right  or  the  left,  but  opposite  to  that  of  the  plate 
/.  These  two  quartz  plates,  a  section  of  which  is  represented  in  fig.  590,  are 
obtained  by  cutting  obliquely  a  quartz  plate  with  parallel  sides,  so  as  to  form 
two  prisms  of  the  same  angle,  N,  N',  which  is  called  a  biquartz ;  super- 
posing, then,  these  two  prisms,  as  shown  in  the  figure,  a  single  plate  is 
obtained  with  parallel  faces,  which  can  be  varied  at  will.  This  is  effected 
by  fixing  each  prism  to  a  slide,  so  as  to  move  it  in  either  direction  without 
disturbing  the  parallelism.  This  motion  is  effected  by  means  of  a  double 
rackwork  and  pinion  motion  turned  by  a  milled  head,  b  (figs.  588,  589). 

When  these  plates  move  in  the  direction  indicated  by  the  arrows  (fig.  590), 
it  is  clear  that  the  sum  of  their  thicknesses  increases,  and  that  it  diminishes 
when  the  plates  are  moved  in  the  contrary  direction.  A  scale  and  a  vernier 


620 


On  Light. 


[677 


follow  the  plates  in  their  motion,  and  measure  the  thickness  of  the  compen- 
sator. This  scale,  represented  with  its  vernier  in  fig.  591,  has  two  divisions 
with  a  common  zero,  one  from  left  to  right  for  right-handed  liquids,  and 
another  from  right  to  left  for  left-handed. 

When  the  vernier  is  at  zero  of  the  scale,  the  sum  of  the  thicknesses  or 
the  plates  NN'  is  exactly  equal  to  that  of  the  plate  z,  and  as  the  rotation  of 

Fig.  589. 


Fig.  592. 


the  latter  is  opposed  to  that  of  the  compensator,  the  effect  is  zero.  But  by 
moving  the  plates  of  the  compensator  in  one  or  the  other  direction  either 
the  compensator  or  the  quartz,  z',  preponderates,  and  there  is  a  rotation  from 
left  to  right. 

Behind  the  compensator  is  a  double-refracting  prism,  c  (fig.  589),  serving 
as  analyser  to  observe  the  polarised  ray  which  has  traversed  the  liquid  and 
the  various  quartz  plates.  In  order  to  understand  more  easily  the  object  or 
the  prism  c,  we  will  neglect  for  a  moment  the  crystals  and  the  lenses  on  the 
left  of  the  drawing.  If  at  first  the  zero  of  the  vernier  v  coincides  with  that 
of  the  scale,  and  if  the  liquid  in  the  tube  is  inactive,  the  actions  of  the  com- 
pensator, and  of  the  plate  z',  neutralise  each  other  ;  and,  the  liquid  having  no 
action,  the  two  halves  of  the  plate  q>,  seen  through  the  prism  ^,  give  exactly 
the  same  tint  as  has  been  observed  above.  But  if  the  tube  filled  with  inac- 
tive liquid  be  replaced  by  one  full  of  solution  of  sugar,  the  rotatory  power  of 
this  solution  is  added  to  that  of  one  of  the  halves  (a  or  b]  of  the  plate  q  (viz. 
that  half  which  tends  to  turn  the  plane  of  polarisation  in  the  same  direction 
as  the  solution),  and  subtracted  from  that  of  the  other.  Hence  the  two 
halves  of  the  plate  q  no  longer  show  the  same  tint  ;  the  half  <z,  for  instance, 
is  red,  while  the  half  b  is  blue.  The  prisms  of  the  compensator  are  then 
moved  by  turning  the  milled  head  ^,  either  to  the  right  or  to  the  left,  until 
the  difference  of  action  of  the  compensator  and  of  the  plate  z  compensates 
the  rotatory  power  of  the  solution,  which  takes  place  when  the  two  halves 
of  the  plate  q,  with  double  rotation,  revert  to  their  original  tint. 

The  direction  of  the  deviation  and  the  thickness  of  the  compensator  are 
measured  by  the  relative  displacement  of  the  scale  <?,  and  of  the  vernier  v. 
Ten  of  the  divisions  on  the  scale  correspond  to  a  difference  of  i  millimetre 
in  the  thickness  of  the  compensator ;  and  as  the  vernier  gives  itself  tenths 


-678]  Analysis  of  Diabetic  Urine,  621 

of  these  divisions,  it  therefore  measures  differences  of  T^  in  the  thickness  of 
the  compensator. 

When  once  the  tints  of  the  two  halves  of  the  plate  are  exactly  the  same, 
and  therefore  the  same  as  before  interposing  the  solution  of  sugar,  the 
division  on  the  scale  corresponding  to  the  vernier  is  read  off,  and  the  cor- 
responding number  gives  the  strength  of  the  solution.  This  depends  on  the 
experimental  fact  that  16-471  grains  of  pure  and  well-dried  sugar-candy  being 
dissolved  in  water,  and  the  solution  diluted  to  the  volume  of  100  cubic  cen- 
timetres, and  observed  in  a  tube  of  20  centimetres  in  length,  the  deviation 
produced  is  the  same  as  that  effected  by  a  quartz  plate  a  millimetre  thick. 
In  making  the  analysis  of  raw  sugar,  a  weight  of  16*471  grains  of  sugar  is 
taken,  dissolved  in  water,  and  the  solution  made  up  to  100  cubic  centimetres, 
with  which  a  tube  20  centimetres  in  length  is  filled,  and  the  number  indicated 
by  the  vernier  read  off,  when  the  primitive  tint  has  been  obtained.  This 
number  being  42,  for  example,  it  is  concluded  that  the  amount  of  crystallisable 
sugar  in  the  solution  is  42  per  cent,  of  that  which  the  solution  of  sugar-candy 
contained,  and,  therefore,  16-471  grains  x  j4—,  or  6-918  grains.  This  result 
is  only  valid  when  the  sugar  is  not  mixed  with  uncrystallisable  sugar  or 
some  other  left-handed  substance.  In  that  case  the  crystallisable  sugar, 
which  is  right-handed,  must  be,  by  means  of  hydrochloric  acid,  converted 
into  uncrystallisable  sugar,  which  is  left-handed  ;  and  a  new  determination 
is  made,  which,  together  with  the  first,  gives  the  quantity  of  crystallisable 
sugar. 

The  arrangement  of  crystals  and  lenses,  o,  g,f,  and  a,  placed  behind  the 
prism  c,  forms  what  Soleil  calls  the  producer  of  sensible  tints.  For  the 
most  delicate  tint — that  by  which  a  very  feeble  difference  in  the  coloration 
of  the  two  halves  of  the  rotation  plate  can  be  distinguished — is  not  the  same 
for  all  eyes  ;  for  most  people  it  is  of  a  violet-blue  tint,  like  flax  blossom  ;  and 
it  is  important  either  to  produce  this  tint,  or  some  other  equally  sensible  to 
the  eye  of  the  observer.  This  is  effected  by  placing  in  front  of  the  prism,  c, 
at  first  a  quartz  plate,  <?,  cut  perpendicular  to  the  axis,  then  a  small  Galileo's 
telescope  consisting  of  a  double  convex  glass,  g,  and  a  double  concave  glass, 
fj  which  can  be  approximated  or  removed  from  each  other  according  to  the 
distance  of  distinct  vision  of  each  observer.  Lastly,  there  is  a  double-re- 
fracting prism,  c,  acting  as  polariser  in  reference  to  the  quartz,  and  the  prism 
a  as  analyser  ;  and  hence,  when  the  latter  is  turned  either  right  or  left,  the 
light  which  has  traversed  the  prism  <r,  and  the  plate  a,  changes  its  tint,  and 
finally  gives  that  which  is  the  most  delicate  for  the  experimenter. 

678.  Analysis  of  diabetic  urine. — In  the  disease  diabetes,  the  urine 
contains  a  large  quantity  of  fermentable  sugar,  called  diabetic  sugar, 
which  in  the  natural  condition  of  the  urine  turns  the  plane  of  polarisation  to 
the  right.  To  estimate  the  quantity  of  this  sugar,  the  urine  is  first  clarified 
by  heating  it  with  acetate  of  lead  and  filtering ;  the  tube  is  filled  with  the 
•clear  liquid  thus  obtained  ;  and  the  milled  head  b  turned  until,  by  means  of 
the  double-rotating  plate,  the  same  tint  is  obtained  as  before  the  interposition 
of  the  urine.  Experiment  has  shown  that  100  parts  of  the  saccharimetric 
scale  represent  the  displacement  which  the  quartz  compensators  must  have 
when  there  are  225-6  grains  of  sugar  in  a  litre  ;  hence  each  division  of  the 
scale  represents  2-256  of  sugar.  Accordingly,  to  obtain  the  quantity  of  sugar 


622  On  Light.  [678- 

in  a  given  urine,  the  number  indicated  by  the  vernier,  at  the  moment  at 
which  the  primitive  tint  reappears,  must  be  multiplied  by  2-256. 

679.  Polarisation  of  heat. — The  rays  of  heat,  like  those  of  light,  may 
become  polarised  by  reflection  and  by  refraction.  The  experiments  on  this 
subject  are  difficult  of  execution ;  they  were  first  made  by  Malus  and 
Berard,  in  1810 ;  after  the  death  of  Malus  they  were  continued  by  the  latter 
philosopher. 

In  his  experiments,  the  calorific  rays  reflected  from  one  mirror  were  re- 
ceived upon  a  second,  just  as  in  Norremberg's  apparatus  ;  from  the  second 
they  fell  upon  a  small  metallic  reflector,  which  concentrated  them  upon  the 
bulb  of  a  differential  thermometer.  Berard  observed  that  heat  was  not 
reflected  when  the  plane  of  reflection  of  the  second  mirror  was  at  right  angles 
to  that  of  the  first.  As  this  phenomenon  is  the  same  as  that  presented  by 
light  under  the  same  circumstances,  Berard  concluded  that  heat  became 
polarised  in  being  reflected. 

The  double  refraction  of  heat  may  be  shown  by  concentrating  the  sun's 
rays  by  means  of  a  heliostat  on  a  prism  of  Iceland  spar,  and  investigating 
the  resultant  pencil  by  means  of  a  thermopile,  which  must  have  a  sharp 
narrow  edge.  In  this  case  also  there  is  an  ordinary  and  an  extraordinary 
ray,  which  follow  the  same  laws  as  those  of  light.  In  the  optic  axis  of  the 
calcspar,  heat  is  not  doubly  refracted.  A  Nicol's  prism  can  be  used  for  the 
polarisation  of  heat  as  well  as  for  that  of  light ;  a  polarised  ray  does  not 
traverse  the  second  Nicol  if  the  plane  of  its  principal  section  is  perpendicular 
to  the  vibrations  of  the  ray.  The  phenomena  of  the  polarisation  of  heat 
may  also  be  studied  by  means  of  plates  of  tourmaline  and  of  mica.  The 
angle  of  polarisation  is  virtually  the  same  for  heat  as  for  light.  In  all  these 
experiments  the  prisms  must  be  very  near  each  other. 

The  diffraction,  and  therefore  the  interference,  of  rays  of  heat  has  recently 
been  established  by  the  experiments  of  Knoblauch  and  others.  And  Forbes, 
who  has  repeated  Fresnel's  experiment  with  a  rhombohedron  of  rock  salt, 
has  found  that  by  two  total  internal  reflections,  heat  is  circularly  polarised,, 
just  as  is  the  case  with  light. 


-681]  Poles  and  Neutral  Lines.  623, 


BOOK   VIII. 

ON     MAGNETISM. 


CHAPTER    I. 

PROPERTIES   OF  MAGNETS. 

•  680.  Natural  and  artificial  mag-nets. — Magnets  are  substances  which 
have  the  property  of  attracting  iron,  and  the  term  magnetism  is  applied  to. 
the  cause  of  this  attraction  and  to  the  resulting  phenomena. 

This  property  was  known  to  the  ancients  ;  it  exists  in  the  highest  degree 
in  an  ore  of  iron  which  is  known  in  chemistry  as  the  magnetic  oxide  of  iron. 
Its  composition  is  represented  by  the  formula  Fe3O4. 

This  magnetic  oxide  of  iron,  or  lodestone,  as  it  is  called,  was  first  found 
at  Magnesia,  in  Asia  Minor,  the  name  magnet  being  derived  from  this  cir- 
cumstance. The  name  lodestone,  which  is  applied  to  this  natural  magnet, 
was  given  on  account  of  its  being  used  when  suspended  as  a  guiding  or  lead- 
ing stone,  from  the  Saxon  Icedan,  to  lead ;  so  also  the  word  lodestar.  Lode- 
stone  is  very  abundant  in  nature  :  it  is  met  with  in  the  older  geological  forma- 
tions, especially  in  Sweden  and  Norway,  where  it  is  wrorked  as  an  iron  ore, 
and  furnishes  the  best  quality  of  iron. 

When  a  bar  or  needle  of  steel  is  rubbed  with  a  magnet,  it  acquires 
magnetic  properties.  Such  bars  are  called  artificial  magnets  :  they  are 
more  powerful  than  natural  magnets,  and,  as  they  are  also  more  convenient, 
they  will  be  exclusively  referred  to  in  describing  the  phenomena  of  magnet- 
ism. The  best  modes  of  preparing  them  will  be  explained  in  a  subsequent 
article. 

68 1.  Poles  and  neutral  lines. — When  a  small  piece  of  soft  iron  is  sus- 
pended by  a  thread  and  a  magnet  is  approached  to  it,  the  iron  is  attracted 
towards  the  magnet,  and  some  force  is  required  for  its  removal.  The  force 
of  the  attraction  varies  in  different  parts  of  the  magnet ;  it  is  strongest  at  the 
two  ends,  and  is  totally  wanting  in  the  middle. 

This  variation  may  also  be  seen  very  clearly  when  a  bar  magnet  is 
placed  in  iron  filings ;  these  become  arranged  round  the  ends  of  the  bar 
in  feathery  tufts,  which  decrease  towards  the  middle  of  the  bar,  where 
there  are  none.  That  part  of  the  surface  of  the  bar  where  there  is  no 
visible  magnetic  force  is  called  the  neutral  line ;  and  the  parts  near  the 
ends  of  the  bar  where  the  attraction  is  greatest  are  called  the  poles.  Eveiy 


624 


On  Magnetism. 


[681 


magnet,  whether  natural  or  artificial,  has  two  poles  and  a  neutral  line  : 
sometimes,  however,  in  magnetising  bars  and  needles,  poles  are  produced 
lying  between  the  extreme  points.  Such  magnets  are  abnormal,  and  these 
points  are  called  intermediate  or  consequent  poles.  The  shortest  line  joining 
the  two  poles  is  termed  the  axis  of  the  magnet ;  in  a  horseshoe  magnet  the 
axis  is  in  the  direction  of  the  keeper.  The  plane  at  right  angles  to  the  axis 
of  a  bar  magnet  and  passing  through  the  neutral  line  is  sometimes  called  the 
equator  of  the  magnet,  and  the  length  of  a  magnet,  as  far  as  magnetic  actions 
are  concerned,  is  the  distance  of  the  poles. 

We  shall  presently  see  that  a  freely  suspended  magnet  always  sets  with 
one  pole  pointing  towards  the  north,  and  the  other  towards  the  south.  The 

end  pointing  towards  the 

JIIBfe&Mt^...,. .....^mWJSi^K.    north    is    called   in    this 

country  the  north  pole, 
and  the  other  end  is 
the  south  pole.  The  end 
of  the  magnetic  needle 
Fig-  593-  pointing  to  the  north  is 

also  sometimes  called  the  marked  end  of  the  needle.  Sometimes  also  the 
end  pointing  to  the  north  is  called  the  red  pole,  and  that  to  the  south  the 
blue  pole  ;  the  corresponding  terms  red  and  blue  magnetisms  are  also  some- 
times used. 

682.  Reciprocal  action  of  two  poles. — The  two  poles  of  a  magnet  appear 

identical  when  they  are  brought  in  contact 
with  iron  filings  (fig.  593),  but  this  identity 
is  only  apparent,  for  when  a  small  mag- 
netic needle,  ab  (fig.  594),  is  suspended  by 
a  fine  thread,  and  the  north  pole,  A,  of 
another  needle  is  brought  near  its  north 
pole,  a,  a  repulsion  takes  place.  If,  on 
the  contrary,  A  is  brought  near  the  south 
pole,  b,  of  the  movable  needle,  the  latter 
is  strongly  attracted.  Hence  these  two 
poles,  a  and  b,  are  not  identical,  for  one 
is  repelled,  and  the  other  attracted  by  the 
same  pole  of  the  magnet  A.  It  may  be 
shown  in  the  same  manner  that  the  two 
poles  of  the  latter  are  also  different,  by 
successively  presenting  them  to  the  same 
pole,  a,  of  the  movable  needle.  In  one 
•case  there  is  repulsion,  in  the  other  attraction.  Hence  the  following  law 
may  be  enunciated  : — 

Poles  of  the  same  name  repel,  and  poles  of  contrary  name  attract,  one 
another. 

The  opposite  actions  of  the  north  and  south  poles  may  be  shown  by  the 
following  experiment  : — A  piece  of  iron,  a  key  for  example,  is  supported 
by  a  bar  magnet.  A  second  bar  magnet  of  the  same  dimensions  is  then 
moved  along  the  first,  so  that  their  poles  are  contrary  (fig.  595).  The  key 
remains  suspended  so  long  as  the  two  poles  are  at  some  distance,  but  when 


r\ 


Fig.  594- 


-684]  Precise  Definition  of  Poles.  62$ 

they  are  sufficiently  near,  the  key  drops,  just  as  if  the  bar  which  supported 
it  had  lost  its  magnetism.     This,  however,  is  not  the  case,  for  the  key  would 
be  again   supported   if  the 
first  magnet  were  presented 
to  it  after  the   removal  of 
the  second  bar. 

The  attraction  which  a 
magnet  exerts  upon  iron  is 
reciprocal,  which  is  indeed 
a  general  principle  of  all 

attractions.    It  is  easily  veri-  p. 

fied  by  presenting  a  mass  of 

C"  on  to  a  movable  magnet,  when  the  latter  is  attracted. 
683.  Hypothesis  of  two  magnetic  fluids. — In  order  to  explain  the  phe- 
nomena of  magnetism,  the  existence  of  two  hypothetical  magnetic  fluids  has 
been  assumed,  each  of  which  acts  repulsively  on  itself,  but  attracts  the  other 
fluid.  The  fluid  whose  action  predominates  at  the  north  pole  of  the  magnet 
is  called  the  north  fluid,  or  red  magnetism  ;  and  that  at  the  south  pole  the 
south  fluid,  or  blue  magnetism.  The  term  *  fluid  '  is  apt  to  puzzle  beginners, 
from  its  ambiguity.  Ordinarily  the  idea  of  a  liquid  is  associated  with  the 
term  '  a  fluid  ; '  hence  the  use  of  this  term  to  explain  the  phenomena  of  mag- 
netism and  electricity  has  produced  a  widely  prevailing  impression  of  the 
material  nature  of  these  two/orces.  The  word '  fluid,'  it  must  be  remembered, 
embraces  gases  as  well  as  liquids,  and  here  it  must  be  pictured  to  the  mind 
as  representing  an  invisible,  elastic,  gaseous  atmosphere  or  shell  surrounding 
the  particles  of  all  magnetic  substances. 

It  is  assumed  that,  before  magnetisation,  these  fluids  are  combined  round 
each  molecule,  and  mutually  neutralise  each  other ;  they  can  be  separated 
by  the  influence  of  a  force  greater  than  that  of  their  mutual  attraction,  and 
can  arrange  themselves  round  the  molecules  to  which  they  are  attached,  but 
cannot  be  removed  from  them. 

The  hypothesis  of  the  two  fluids  is  convenient  in  explaining  magnetic 
phenomena,  and  will  be  adhered  to  in  what  follows.  But  it  must  not  be 
regarded  as  anything  more  than  a  provisional  hypothesis,  and  it  will  after- 
wards be  shown  (879)  that  magnetic  phenomena  appear  to  result  from  elec- 
trical currents,  circulating  in  magnetic  bodies  ;  a  mode  of  view  which  connects 
the  theory  of  magnetism  with  that  of  electricity. 

>J  684.  Precise  definition  of  poles. — By  aid  of  the  preceding  hypothesis 
we  are  enabled  to  obtain  a  clear  idea  of  the  distribution  of  the  magnetism 
in  a  magnetised  bar,  and  to  account  for  the  circumstance  that  there  is  no 
free  magnetism  in  the  middle  of  the  bar,  and  that  it  is  strongest  at  the  poles. 
If  AB  (fig.  596)  represent  a  magnet,  then  the  alternate  black  and  white 
spaces  may  be  taken  to  represent  the  position  of  the  magnetic  fluids  in  a 
series  of  particles  after  magnetisation  :  in  accordance  with  what  has  been 
said,  the  black  spaces,  representing  the  south  fluid,  all  point  in  one  direction, 
and  the  north  fluid  in  the  opposite  direction.  The  last  half  of  the  terminal 
molecule  at  one  end  would  have  north  polarity,  and  at  the  other  south 
polarity.  Let  N  represent  the  north  pole  of  a  magnetic  needle  placed  near 
the  magnet  AB  ;  then  the  south  fluid  s  in  the  terminal  molecule  would  tend 

ss 


626  On  Magnetism.  [684- 

to  attract  N,  and  the  north  fluid  n  would  tend  to  repel  it ;  but  as  the  mole- 
cule of  south  fluid  s  is  nearer  N  than  the  molecule  of  the  north  fluid  72,  the 
attraction  between  s  and  N  would  be  greater  than  the  repulsion  between  n 
and  N.  Similarly  the  attraction  between  j'  and  N  would  be  greater  than 


n"  s"  n  s'  n  s 


Fig.  596- 

the  repulsion  between  n'  and  N,  and  so  on  with  the  following  s"  and  n",  &c.. 
And  all  these  forces  would  give  a  resultant  tending  to  attract  N,  whose 
point  of  application  would  have  a  certain  fixed  position,  which  would  be  the 
south  pole  of  AB.  In  like  manner  it  might  be  shown  that  the  resultant  of 
the  forces  acting  at  the  other  end  of  the  bar  would  form  a  north  pole,  and 
would  hence  repel  the  north  pole  of  the  needle,  but  would  attract  its  south 
pole. 

That  such  a  series  of  polarised  particles  really  acts  like  an  ordinary 
magnet  may  be  shown  by  partly  filling  a  glass  tube  with  steel  filings,  and 
passing  the  pole  of  a  strong  magnet  several  times  along  the  outside  in  one 
constant  direction,  taking  care  not  to  shake  the  tube.  The  individual  filings 
will  thus  be  magnetised,  and  the  whole  column  of  them  presented  to  a  mag- 
netic needle  will  attract  and  repel  its  poles  just  like  an  ordinary  bar  magnet, 
exhibiting  a  north  pole  at  one  end,  a  south  pole  at  the  other,  and  no  polarity 
in  the  middle ;  but  on  shaking  the  tube,  or  turning  out  the  filings,  and  put- 
ting them  in  again  so  as  to  destroy  the  regularity,  every  trace  of  polarity  will 
disappear.  It  appears  hence  that  the  polarity  at  each  end  of  a  magnet  is 
caused  by  the  fact  that  the  resultant  action  on  a  magnetic  body  is  strongest 
near  the  ends,  and  does  not  arise  from  any  accumulation  of  magnetisms  at 
the  ends. 

The  same  point  may  be  illustrated  by  the  following  experiment,  which  is 
due  to  Sir  W.  Grove  :— In  a  glass  tube  with  flat  glass  ends  is  placed  water  in 
which  is  diffused  magnetic  oxide  of  iron.  Round  the  outside  of  the  tube  is 
coiled  some  insulated  wire.  On  looking  at  a  light  through  the  tube  the 
liquid  appears  dark  and  muddy,  but  on  passing  a  current  of  electricity  through 
the  wire  it  becomes  clearer  (879).  This  is  due  to  the  fact  that  by  the  mag- 
netising action  of  the  current,  the  particles,  becoming  magnetised,  set  with 
their  longest  dimension  parallel  to  the  axis  of  the  tube,  in  which  position 
they  obstruct  the  passage  of  light  to  a  less  extent. 

685.  Experiments  with  broken  mag-nets. — That  the  two  magnetisms 
are  present  in  all  parts  of  the  bar,  and  are  not  simply  accumulated  at  the 
ends,  is  also  evident  from  the  following  experiment : — A  steel  knitting- 
needle  is  magnetised  by  rubbing  it  with  one  of  the  poles  of  a  magnet,  and  then, 
the  existence  of  the  two  poles  and  of  the  neutral  line  having  been  ascertained 
by  means  of  iron  filings,  it  is  broken  in  the  middle.  But  now,  on  presenting 


-686]  Magnetic  Induction.  627 

successively  the  two  halves  to  a  magnet,  each  will  be  found  to  possess  two 
opposite  poles  and  a  neutral  line,  and  in  fact  is  a  perfect  magnet.  If  these 
new  magnets  are  broken  in  turn  into  two  halves,  each  will  be  a  complete 
magnet  with  its  two  poles  and  neutral  line,  and  so  on,  as  far  as  the  division 
can  be  continued.  It  is,  therefore,  concluded  by  analogy  that  the  smallest 
parts  of  a  magnet,  the  ultimate  molecules,  contain  the  two  magnetisms. 
^ 686.  Magnetic  induction. — When  a  magnetic  substance  is  placed  in 
contact  with  a  magnet,  the  two  magnetisms  of  the  former  become  separated  ; 
and  so  long  as  the  contact  remains,  it  is  a  complete  magnet,  having  its  two 
poles  and  its  neutral  line.  For  instance,  if  a  small  cylinder  of  soft  iron,  ab 
(fig.  597),  be  placed  in  contact  with  one  of  the  poles  of  a  magnet,  the  cylinder 


Fig-  597- 

can  in  turn  support  a  second  cylinder  ;  this  in  turn  a  third,  and  so  on,  to  as 
many  as  seven  or  eight,  according  to  the  power  of  the  magnet.  Each  of  these 
little  cylinders  is  a  magnet ;  if  it  be  the  north  pole  of  the  magnet  to  which 
the  cylinders  are  attached,  the  part  a  will  have  south,  and  b  north  magnetism  ; 
b  will  in  like  manner  develop  in  the  nearest  end  of  the  next  cylinder  south 
magnetism,  and  so  on.  But  these  cylinders  are  only  magnets  so  long  as  the 
influence  of  a  magnetised  bar  continues.  For,  if  the  first  cylinder  be  re- 
moved from  the  magnet,  the  other  cylinders  immediately  drop,  and  retain  no 
trace  of  magnetism.  The  separation  of  the  two  magnetisms  is  only  moment- 
ary, which  proves  that  the  magnet  yields  nothing  to  the  iron.  Hence  we 
may  have  temporary  magnets  as  well  as  permanent  magnets  ;  the  former  of 
iron  and  nickel,  the  latter  of  steel  and  cobalt  (688). 

This  action,  in  virtue  of  which  a  magnet  can  develop  magnetism  in 
iron,  is  called  magnetic  induction  or  influence,  and  it  can  take  place  without 
actual  contact  between  the  magnet  and  the  iron,  as  is  seen  in  the  following 
experiment : — A  bar  of  soft  iron  is  held  with  one  end  near  a  magnetic  needle. 
If  now  the  north  pole  of  a  magnet  be  approached  to  the  iron  without  touch- 
ing it,  the  needle  will  be  attracted  or  repelled,  according  as  its  south  or 
north  pole  is  near  the  bar.  For  the  north  pole  of  the  magnet  will  develop 
south  magnetism  in  the  end  of  the  bar  nearest  it,  and  therefore  north  mag- 
netism at  the  other  end,  which  would  thus  attract  the  south,  but  repel  the 
north  end  of  the  needle.  Obviously,  if  the  other  end  of  the  magnet  were 
brought  near  the  iron,  the  opposite  effects  would  be  produced  on  the  needle ; 
or  if  the  opposite  pole  of  a  second  magnet  of  equal  strength  simultaneously 
be  brought  near  the  iron,  the  needle  would  be  unaffected,  as  one  magnet 
would  undo  the  work  of  the  other. 

Among  other  things,  magnetic  induction  explains  the  formation  of  the 
tufts  of  iron  filings  which  become  attached  to  the  poles  of  magnets.  The 

s  s  2 


628  On  Magnetism.  [686- 

parts  in  contact  with  the  magnet  are  converted  into  magnets  ;  these  act 
inductively  on  the  adjacent  parts,  these  again  on  the  following  ones,  and 
so  on,  producing  a  filamentary  arrangement  of  the  filings.  The  bush-like 
appearance  of  these  filaments  is  due  to  the  repulsive  action  which  the 
free  poles  exert  upon  each  other.  Any  piece  of  soft  iron  while  being 
attracted  by  a  magnet  is  for  the  time  being  converted  into  a  magnet  ; 
hence  is  explained  the  paradoxical  statement  that  '  magnets  only  attract 
'magnets.' 

»  687.  Coercive  force. — We  have  seen  from  the  above  experiments  that 
soft  iron  becomes  instantaneously  magnetised  under  the  influence  of  a 
magnet,  but  that  this  magnetism  is  not  permanent,  and  ceases  when  the 
magnet  is  removed.  Steel  likewise  becomes  magnetised  by  contact  with  a 
magnet ;  but  the  operation  is  effected  with  difficulty,  and  the  more  so  as  the 
steel  is  more  highly  tempered.  Placed  in  contact  with  a  magnet,  a  steel  bar 
acquires  magnetic  properties  very  slowly  ;  and,  to  make  the  magnetism 
complete,  the  steel  must  be  rubbed  with  one  of  the  poles.  But  this  mag- 
netism, once  evoked  in  steel,  is  permanent,  and  does  not  disappear  when  the 
inducing  force  is  removed. 

These  different  effects  in  soft  iron  and  steel  are  ascribed  to  a  kind  of 
resistance  which  is  often  called  coercive  force^  and  which,  in  a  magnetic  sub- 
stance, offers  a  hindrance  to  the  separation  of  the  two  magnetisms,  but  which 
also  prevents  their  recombination  when  once  separated.  In  steel  this  coercive 
force  is  very  great  ;  in  soft  iron  it  is  very  small  or  almost  absent.  By  oxida- 
tion, pressure,  torsion  or  hammering,  &c.,  a  certain  amount  of  coercive  force 
may  be  imparted  to  soft  iron  ;  and  by  heat,  the  coercive  force  may  be  lessened, 
as  will  be  afterwards  seen. 

\  688.  Difference  between  magnets  and  magnetic  substances. — Mag- 

netic substances  are  substances  which,  like  iron,  steel,  and  nickel,  are  attracted 
by  the  magnet.  They  contain  the  two  magnetisms,  but  in  a  state  of  neu- 
tralisation. Compounds  containing  iron  are  usually  magnetic,  and  the  more 
so  in  proportion  as  they  contain  a  larger  quantity  of  iron.  Some,  however, 
like  iron  pyrites,  are  not  attracted  by  the  magnet. 

A  magnetic  substance  is  readily  distinguished  from  a  magnet.  The 
former  has  no  poles  ;  if  successively  presented  to  the  two  ends  of  a  magnetic 
needle,  ab  (fig.  594),  it  will  attract  both  ends  equally,  while  with  one  and  the 
same  end  a  magnet  would  attract  the  one  end  of  the  needle,  but  repel  the 
other.  Magnetic  substances  also  have  no  action  on  each  other  ;  while  mag- 
nets attract  or  repel  each  other,  according  as  unlike  or  like  poles  are  pre- 
sented. Attraction  is  no  proof  that  a  body  is  a  magnet ;  repulsion  is. 

Iron  is  not  the  only  substance  which  possesses  magnetic  properties  ; 
nickel  has  considerable  magnetic  power,  but  far  less  than  that  of  iron  ;  cobalt 
is  less  magnetic  than  nickel ;  while  to  even  a  slighter  extent  chromium  and 
manganese  are  magnetic.  Further,  we  shall  see  that  powerful  magnets  exert 
a  peculiar  influence  on  all  substances. 


_690]  Terrestrial  Magnetic  Couple.  629 


CHAPTER   II. 

TERRESTRIAL  MAGNETISM.      COMPASSES. 

689.  Directive  action  of  the  earth  on  magnets. — When   a  magnetic 
needle  is  suspended  by  a  thread,  as  represented  in  fig.  594,  or  when  placed 
on  a  pivot  on  which  it  can  move  freely  (fig.  598),  it  ultimately  sets  in  a 
position   which   is   more   or   less  north  and 
south.      If    removed   from  this   position   it 
always  returns  to  it  after  making  a  certain 
number  of  oscillations. 

Analogous  observations  have  been  made 
in  different  parts  of  the  globe,  from  which  the 
earth  has  been  compared  to  an  immense  mag-  s 
net,  whose  poles  are  very  near  the  terrestrial 
poles,  and  whose  neutral  line  virtually  coin- 
cides with  the  equator. 

The  polarity  in  the  northern  hemisphere 
is  called  the  northern  or  boreal  polarity,  and 
that  in  the  southern  hemisphere  the  southern 
or  austral  polarity.  In  French  works  the  end 

of  the  needle  pointing  north  is  called  the  austral  or  southern  pole,  and  that 
pointing  to  the  south  the  boreal  or  northern  pole  ;  a  designation  based  on 
this  hypothesis  of  a  terrestrial  magnet,  and  on  the  law  that  unlike  magnet- 
isms attract  each  other.  In  practice  it  will  be  found  more  convenient  to 
use  the  English  names,  and  call  that  end  of  the  magnet  which  points  to  the 
north  the  north  pole,  and  that  which  points  to  the  south  the  south  pole ;  the 
north  pole  of  a  magnet  is  a  north-seeking  pole,  and  a  south  pole  a  south-seek- 
ing pole.  To  avoid  ambiguity  that  end  of  the  needle  pointing  north  is  in 
/England  sometimes  spoken  of  as  the  marked  end  of  the  needle  (68 1). 
\  690.  Terrestrial  magnetic  couple. —  From  what  has  been  stated,  it  is 
clear  that  the  magnetic  action  of  the  earth  on  a  magnetised  needle  may  be 
compared  to  a  couple  ;  that  is,  to  a  system  of  two  equal  forces,  parallel,  but 
acting  in  contrary  directions. 

For  let  ab  (fig.  599)  be  a  movable  magnetic  needle  making  an  angle  with 
the  magnetic  meridian  M'M  (691).  The  earth's  north  pole  acts  attractively 
on  the  marked  pole,  «,  and  repulsively  on  the  other  pole,  b,  and  two  contrary 
forces  are  produced,  an  and  bnf,  which  are  equal  and  parallel  :  for  the 
terrestrial  pole  is  so  distant,  and  the  needle  so  small,  as  to  justify  the  assump- 
tion that  the  two  directions  an  and  bnf,  are  parallel,  and  that  the  two  poles 
are  equidistant  from  the  earth's  north  pole.  But  the  earth's  south  pole  acts 
similarly  on  the  poles  of  the  needle,  and  produces  two  other  forces,  as  and  bs, 
which  are  also  equal  and  parallel ;  but  the  two  forces  an  and  as  may  be  re- 


630  On  Magnetism.  [690- 

duced  to  a  single  resultant  aN  (33),  and  the  forces  bn'  and  bs'  to  a  resultant 
£S  ;  the  two  forces  aN  and  £S  are  equal,  parallel,  and  act  in  opposite  direc- 
tions, and  they  constitute  the  terrestrial  magnetic  couple  ;  it  is  this  couple 

which  makes 
the  needle  set 
ultimately  in 
the  magnetic 
— -M  meridian — a  po- 
sition in  which 
the  two  forces 

Fig.  599-  N    *nd    S  arC  in 

equilibrium. 

The  force  which  determines  the  direction  of  the  needle  thus  is  neither 
attractive  nor  repulsive,  but  simply  directive.  If  a  small  magnet  be  placed 
on  a  cork  floating  in  water,  it  will  at  first  oscillate,  and  then  gradually  set  in 
a  line  which  is  virtually  north  and  south.  But  if  the  surface  of  the  water  be 
quite  smooth,  the  needle  will  not  move  either  towards  the  north  or  towards 
the  south. 

If,  however,  a  magnet  be  approached  to  a  floating  needle,  attraction  or 
repulsion  ensues,  according  as  one  or  the  other  of  the  poles  is  presented. 
The  reason  of  the  different  actions  exerted  by  the  earth  and  by  a  magnet  on 
a  floating  needle  is  as  follows  : — When  the  north  pole,  for  instance,  of  the 
magnet  is  presented  to  the  south  pole  of  the  needle,  the  latter  is  attracted  ; 
it  is,  however,  repelled  by  the  south  pole  of  the  magnet.  Now  the  force  of 
magnetic  attraction  or  repulsion  decreases  with  the  distance  ;  and,  as  the  dis- 
tance between  the  south  pole  of  the  needle  and  the  north  pole  of  the  magnet 
is  less  than  the  distance  between  the  south  pole  of  the  needle  and  the  south 
pole  of  the  magnet,  the  attraction  predominates  over  the  repulsion,  and  the 
needle  moves  towards  the  magnet.  But  the  earth's  magnetic  north  pole  is 
so  distant  from  the  floating  needle  that  its  length  may  be  considered  in- 
finitely small  in  comparison,  and  one  pole  of  the  needle  is  just  as  strongly 
repelled  as  the  other  is  attracted. 

691.  Magnetic  elements.  Declination. — In  order  to  obtain  a  full 
knowledge  of  the  earth's  magnetism  at  any  place  three  essentials  are  re- 
quisite ;  these  are — i.  Declination  ;  ii.  Inclination  ;  iii.  Force  or  Intensity. 
These  three  are  termed  the  magnetic  elements  of  the  place.  We  shall  explain 
them  in  the  order  in  which  they  stand. 

The  geographical  meridian  of  a  place  is  the  imaginary  plane  passing 
through  this  place  and  through  the  two  terrestrial  poles,  and  the  meridian 
is  the  outline  of  this  plane  upon  the  surface  of  the  globe.  Similarly  the 
magnetic  meridian  of  a  place  is  the  vertical  plane  passing  at  this  place 
through  the  two  poles  of  a  movable  magnetic  needle  in  equilibrium  about  its 
vertical  axis. 

In  general  the  magnetic  meridian  does  not  coincide  with  the  geogra- 
phical meridian,  and  the  angle  which  the  magnetic  makes  with  the  geogra- 
phical meridian — that  is  to  say,  the  angle  which  the  direction  of  the  needle 
makes  with  the  meridian — is  called  the  declination  or  variation  of  the  mag- 
netic needle.  The  declination  is  said  to  be  east  or  west,  according  as  the 
north  pole  of  the  needle  is  to  the  east  or  west  of  the  geographical  meridian. 


-692] 


Variations  in  Declination. 


631 


692.  Variations  in  declination. — The  declination  of  the  magnetic 
needle,  which  varies  in  different  places,  is  at  present  west  in  Europe  and  in 
Africa,  but  east  in  Asia  and  in  the  greater  part  of  North  and  South  America. 
It  shows  further  considerable  variations  even  in  the  same  place.  These  vari- 
ations are  of  two  kinds  ;  some  are  regular,  and  are  either  secular,  annual, 
or  diurnal ;  others,  which  are  irregular,  are  called  magnetic  storms  (694). 

Secular  variations. — In  the  same  place  the  declination  varies  in  the 
course  of  time,  and  the  needle  appears  to  make  oscillations  to  the  east  and 
west  of  the  meridian,  the  duration  of  which  extends  over  centuries.  The 
declination  has  been  known  at  Paris  since  1580,  and  the  following  table 
represents  the  variations  which  it  has  undergone  : — 


Year 

Declination 

Year 

Declination 

1580 

11°  30'  E. 

1830 

22°  12'  W.' 

1663 

0° 

1835 

22°     A'W. 

1700 

8°  10'  W. 

1850                  20°  30'  W. 

1780 

i9°55/W. 

1855 

19°  57'  W. 

1785 

22°  00'  W. 

1860 

19°  32'  W. 

1805 

22°      5/W. 

1865 

1  8°  44'  W. 

l8l4 

22°  34'  W. 

1875             i7°2i/W. 

1825 

22°  22'  W. 

1878             i7°oc/W. 

This  table  shows  that  since  1580  the  declination  has  varied  at  Paris  as 
much  as  34°,  and  that  the  greatest  westerly  declination  was  attained  in  1814, 
since  which  time  the  needle  has  gradually  tended  towards  the  east. 

At  London,  the  needle  showed  in  1580  an  easterly  declination  of  11°  36'; 
in  1663  it  was  at  zero  ;  from  that  time  it  gradually  tended  towards  the  west, 
and  reached  its  maximum  declination  of  24°  41'  in  1818  ;  since  then  it  has 
steadily  diminished  ;  it  was  22°  30'  in  1850,  19°  32'  in  1873,  19°  24'  in  1874, 
19°  1 6'  in  1875,  19°  ic/  in  1876,  19°  3'  in  1877,  18°  52'  in  1878,  18°  40'  in 
1 88 1,  1 8°  1 5',  in  1883,  and  is  now  (1886)  17°  42' W. 

At  Yarmouth  and  Dover  the  variation  is  about  40'  less  than  at  London  ; 
at  Hull  and  Southampton  about  20'  greater ;  at  Newcastle  and  Swansea 
about  i°  45',  and  at  Liverpool  2°  o',  at  Edinburgh  3°  c/,  and  at  Glasgow  and 
Dublin  about  3°  50'  greater  than  at  London. 

The  following  are  the  observations  of  the  magnetic  elements  at  Kew 
extending  over  the  last  twenty  years  : — 


Year 

Declination 

Inclination 

Horizontal 
force 

1865 

20°  59' 

68°    7'               3-829 

1867 

20°  40' 

68°    3' 

3'844 

1869 

20°  25' 

68°    i'               3-852 

1871 

20°  10' 

67°  57'               3-863 

1873 

19°  57' 

67°  52'               3-877 

1875 

19°  41' 

67°  48' 

3-885 

1877                     I9°  22' 

67°  45' 

3-89I 

1878                    19°  14' 

67°  44' 

3-895 

1879              19°    6' 

67°  42' 

3-900 

1880      |         1  8°  59' 

67°  42' 

3-899 

632 


On  Magnetism. 


[692- 


Year 

Declination 

Inclination 

1881 

18°  50' 

67°4i/ 

1882 

i8°45' 

67°4i/ 

I883 

i8°4i' 

67°  41' 

1884 

18°  32' 

67°  39' 

1885 

1  8°  26' 

67°  3»' 

Horizontal 
force 


3^04 
3-909 
3-916 

3-9I7 


In  certain  parts  of  the  earth  the  magnet  coincides  with  the  geographical 
meridian.  These  points  are  connected  by  an  irregularly  curved  imaginary 
line,  called  a  line  of  no  variation  or  agonic  line.  Such  a  line  cuts  the  east 
of  South  America,  and  passing  east  of  the  West  Indies,  enters  North 
America  near  Philadelphia,  and  traverses  Hudson's  Bay ;  thence  it  passes 
through  the  North  Pole,  entering  the  Old  World  east  of  the  White  Sea, 
traverses  the  Caspian,  cuts  the  east  of  Arabia,  turns  then  towards  Australia, 
and  passes  through  the  South  Pole,  to  join  itself  again. 

Isogonic  lines  are  lines  connecting  those  places  on  the  earth's  surface  in 
which  the  declination  is  the  same.  The  first  of  the  kind  was  constructed  in 
1700  by  Halley;  as  the  elements  of  the  earth's  magnetism  are  continually 
changing,  the  course  of  such  a  line  can  only  be  determined  for  a  certain  time. 

Maps  on  which  such  isogonic  lines  are  depicted  are  called  declination 
or  variation  maps  •  and  a  comparison  of  these  in  various  years  is  well  fitted 
to  show  the  variation  which  this  magnetic  element  undergoes.  Plate  III. 
represents  a  map  in  Mercator's  projection  giving  these  lines  for  the  year  1882. 
It  will  be  seen  that  the  surface  of  the  globe  is  divided  by  these  lines  into  two 
regions  :  one,  the  smaller,  in  which  the  variation  is  westerly,  asjndicated  by 
the  continuous  lines  ;  the  other  in  which  the  variation  is  easterly,  as  indicated 
by  the  dotted  lines.  This  chart  is  useful  to  the  mariner  as  not  only  giving 
him  the  declination  in  any  place,  but  also  as  showing  him  the  places  on  the 
globe  where  the  declination  changes  most  rapidly.  Of  these  the  most 
remarkable  are  the  coast  of  Newfoundland,  the  Gulf  of  St.  Lawrence,  the 
seaboard  of  North  America,  and  the  English  Channel  and  its  approaches. 

693.  Annual  variations. — Cassini  first  discovered  in  1780  that  the 
declination  is  subject  to  small  annual  variations.  At  Paris  and  London  it  is 
greatest  about  the  vernal  equinox,  diminishes  from  that  time  to  the  summer 
solstice,  and  increases  again  during  the  nine  following  months.  It  does  not 
exceed  from  15'  to  18',  and  it  varies  somewhat  at  different  epochs. 

The  diurnal  variations  were  first  discovered  by  Graham  in  1722  ;  they 
can  only  be  observed  by  means  of  long  needles  or  delicate  indicators  such 
as  the  reflection  of  a  ray  of  light  (522)  and  very  sensitive  instruments  (702). 
In  this  country  the  north  pole  moves  every  day  from  east  to  west  from  sun- 
rise until  one  or  two  o'clock  ;  it  then  tends  towards  the  east,  and  at  about 
ten  o'clock  regains  its  original  position.  During  the  night  the  needle  is 
almost  stationary.  Thus  the  westerly  declination  is  greatest  during  the 
warmest  part  of  the  day. 

At  Paris  the  mean  amplitude  of  the  diurnal  variation  from  April  to 
September  is  from  13'  to  15',  and  for  the  other  months  from  8'  to  10'.  On 
some  days  it  amounts  to  25',  and  on  others  does  not  exceed  5'.  The  greatest 


-695] 


Declination  Compass. 


633 


variation  is  not  always  at  the  same  time.  The  amplitude  of  the  daily  varia- 
tions decreases  from  the  poles  towards  the  equator,  where  it  is  very  feeble. 
Thus  in  the  island  of  Rewak  it  never  exceeds  3'  to  4'. 

694.  Accidental  variations  and  perturbations.  —  The  declination  is 
accidentally  disturbed  in  its  daily  variations  by  many  causes,  such  as  earth- 
quakes, the  aurora  borealis,  and  volcanic  eruptions.  The  effect  of  the 
aurora  is  felt  at  great  distances.  Auroras,  which  are  only  visible  in  the  most 
northerly  parts  of  Europe,  act  on  the  needle  even  in  these  latitudes,  where 
accidental  variations  of  i°  or  2°  have  been  observed.  In  polar  regions  the 
needle  frequently  oscillates  several  degrees  ;  its  irregularity  on  the  day  before 
the  aurora  borealis  is  a  presage  of  the  occurrence  of  this  phenomenon. 

Another  remarkable  phenomenon  is  the  simultaneous  occurrence  of 
magnetic  perturbations  in  very  distant  countries.  Thus  Sabine  mentions 
a  magnetic  disturbance  which  was  felt  simultaneously  at  Toronto,  the  Cape, 
Prague,  and  Van  Diemen's  Land.  Such  simultaneous  perturbations  have 
received  the  name  of  magnetic  storms. 

^~  695.  Declination  compass.  —  The  declination  compass  is  an  instrument 
by  which  the  magnetic  declination  of  any  place  may  be  determined  when 
its  astronomical  meridian  is 
known.  The  form  repre- 
sented in  fig.  600  consists  of 
a  brass  box,  AB,  in  the  bot- 
tom of  which  is  a  graduated 
circle,  M.  In  the  centre  is  a 
pivot  on  which  oscillates  a 
very  light  lozenge-shaped 
magnetic  needle,  ab.  To  the 
box  are  attached  two  uprights 
supporting  a  horizontal  axis, 
X,  on  which  is  fixed  an  as- 
tronomical telescope,  L, 
movable  in  a  vertical  plane. 
The  box  rests  on  a  foot,  P, 
about  which  it  can  turn  in  a 
horizontal  plane,  taking  with 
it  the  telescope.  A  fixed 
circle,  QR,  which  is  called 
the  azimuthal  circle,  mea- 
sures the  number  of  degrees 
through  which  the  telescope 
has  been  turned,  by  means 
of  a  vernier,  V,  fixed  to  the 
box.  The  inclination  of  the 
telescope,  in  reference  to  the 
horizon,  may  be  measured  by 


Fig.  600. 


another  vernier,  K,  which  moves  with  the  axis  of  the  telescope,  and  is  read 
off  on  a  fixed  graduated  arc,  x. 

The  first  thing  in  determining  the  declination  is  to  adjust  the  compass 
horizontally  by  means  of  the  screws  SS,  and  the  level  n.     The  astronomical 


On  Magnetism. 


[695- 


meridian  is  then  found,  either  by  an  observation  of  the  sun  at  noon  exactly, 
or  by  any  of  the  ready  methods  known  to  astronomers.  The  box  AB  is 
then  turned  until  the  telescope  is  in  the  plane  of  the  astronomical  meridian. 
The  angle  made  by  the  magnetic  needle  with  the  diameter  N,  which  corre- 
sponds with  the  zero  of  the  scale,  and  is  exactly  in  the  plane  of  the  telescope, 
is  then  read  off  on  the  graduated  limb,  and  this  is  east  or  west,  according  as 
the  pole  a  of  the  needle  stops  at  the  east  or  west  of  the  diameter  N. 
y"  696.  Correction  of  errors. — These  indications  of  the  compass  are  only 
correct  when  the  magnetic  axis  of  the  needle — that  is,  the  right  line  passing 
through  the  two  poles — coincides  with  its  axis  of  figure,  or  the  line  connect- 
ing its  two  ends.  This 
is  not  usually  the  case, 
and  a  correction  must 
therefore  be  made, 
which  is  done  by  the 
method  of  reversion. 
For  this  purpose  the 
needle  is  not  fixed  in 
the  cap,  but  merely 
rests  on  it,  so  that  it 
can  be  removed  and 
its  positions  reversed  ; 
thus  what  was  before 
the  lower  is  now  the 


Fig.  601. 


tne  lower  is 

ripper  face.      The  mean  between  the  observations  made  in  the  two  cases 
gives  the  true  declination. 

For,  let  NS  be  the  astronomical  meridian,  ab  the  axis  of  figure  of  the 
needle,  and  mn  its  magnetic  axis  (fig.  601).  The  true  declination  is  not  the 
.arc  N<z,  but  the  arc  Nm,  which  is  greater.  If  now  the  needle  be  turned,  the 
line  mn  makes  the  same  angle  with  the  meridian  NS  ;  but  the  north  end  of 
the  needle,  which  was  on  the  right  of  mn,  is  now  on  the  left  (fig.  602),  so  that 
the  declination,  which  was  previously  too  small  by  a  certain  amount,  is  now 
too  large  by  the  same  amount.  Hence  the  true  declination  is  given  by  the 
mean  of  these  two  observations. 

697.  Mariner's  compass. — The  magnetic  action  of  the  earth  has  received 
its  most  important  application  in  the  mariner's  compass.  This  is  a  declina- 
tion compass  used  in  guiding  the  course  of  a  ship.  Fig.  603  represents  a 
view  of  the  whole,  and  fig.  604  a  vertical  section.  It  consists  of  a  cylindrical 
case,  BB',  which,  to  keep  the  compass  in  a  horizontal  position  in  spite  of  the 
rolling  of  the  vessel,  is  supported  on  gimbals.  These  are  two  concentric 
rings,  one  of  which,  attached  to  the  case  itself,  moves  about  the  axis  xd  which 
plays  in  the  outer  ring  AB,  and  this  moves  in  the  supports  PQ,  about  the 
axis  mn,  at  right  angles  to  the  first. 

In  the  bottom  of  the  box  is  a  pivot,  on  which  is  placed,  by  means  of  an 
agate  cap,  a  magnetic  bar,  ab,  which  is  the  needle  of  the  compass.  On  this 
is  fixed  a  disc  of  mica,  a  little  larger  than  the  length  of  the  needle,  on  which 
is  traced  a  star  or  rose,  with  thirty-two  branches,  making  the  eight  points  or 
rhumbs  of  the  wind,  the  demi-rhumbs,  and  the  quarters.  The  branch  ending 
in  a  small  star,  and  called  N,  corresponds  to  the  bar  ab,  which  is  underneath 
the  disc. 


-697] 


Mariner's  Compass. 


635 


The  compass  is  placed  near  the  stern  of  the  vessel  in  the  binnacle. 
Knowing  the  direction  of  the  compass  in  which  the  ship  is  to  be  steered,  the 
pilot  has  the  rudder  turned  till  the  direction  coincides  with  the  sight  vane 


passing  through  a  line  d  marked  on  the  inside  of  the  box,  and  parallel  with 
the  keel  of  the  vessel. 

The  prismatic  compass  differs  from  the  mariner's  compass  mainly  in  its 
•di'nensions,  and  in  the  way  in  which  observations  are  made.  It  consists  of  a 
.shallow  metal  box  about  2^  inches  in  diameter  (fig.  605) ;  the  needle,  which  is 
fixed  below  the  compass  card,  plays  on  a  pivot  much  as  in  fig.  604.  A  is  a  metal 
frame  across  which  is  stretched  a  horse-hair,  forming  a  sight-vane.  Exactly  op- 
posite this  is  a  right-angled  prism  P  enclosed 
in  a  metal  case,  with  an  eyehole  and  a  slit  as 
represented  at  the  side  of  the  figure  fig.  605. 

In  order   to   make  an   observation  the 
-compass  is  held  horizontally,  and  so  that 


Fig.  604. 


Fig.  605. 


the  slit  in  the  prism,  the  hair  of  the  sight-vane,  and  the  distant  object  are 
seen  to  be  in  the  same  line  ;  looking  through  the  eyehole,  the  angle  which 
the  needle  makes  is  then  noted  ;  a  similar  observation  is  made  with  another 
object,  and  thus  the  angle  between  them,  or  their  bearing,  is  given. 

The  sight-vane  is  connected  with  a  lever,  and  can  be  turned  down  when 
it  presses  the  magnet  on  the  pivot,  thus  keeping  it  rigid,  so  that  the  compass 
can  be  transported  in  any  position. 

As  the  image  is  seen  through  the  convex  face  of  the  prism  it  is  magnified, 


636  On  Magnetism.  [697- 

and  as  it  is  seen  by  reflection  it  is  reversed,  so  that  in  order  to  read  the  figures 
correctly  they  must  be  reversed  on  the  card. 

698.  Inclination.  Magnetic  equator. —  It  might  be  supposed,  from  the 
northerly  direction  which  the  magnetic  needle  takes,  that  the  force  acting 
upon  it  is  situated  in  a  point  of  the  horizon.  This  is  not  the  case,  for  if  the 
needle  be  so  arranged  that  it  can  move  freely  in  a  vertical  plane  about  a  hori- 
zontal axis,  it  will  be  seen  that,  although  the  centre  of  gravity  of  the  needle 
coincides  with  the  centre  of  suspension,  the  north  pole  in  our  hemisphere  dips 
downwards.  In  the  other  hemisphere  the  south  pole  is  inclined  downwards. 
The  angle  which  the  magnetic  needle  makes  with  the  horizon,  when  the 
vertical  plane,  in  which  it  moves,  coincides  with  the  magnetic  meridian,  is 
called  the  inclination  or  dip  of  the  needle.  In  any  other  plane  than  the 
magnetic  meridian  the  inclination  increases^  and  is  90°  in  a  plane  at  right 
angles  to  the  magnetic  meridian.  For  the  magnetic  inclination  represents 
the  direction  of  the  total  magnetic  force,  and  may  be  decomposed  into  two 
forces,  one  acting  in  a  horizontal  and  the  other  in  a  vertical  plane.  When 
the  needle  is  moved  so  that  it  is  at  right  angles  to  the  magnetic  meridian, 
the  horizontal  component  can  only  act  in  the  direction  of  the  axis  of  suspen- 
sion, and,  therefore,  cannot  affect  the  needle,  which  is  then  solely  influenced 
by  the  vertical  component,  and  stands  vertically.  The  following  considera- 
tions will  make  this  clearer  : — 

Let  NS  (fig.  606}  represent  a  magnetic  needle  capable  of  moving  in  a 
vertical  plane.  Let  NT  represent,  in  direction  and  intensity,  the  entire 

force  of  the  each's  magnetism  acting 
on  the  pole  N.  Then  NT  can  be  re- 
solved into  the  forces  N-&  and  NV  : 
TN^  being  the  angle  of  inclination  or 
dip. 

NT  is   termed  the  total  force  M  ; 
Fig.  606.  an(j  jj-s  components  are  N^t,  or  the  hori- 

zontal force  H,  and  NV,  or  the  vertical  force  Z. 

Now,  it  is  clear  that  the  greater  the  angle  of  dip,  TN/^,  the  less  becomes 
N^,  or  the  horizontal  force,  and  the  greater,  NV,  or  the  vertical  force. 
Hence,  in  high  latitudes,  the  directive  force  of  a  compass,  which  depends  on 
the  horizontal  force,  is  less  than  in  low  latitudes.  At  the  magnetic  poles  the 
horizontal  force  will  be  nil,  and  the  vertical  force  a  maximum  ;  here,  there- 
fore, the  needle  will  be  vertical.  At  the  magnetic  equator  the  reverse  is  the 
case,  and  the  needle  will  be  horizontal.  Hence,  the  oscillations  of  a  compass 
needle,  by  which,  as  will  presently  be  explained,  the  strength  of  the  earth's 
magnetism  is  measured,  become  fewer  and  fewer  in  a  given  time  as  the 
magnetic  poles  are  approached,  although  there  is  really  an  increase  in  the 
total  force  of  the  earth. 

Again,  the  reason  why  a  dip  needle  stands  vertical  when  placed  E. 
and  W.  is  clearly  because  in  those  positions  the  horizontal  force  now  acting 
at  right  angles  to  the  plane  of  motion  of  the  needle  is  ineffectual  to  move  it, 
and  therefore  merely  produces  a  pressure  on  the  pivot  which  supports  the 
needle.  But  the  vertical  component  of  the  total  force  remains  unaffected 
by  the  new  position  of  the  needle.  Acting,  therefore,  entirely  alone  when 
the  dip  needle  is  exactly  E.  and  W.,  this  vertical  component  drags  the 
needle  into  a  line  with  itself ;  that  is,  90°  from  the  horizontal  plane. 


/    / 

1     ?,l      %       Si 


-699] 


Inclination  Compass. 


637 


The  value  of  the  dip,  like  that  of  the  declination,  differs  in  different 
localities.  It  is  greatest  in  the  polar  regions,  and  decreases  with  the  latitude 
to  the  equator,  where  it  is  approximately  zero.  In  London  at  the  present  time 
(1886)  the  dip  is  67°  26',  reckoning  from  the  horizontal  line.  In  the  southern 
hemisphere  the  inclination  is  again  seen,  but  in  a  contrary  direction  ;  that  is, 
the  south  pole  of  the  needle  dips  below  the  horizontal  line. 

The  magnetic  poles  are  those  places  in  which  the  dipping-needle  stands 
vertical  ;  that  is,  where  the  inclination  is  90°.  In  1830  the  first  of  these,  the 
terrestrial  north  pole,  was  found  by  Sir  James  Ross  in  96°  43'  west  longitude 
and  70°  north  latitude.  The  same  observer  found  in  the  South  Sea,  in  76° 
south  latitude  and  168°  east  longitude,  that  the  inclination  was  88°  37'. 
From  this  and  other  observations,  it  has  been  calculated  that  the  position  of 
the  magnetic  south  pole  was  at  that  time  in  about  154°  east  longitude  and 
75 i°  south  latitude.  The  line  of  no  declination  passes  through  these  poles, 
and  the  lines  of  equal  declination  converge  towards  them. 

The  magnetic  equator,  or  aclinic  line,  is  the  line  which  joins  all  those 
places  on  the  earth  where  there  is  no  dip  ;  that  is,  all  those  in  which  the 
dipping-needle  is  quite  horizontal.  It  is  a  somewhat  sinuous  line,  not  differ- 
ing much  from  a  great  circle  inclined  to  the  equator  at  an  angle  of  12°,  and 
cutting  it  on  two  points  almost  exactly  opposite  each  other — one  in  the 
Atlantic,  and  one  in  the  Pacific.  These  points  appear  to  be  gradually  moving 
their  position,  and  travelling  from  east  to  west. 

Lines  connecting  places  in  which  the  dipping-needle  makes  equal  angles 
are  called  isoclinic  lines.  They  have  a  certain  analogy  and  parallelism  with 
the  parallels  of  latitude,  and  the  term  magnetic  latitude  is  sometimes  used  to 
denote  positions  on  the  earth  with  reference  to  the  magnetic  dip.  Plate  IV. 
is  an  inclination  map  for  the  year  1882,  the  construction  of  which  is  quite 
analogous  to  that  of  the  map  of  declination. 

The  inclination  is  subject  to  secular  variations,  like  the  declination,  as  is 
readily  seen  from  a  comparison  of  maps  of  inclination  for  different  epochs. 
At  Paris,  in  1671,  the  inclination  was  75°  ;  since  then  it  has  been  continually 
decreasing  :  in  1835  it  was  67°  14'  ;  in  1849,  67°  ;  in  1859,  66°  14' ;  and  in 
1874,  65°  23'. 

The  following  table  gives  the  alterations  in  the  inclination  at  London,  from 
which  it  will  be  seen  that  since  1723,  in  which  it  was  at  its  maximum,  it  has 
continually  diminished  by  something  more  than  two  minutes  in  each  year. 


Year 

Inclination 

Year 

Inclination 

1576 

7i°  50' 

1828 

69°  47' 

I600 

72° 

1838 

69°  17' 

1676 

73°  30' 

I854 

68°  31' 

1723 

74°  V 

1859 

68°  21' 

1773 

72°  19' 

I874 

67°  43' 

1780 

72°    8' 

1876 

67°  39' 

1790 

7i°  33' 

1878 

67°  36' 

1800 

70°  35' 

1880 

67°  35' 

1821 

70°  3*' 

1881 

67°  35' 

699.  Inclination  compass. — An  inclination  compass,  or  dip  needle,  is  an 
instrument  for  measuring  the  magnetic  inclination  or  dip.     One  form,  repre- 


638 


On  Magnetism. 


sented  in  fig.  607,  though  not  best  adapted  for  the  most  accurate  measure- 
ments, is  well  suited  for  illustrating  the  principle.  It  consists  of  a  graduated 
horizontal  brass  circle  m,  supported  on  three  legs,  provided  with  levelling 
screws.  Above  this  circle  there  is  a  plate  A,  movable  about  a  vertical1 
axis,  and  supporting,  by  means  of  two  columns,  a  second  graduated  circle  M, 
which  measures  the  inclination.  The  needle  rests  on  a  frame  r,  and  the 
diameter  passing  through  the  two  zeros  of  the  circle  N  can  be  ascertained 
to  be  perfectly  horizontal  by  means  of  the  spirit-level  n. 

To  observe  the  inclination,  the  magnetic  meridian  must  first  be  deter- 
mined, which  is  effected  by  turning  the  plate  A  on  the  circle  »/,  until  the 
needle  is  vertical,  which  is  the  case  when  it  is  in  a  plane  at  right  angles  to 
the  magnetic  meridian  (698).  The  plate  A  is  then  turned  90°  on  the  circle 
m^  by  which  the  vertical  circle  M  is  brought  into  the  magnetic  meridian. 
The  angle  dca,  which  the  magnetic  needle  makes  with  the  horizontal  dia- 
meter, is  the  angle  of  inclination. 

There  are  here  several  sources  of  error,  which  must  be  allowed  for.  The 
most  important  are  these: — i.  The  magnetic  axis  of  the  needle  may  not 

coincide  with  its  axis  of  figure  : 
hence  an  error  which  is  cor- 
rected by  a  method  of  reversion 
analogous  to  that  already  de- 
scribed (696).  ii.  The  centre  of 
gravity  of  the  needle  may  not 
coincide  with  the  axis  of  suspen- 
sion, and  then  the  angle  dca  is 
too  great  or  too  small,  according 
as  the  centre  of  gravity  is  below 
or  above  the  centre  of  suspen- 
sion ;  for  in  the  first  case  the 
action  of  gravity  is  in  the  same 
direction  as  that  of  magnetism, 
and  in  the  second  it  is  in  the 
opposite  direction.  To  correct 
this  error,  the  poles  of  the 
needle  must  be  reversed  by  first 
demagnetising  it,  and  then  im- 
parting a  contrary  magnetism 
to  what  it  had  at  first.  The 
inclination  is  now  re-determined, 
and  the  mean  taken  of  the  re- 
sults obtained  in  the  two  groups 


Fig.  607. 


of  operations,  iii.  The  plane  of  the  ring  may  not  coincide  with  the  true  mag- 
netic meridian.  It  should  be  in  that  plane  when  the  needle  has  its  minimum 
deviation  ;  an  observation  of  this  kind  should  therefore  be  taken  along  with 
that  previously  described,  by  which  the  needle  is  moved  90°  from  its  maxi- 
mum deviation. 

The  dip  needle  may  be  used  to  determine  the  inclination  in  another 
way.  It  is  first  allowed  to  oscillate  in  the  magnetic  meridian,  and  then  in 
a  plane  at  right  angles  to  it.  If  the  number  of  oscillations  in  a  given  time 


-701]  Force  of  the  Earth's  Magnetism.  639 

in  the  first  position  be  #,  and  in  the  second  position  »„  then  in  the  first  position 
the  whole  force  of  the  earth's  magnetism  E  acts,  and  in  the  second  posi- 
tion only  the  vertical  component,  which  is  E  sin  .r,  x  being  the  angle  of  dip. 
Now,  since  the  forces  acting  on  the  needle  are,  from  the  laws  of  the  pendulum 
(55),  as  the  squares  of  the  number  of  oscillations  in  a  given  time,  we  have 

_J5 w2,from  which  sin  *•=  ^. 

E  sin  x    n?  n* 

y^yoo.  Astatic  needle  and  astatic  system. — An  astatic  needle  is  one 
which  is  uninfluenced  by  the  earth's  magnetism.  A  needle  movable  about 
an  axis  in  the  plane  of  the  magnetic  meridian  and  parallel  to  the  inclination 
would  be  one  of  this  kind  ;  for  the  terrestrial  magnetic  couple,  acting  then  in 
the  direction  of  the  axis,  cannot  impart  to  the  needle  any  determinate  direction. 

An  astatic  system  is  a  combination  of  two  needles  of  the  same  force 
joined  parallel  to  each  other  with  the  poles  in  contrary  directions,  as  shown 
in  fig.  608.  If  the  two  needles  have  exactly  the 
same  magnetic  force,  the  opposite  actions  of  the 
earth's  magnetism  on  the  poles  a'  and  b  and  on 
the  poles  a  and  b'  counterbalance  each  other  ;  the 
system  is  then  completely  astatic,  and  sets  at 
right  angles  to  the  magnetic  meridian. 

A  single  magnetic  needle  may  also  be  rendered 
astatic  by  placing  a  large  magnet  near  it.  By 
repeated  trials  a  certain  position  and  distance 
can  be  found  at  which  the  action  of  the  magnet 
on  the  needle  just  neutralises  that  of  the  earth's 
magnetism,  and  the  needle  is  free  to  obey  any  Fig.  608. 

third  force. 

Y  701.  Force  of  the  earth's  magnetism. —  If  a  magnetic  needle  be 
moved  from  its  position  of  equilibrium  it  will  revert  to  it  after  a  series  of 
oscillations,  which  follow  laws  analogous  to  those  of  the  pendulum  (80).  If 
the  magnet  be  removed  to  another  place,  and  caused  to  oscillate  during 
the  same  length  of  time  as  the  first,  a  different  number  of  oscillations 
will  be  observed.  And  the  earth's  magnetic  force  in  the  two  places 
will  be  respectively  proportional  to  the  squares  of  the  number  of  oscilla- 
tions. 

If  at  M  the  number  of  oscillations  in  a  minute  had  been  25  =  «,  and  at 
another  place  M',  24  =  7/5  we  should  have — 

Force  of  the  earth's  magnetism  at  M  ^n*  _625_ 
Force  oflhe  earth's  magnetism  at  M/"**/"^""     3  ^' 

That  is,  if  the  force  of  the  magnetism  at  the  second  place  is  taken  as 
unity,  that  of  the  first  is  1-085.  If  the  magnetic  condition  of  the  needle  had 
not  changed  in  the  interval  between  the  two  observations,  this  method  would 
give  the  relation  between  the  force  at  the  two  places. 

In  these  determinations  of  the  force,  it  would  be  necessary  to  have  the 
oscillations  of  the  dip-needle,  which  are  produced  by  the  total  force  of 
the  earth's  magnetism.  These,  however,  are  difficult  to  obtain  with 
accuracy,  and,  therefore,  those  of  the  declination  needle  are  usually  taken. 
The  force  which  makes  the  declination  needle  oscillate  is  only  a  portion. 


€t* 


640  On  Magnetism.  [701- 

of  the  total  magnetic  force,  and  is  smaller  in  proportion  as  the  inclination 
is  greater.  If  a  line  ac=  M  (fig.  609)  represent  the  total  force,  the  angle  i  the 
inclination,  then  the  horizontal  component  #£  =  H  is  M  cos  i.  Hence  to 
express  the  total  force  in  the  two  places  by  the  oscillations  of  the  declina- 
tion needle,  we  must  substitute  the  values  M  cos  i  and  M'  cos  i'  for  M 
and  Mx  in  the  preceding  equation,  and  we  have — 

M__cos_i  =  ^:  •  hence  M  *X~  col*' 
M'  cos  i'    nf'2 '  M'     n''z  cos  i ' 

That  is  to  say,  having  observed  in  two  different  places  the 
number  of  oscillations,  n  and  n',  that  the  same  needle  makes 
in  the  same  time,  the  ratio  of  the  magnetic  force  in  the  two 
places  will  be  found  by  multiplying  the  ratio  of  the  square  of 


F-    6o  the  number  of  oscillations  by  the  inverse  ratio  of  the  cosine  of 

the  angle  of  dip. 

Plate  V.  is  a  chart  representing  the  horizontal  component  of  the  earth's 
force.  Knowing  the  angle  of  dip  2',  the  total  force  M,  or  the  vertical  force  Z, 
in  any  place,  may  be  obtained  from  the  values  in  the  chart  by  the  formula 
M  =  H  sec  /  ;  and  Z  =  H  tan  i. 

The  total  force  is  least  near  the  magnetic  equator,  and  increasing  with 
the  latitude,  is  greatest  near,  but  not  quite  at,  the  magnetic  poles  ;  the  places 
of  maximum  intensity  are  conveniently  named  the  magnetic  foci.  The  chart 
•shows  that  the  horizontal  force  diminishes  as  we  go  towards  the  poles  :  this  is 
not  inconsistent  with  the  above  statement  if  we  take  the  dip  into  account  (698). 

The  lines  connecting  places  of  equal  force  are  called  isodynamic  lines. 
They  are  not  parallel  to  the  magnetic  equator,  but  seem  to  have  about  the 
•same  direction  as  the  isothermal  lines.  According  to  Kuppfer,  the  force 
appears  to  diminish  as  the  height  of  the  place  is  greater ;  a  needle  which 
made  one  oscillation  in  24"  vibrated  more  slowly  by  croi"  at  a  height  of 
1,000  feet :  but,  according  to  Forbes,  the  force  is  only  Ti^  less  at  a  height 
of  3,000  feet.  There  is,  however,  some  doubt  as  to  the  accuracy  of  these 
observations,  owing  to  the  uncertainty  of  the  correction  for  temperature. 

The  intensity  varies  in  the  same  place  with  the  time  of  day  :  it  attains  its 
maximum  between  4  and  5  in  the  afternoon,  and  is  at  its  minimum  between 
10  and  ii  in  the  morning. 

According  to  Gauss,  the  total  magnetic  action  of  the  earth  is  the  same  as 
that  which  would  be  exerted  if  in  each  cubic  yard  there  were  eight  bar 
magnets  each  weighing  a  pound. 

It  is  probable,  though  it  has  not  yet  been  ascertained  with  certainty,  that 
the  force  undergoes  secular  variations.  From  measurements  made  at 
Kew,  it  appears  that  ori  the  whole,  the  total  force  experiences  a  very  slight 
annual  increase  (692). 

702.  Magnetic  observatories. — During  the  last  few  years  great  atten- 
tion has  been  devoted  to  the  observation  of  the  magnetic  elements,  and  obser- 
vatories for  this  purpose  have  been  fitted  up  in  different  parts  of  the  globe. 
These  observations  have  led  to  the  discovery  that  the  magnetism  of  the  earth 
is  in  a  state  of  constant  fluctuation,  like  the  waves  of  the  sea.  And  in  study- 
ing the  variations  of  the  declination,  £c.,  the  mean  of  a  great  number  of 
observations  must  be  taken,  so  as  to  eliminate  the  irregular  disturbances, 
and  bring  out  the  general  laws. 


-702]  Magnetic  Observatories.  641 

The  principle  on  which  magnetic  observations  are  automatically  recorded 
is  as  follows : — Suppose  that  in  a  dark  room  a  bar  magnet  is  suspended 
horizontally,  and  at  its  centre  is  a  small  mirror  ;  suppose  further  that  a  lamp 
sends  a  ray  of  light  to  this  mirror,  the  inclination  of  which  is  such  that  the  ray 
is  reflected,  and  is  received  on  a  horizontal  drum  placed  underneath  the  lamp. 
The  axis  of  the  drum  is  at  right  angles  to  the  axis  of  the  magnet ;  it  is  covered 
with  sensitive  photographic  paper,  and  is  rotated  uniformly  by  clockwork. 
If  now  the  magnet  is  quite  stationary,  and  the  drum  rotates,  the  reflected 
spot  of  light  will  trace  a  straight  line  on  the  paper  with  which  the  revolving 
drum  is  covered.     But  if,  as  is  always  the  case,  the  position  of  the  magnet 
varies  during  the  twenty-four  hours,  the  effect  will  be  to  trace  a  sinuous  line 
on  the  paper.     These  lines  can  afterwards  be  fixed  by  ordinary  photographic 
methods.     Knowing  the  distance  of  the  mirror  from  the  drum,  and  the  length 
of  the  paper  band  which  comes  under  the  influence  of  the  spot  of  light  in  a 
given  time — twenty-four  hours,  for  instance — the  angular  deflection  at  any 
given  moment  may  be  deduced  by  a  simple  calculation  (522). 

The  observations  made  in  the  English  magnetic  observatories  were 
reduced  by  Sabine,  and  revealed  some  curious  facts  in  reference  to  mag- 
netic storms  (694).  He  found  that  there  is  a  certain  periodicity  in  their 
appearance  and  that  they  attain  their  greatest  frequency  about  every  ten 
years.  Independently  of  this,  Schwabe,  who  for  many  years  studied  the  sub- 
ject, found  that  the  spots  on  the  sun,  seen  on  looking  at  it  through  a 
coloured  glass,  vary  in  their  number,  size,  and  frequency,  but  attain  their 
maximum  between  every  ten  or  eleven  years.  Now  Sabine  established  the 
interesting  fact  that  the  period  of  their  greatest  frequency  coincides  with  the 
period  of  greatest  magnetic  disturbance.  Other  remarkable  connections 
between  the  sun  and  terrestrial  magnetism  have  been  observed ;  one, 
especially,  of  recent  occurrence  has  attracted  considerable  attention.  It  was 
the  flight  of  a  large  luminous  mass  across  a  vast  sun-spot,  while  a  simul- 
taneous perturbation  of  the  magnetic  needle  was  observed  in  the  observatory 
at  Kew  :  subsequent  examination  of  magnetic  observations  in  various  parts 
of  the  world  showed  that  within  a  few  hours  one  of  the  most  violent  magnetic 
storms  ever  known  had  prevailed. 

It  seems,  however,  that  these  accidental  variations  in  the  declination  can- 
not be  due  to  changes  in  any  direct  action  of  a  possible  magnetic  condition 
of  either  the  sun  or  the  moon.  For  it  can  be  shown  that  if  the  magneti- 
sation of  the  latter  were  as  powerful  as  that  of  the  earth,  the  deflection 
which  it  could  produce  would  not  amount  to  the  ^th  of  a  second,  a  quantity 
which  cannot  be  measured.  In  order  to  produce  a  variation  of  10'  such 
as  is  frequently  met  with,  the  magnetisation  of  the  sun  or  of  the  moon 
must  be  12,000  times  that  of  the  earth  ;  in  other  words,  a  more  powerful  de- 
gree of  magnetisation  than  that  of  the  most  powerfully  magnetised  steel  bars. 
Magnetic  storms  are  nearly  always  accompanied  by  the  exhibition  of  the 
aurora  borealis  in  high  latitudes ;  that  this  is  not  universal  may  be  due  to 
the  fact  that  many  auroras  escape  notice.  The  converse  of  this  is  true,  that 
no  great  display  of  the  aurora  takes  place  without  a  violent  magnetic  storm. 

The  centre  or  focus  towards  which  the  rays  of  the  aurora  converge  lies 
approximately  in  the  prolongation  of  the  direction  of  the  dipping-needle. 

TT 


642 


On  Magnetism. 


[703- 


CHAPTER    III. 


LAWS  OF  MAGNETIC  ATTRACTIONS   AND   REPULSIONS. 


703.  taw  of  decrease  with  distance. — -Coulomb  discovered  the  remark- 
able law  in  reference  to  magnetism,  that  magnetic  attractions  and  repul- 
sions are  inversely  as  the  squares  of  the  distances.  He  proved  this  by 
means  of  two  methods : — (i.)  that  of  the  torsion  balance,  and  (ii.)  that  of 
oscillations. 

\T      704.  i.  The  torsion  balance. — This  apparatus  depends  on  the  principle 
'  that,  when  a  wire  is  twisted  through  a  certain  space,  the  angle  of  torsion  is 

proportional  to  the  force  of  torsion 
(90).  It  consists  ('fig.  610)  of  a 
glass  case  closed  by  a  glass  top, 
with  an  aperture  near  the  edge, 
to  allow  the  introduction  of  a  mag- 
net, A.  In  another  aperture  in  the 
centre  of  the  top  a  glass  tube  fits, 
provided  at  its  upper  extremity 
with  a  micrometer.  This  consists 
of  two  circular  pieces  :  d,  which  is 
fixed,  is  divided  .on  the  edge  into 
360°,  while  on  one  e,  which  is  mov- 
able, there  is  a  mark,  c,  to  indicate 
its  rotation.  D  and  E  represent 
the  two  pieces  of  the  micrometer 
on  a  larger  scale.  On  E  there 
are  two  uprights  connected  by  a 
horizontal  axis,  on  which  is  a  very 
fine  silver  wire  supporting  a  mag- 
netic needle,  ab.  On  the  side  of 

the  case  there  is  a  graduated  scale,  which  indicates  the  angle  of  the  needle 
ab,  and  hence  the  torsion  of  the  wire. 

When  the  mark  c  of  the  disc  E  is  at  zero  of  the  scale  D,  the  case  is  so 
arranged  that  the  wire  supporting  the  needle  and  the  zero  of  the  scale  in  the 
case  are  in  the  magnetic  meridian.  The  needle  is  then  removed  from  its 
stirrup,  and  replaced  by  an  exactly  similar  one  of  copper,  or  any  unmagnetic 
substance  ;  the  tube,  and  with  it  the  pieces  D  and  E,  are  then  turned  so  that 
the  needle  stops  at  zero  of  the  graduation.  The  magnetic  needle  ab,  being 
now  replaced,  is  exactly  in  the  magnetic  meridian,  and  the  wire  exerts  no 
torsion. 

Before  introducing  the  magnet  A,  it  is  necessary  to  investigate  the  action 


-705J  Method  of  Oscillations.  643 

of  the  earth's  magnetism  on  the  needle  ab,  when  the  latter  is  removed  out  of 
the  magnetic  meridian.  This  will  vary  with  the  dimensions  and  force  of  the 
needle,  with  the  dimensions  and  nature  of  the  particular  wire  used,  and  with 
the  intensity  of  the  earth's  magnetism  in  the  place  of  observation.  Accord- 
ingly, the  piece  E  is  turned  until  ab  makes  a  certain  angle  with  the  magnetic 
meridian.  Coulomb  found  in  his  experiments  that  E  had  to  be  turned  36° 
in  order  to  move  the  needle  through  i°  ;  that  is,  the  earth's  magnetism  was 
equal  to  a  torsion  of  the  wire  corresponding  to  35°.  As  the  force  of  torsion 
is  proportional  to  the  angle  of  torsion,  when  the  needle  is  deflected  from  the 
meridian  by  2,  3  .  .  .  degrees,  the  directive  action  of  the  earth's  magnetism 
is  equal  to  2.  3  ...  times  35°. 

The  action  of  the  earth's  magnetism  having  been  determined,  the  magnet 
A  is  placed  in  the  case  so  that  similar  poles  are  opposite  each  other.  In  one 
experiment  Coulomb  found  that  the  pole  a  was  repelled  through  24°.  Now 
the  force  which  tended  to  bring  the  needle  into  the  magnetic  meridian 
was  represented  by  24°  +  24  x  35  =  864,  of  which  the  part  24°  was  due  to  the 
torsion  of  the  wire,  and  24  x  35°  was  the  equivalent  in  torsion  of  the  directive 
force  of  the  earth's  magnetism.  As  the  needle  was  in  equilibrium,  it  is  clear 
that  the  repulsive  force  which  counterbalanced  those  forces  must  be  equal 
to  864°.  The  disc  was  then  turned  until  ab  made  an  angle  of  12°.  To  effect 
this,  eight  complete  rotations  of  the  disc  were  necessary.  The  total  force 
which  now  tended  to  bring  the  needle  into  the  magnetic  meridian  was  com- 
posed of: — ist,  the  12°  of  torsion  by  which  the  needle  was  distant  from  its 
starting  point  ;  2nd,  of  8  x  360°  -  2880,  the  torsion  of  the  wire  ;  and  3rd,  the 
force  of  the  earth's  magnetism,  represented  by  a  torsion  of  12  x  35°.  Hence 
the  forces  of  torsion  which  balance  the  repulsive  forces  exerted  at  a  distance 
of  24°  and  of  12°  are — 

24°    ''.  (.V ,."    ...  ^~    864 

12°  .  .  .     "'     .    '"     3312 

Now,  3312  is  very  nearly  four  times  864  ;  hence  for  half  the  distance  the 
repulsive  force  is  four  times  as  great. 

705.  ii.  Method  of  oscillations.— A  magnetic  needle  oscillating  under 
the  influence  of  the  earth's  magnetism  may  be  considered  as  a  pendulum, 
and  the  laws  of  pendulum  motion  apply  to  it  (55).  The  method  of  oscilla- 
tions consists  in  causing  a  magnetic  needle  to 
oscillate  first  under  the  influence  of  the  earth's 
magnetism  alone,  and  then  successively  under  the 
combined  influence  of  the  earth's  magnetism  and 
of  a  magnet  placed  at  unequal  distances. 

The  following  determination  by  Coulomb  will 
illustrate  the  use  of  the  method.  A  magnetic  needle 
was  used  which  made  15  oscillations  in  a  minute 
under  the  influence  of  the  earth's  magnetism  alone. 
A  magnetic  bar  about  2  feet  long  was  then  placed 
vertically  in  the  plane  of  the  magnetic  meridian, 
so  that  its  north  pole  was  downwards  and  presented 

to  the  south  pole  o  of  the  oscillating  needle  (fig,  611),  so  as  to  concur  in  its' 
action  with  that  of  the  earth.     He  found  that  at  a  distance  of  4  inches  the 

TT2 


644  On  Magnetism.  [705- 

needle  made  41  oscillations  in  a  minute,  and  at  a  distance  of  8  inches  24 
oscillations.  Now,  from  the  laws  of  the  pendulum  (55),  the  intensities  of  the 
forces  are  inversely  as  the  squares  of  the  times  of  oscillation.  Hence,  if 
we  call  M  the  force  of  the  earth's  magnetism,  m  the  attractive  force  of  the 
magnet  at  the  distance  of  4  inches,  m'  at  the  distance  of  8  inches,  we  have 

M  :  M  +  m  =15-  :  41°,  and 
M  :  M  +  m'  =  1 52  :  24*, 
eliminating  M 

m  :  7/2'  =  4i2-i5~  :  242— 15-^1456  :  351=4  :  i  nearly, 

or  m  :  ;;£'=•  4  :  i. 

In  other  words,  the  force  acting  at  4  inches  is  quadruple  that  which  acts  at 
double  the  distance. 

The  above  results  do  not  quite  agree  with  the  numbers  required  by  the 
law  of  inverse  squares.  But  this  could  only  be  expected  to  apply  in  the  case 
in  which  the  repulsive  or  attractive  force  is  exerted  between  two  points,  and 
not,  as  is  here  the  case,  between  the  resultant  of  a  system  of  points.  And  it 
is  to  this  fact  that  the  discrepancy  between  the  theoretical  and  observed 
results  is  due. 

When  a  magnet  acts  upon  a  mass  of  soft  iron,  the  law  of  the  variation 
with  the  distance  is  modified.  The  attraction  in  this  case  is  inversely  pro- 
portional to  the  distance  between  the  magnet  and  the  iron. 

When  the  distance  between  the  magnet  and  the  iron  is  small,  Tyndal! 
found  that  the  attraction  is  directly  proportional  to  the  square  of  the  strength 
of  the  magnet ;  but  when  the  iron  and  the  magnet  are  in  contact,  then  the 
attraction  is  directly  proportional  to  the  strength  of  the  magnet. 

706.  Magnetic  curves. — If  a  stout  sheet  of  paper  stretched  on  a  frame 

held  over  a  horse-shoe  magnet,  and  then  some  very  fine  iron  filings  be 


Fig.  612. 

strewn  on  the  paper,  on  tapping  the  frame  the  filings  will  be  found  to  arrange 
themselves  in  thread-like  curved  lines,  stretching  from  pole  to  pole  (fig.  612). 
These  lines  form  what  are  called  magnetic  curves.  The  direction  of  the 


-707]  Magnetic  Definitions.  645 

•curve  at  any  point  represents  the  direction  of  the  lines  of  magnetic  force  at 
this  point. 

To  render  these  curves  permanent,  the  paper  on  which  they  are  formed 
should  be  waxed  ;  if  then  a  hot  iron  plate  be  held  over  them,  this  melts  the 
wax,  which  rises  by  capillary  attraction  (131)  between  the  particles  of  filings, 
-and  on  subsequent  cooling  connects  them  together. 

These  curves  are  a  graphic  representation  of  the  law  of  magnetic  attrac- 
tion and  repulsion  with  regard  to  distance ;  for  under  the  influence  of  the 
two  poles  of  the  magnet,  each  particle  becomes  itself  a  minute  magnet,  the 
poles  of  which  arrange  themselves  in  a  position  dependent  on  the  resultant 
of  the  forces  exerted  upon  them  by  the  two  poles,  and  this  resultant  varies 
with  the  distance  of  the  two  poles  respectively.  A  small  magnetic  needle 
placed  in  any  position  near  the  magnet  will  take  a  direction  which  is  the 
tangent  to  the  curve  at  this  place. 

^  707.  Magnetic  Definitions. — The  space  in  the  immediate  neighbourhood 
•of  any  magnet  undergoes  some  change,  in  consequence  of  the  presence  of  this 
magnet,  and  such  a  space  is  spoken  of  as  a  magnetic  field ;  it  is  indeed  the 
sphere  of  action  of  the  magnet  ;  the  effect  produced  by  the  magnet  is  often 
said  to  be  due  to  the  magnetic  field.  Magnets  of  different  powers  produce 
magnetic  fields  of  different  intensities.  The  strength  of  the  field  diminishes 
with  the  distance  from  the  magnet. 

The  direction  which  represents  the  resultant  of  the  magnetic  forces  at 
any  position  in  a  magnetic  field  is  spoken  of  as  the  direction  of  the  lines  of 
force  of  this  field.  In  the  above  figure  the  magnetic  curves  represent  the 
direction  of  the  lines  of  force  in  the  field  due  to  the  two  poles. 

A  uniform  magnetic  field  is  one  in  which  the  lines  of  force  are  parallel. 
This  is  practically  the  case  with  a  small  portion  of  a  field  at  some  distance 
from  a  long  thin  magnet  of  uniform  magnetisation.  The  dipping-needle, 
when  free  to  oscillate  in  a  vertical  plane  in  the  magnetic  meridian,  represents 
the  direction  of  the  lines  of  force  due  to  the  terrestrial  magnetic  field.  The 
strength  of  the  field  due  to  this  in  any  one  place  is  uniform  in  much  the 
same  sense  in  which  gravity  is  uniform  in  any  place.  A  field  of  unit 
strength  is  one  which  acts  on  a  unit  pole  with  a  force  equal  to  that  of  a  dyne. 

We  have  seen  that  in  speaking  of  the  pendulum  we  distinguish  between  a 
simple  and  a  compound  one  (79).  The  laws  of  the  pendulum  apply  in  strict- 
ness only  to  the  former,  which  in  practice  cannot  be  realised,  although  we 
possess  arrangements  which  produce  the  same  effect  as  a  simple  pendulum, 
and  are  equivalent  to  it.  So  too  in  magnetism  we  may  discriminate  between 
an  ideal  and  an  actual  magnet ;  the  former  being  considered  as  a  long, 
infinitely  thin,  bar  of  magnetised  molecules,  to  which  only  do  the  laws  of 
magnetic  action  apply,  although  they  can  be  realised  with  ordinary  magnets 
with  sufficient  approximation.  Thus  in  the  action  of  magnets  at  a  distance 
we  may  assume  that  all  the  magnetism  is  concentrated  in  the  poles,  provided 
the  fourth  power  of  half  the  length  of  the  magnet  may  be  disregarded  in 
•comparison  with  the  distance  at  which  it  acts. 

In  a  magnet  the  magnetic  moment  is  the  product  of  the  length  of  the 
magnet  into  the  strength  of  one  pole. 

If  a  magnetic  body  be  placed  in  a  magnetic  field,  the  intensity  of  the 
•magnetisation  which  it  acquires  will  be  proportional  to  the  strength  of  the 


646 


On  Magnetism. 


1707- 


field,  and  to  a  coefficient  which  depends  on  the  material  itself  and  which  is 
called  the  coefficient  of  magnetic  induction.  Bodies  such  as  soft  iron,  which 
are  readily  magnetised,  are  said  to  have  great  susceptibility  to  magnetic  in- 
duction. 

7°8.  Total  action  of  two  magnets  on  each  other. — In  the  above  case 
of  the  torsion  balance  one  pole  of  the  magnet  to  be  tested  was  at  so  great 
a  distance  that  it  could  not  appreciably  modify  the  influence  of  the  other. 
When,  however,  the  conditions  are  such  that  both  poles  act,  then  they  follow 
a  different  law,  as  will  now  be  demonstrated. 

Let  ns  (fig.  613)  be  a  small  magnetic  needle,  free  to  move  in  a  horizontal 
plane,  and  let  NS  be  a  bar  magnet  placed  at  right  angles  to  the  magnetic 
meridian,  at  a  distance  which  is  great  compared  with  its  own  dimen- 
sions, and  so  that  the  straight  line  drawn  through  its  middle  point  and 
that  of  the  needle  coincides  with  the  magnetic  meridian.  In  this  case 
the  magnet  NS  is  said  to  be  broadside  on.  The  two  poles  S  and  s  will 
repel  each  other  in  the  direction  sa  ;  if  mm,  is  the  repellent  force  which 

these  two  poles  would  exert  at  the  unit  distance,  then  m?^  is  the  force  which 

they  would  exert  at  the  distance  S.y  =  r ;  let  this 
force  be  represented  in  direction  and  strength  by 
the  line  sa.  Similarly,  the  pole  N  will  act  on  s, 
with  a  force  represented  by  the  line  sc  ;  S  and  N 
being  at  the  same  distance  r  from  s,  sa  and  sc  are 
equal,  and  their  resultant  may  be  represented  by  the 
line  sb.  From  the  similarity  of  the  triangles  bsa 
and  NSj  we  have  the  proportion  S^  :  SN  =  as  :  bs  ;. 
if /is  the  value  of  the  resultant  £r,  that  is  the 


Fig.  614. 

total  action  of  the  magnet  SN  on  the  pole  s,  and  if/  be  half  the  length  of  the 
magnet  SN,  we  have  r  :  il  =  mm'  :  f,  from  which  /=  "I1™'1 ;  that  is,  the 

total  action  of  the  magnet  NS  upon  another  magnet  is  inversely  as  the  cube 
of  the  distance  r. 

If  the  two  magnets  be  placed  '  end  on 'as  represented  in  fig.  614,  the 
needle  being  in  the  magnetic  meridian,  and  the  deflecting  magnet  at  right 
angles  thereto,  and  so  that  the  prolongation  of  its  axis  bisects  the  needle,  then 
if  mml  is  the  force  with  which  the  pole  N  attracts  the  pole  s  at  the  unit  dis- 
tance, m  and  m,  being  the  strength  of  the  poles  in  the  bar  magnet  and  the 
magnetic  needle  respectively,  the  attracting  force  at  the  distance  NJ  will 

be  ^Jn^      I  being  as  before  the  half-length  of  the  magnet,  and  r  the  distance 
of  the  pole  s  from  the  middle  of  the  magnet  NS  ;  in  like  manner  the  repellent 


-709]     Determination  of  Magnetism  in  Absolute  Measure.      64.7 

force  with  which  S  acts  upon  5-  will  be   mm  _     jf  ns  js  small  compared  with 

the  distance  of  the  bar  magnet  NS,  the  direction  of  these  forces  may  be 
assumed  to  be  parallel,  and  at  right  angles  to  ns.  Since  S  is  nearer  than  N 
the  repulsion  will  predominate,  and  the  total  force  with  which  the  magnet 
NS  acts  on  the  pole  s  is 

-p  _   mm,  _  mm, 
-(r-iy>     (r^ 

which,  assuming  that  /  is  so  small  in  comparison  with  r  that  its  square  and 
higher  powers  may  be  neglected,  gives  approximately 

T-  _  4  mm,  I 

r-\ 

so  that  compared  with  the  first  position  of  the  magnet 

F-2/ 

r  709.  Determination  of  magnetism  in  absolute  measure. — The  com- 
parisons of  the  intensity  of  the  earth's  magnetism  in  different  places  (701) 
are  only  relative.  Of  late  years  much  attention  has  been  devoted  to  the 
method  of  expressing  not  only  this,  but  all  other  magnetic  forces  in  what  is 
called  absolute  measure.  This  term  is  used  as  opposed  to  relative,  and  does 
not  imply  that  the  measure  is  absolutely  accurate,  or  that  the  units  of  com- 
parison employed  are  of  perfect  construction ;  it  means  that  the  measure- 
ments, instead  of  being  a  simple  comparison  with  an  arbitrary  quantity  of  the 
same  kind  as  that  measured,  are  referred  to  the  fundamental  units  of  time, 
length,  and  mass  (21). 

The  units  adopted  on  the  proposal  of  the  British  Association,  and  n*w 
almost  universally  received,  are  the  second  as  unit  of  time,  the  centimetre 
as  unit  of  length,  and  the  gramme  as  unit  of  mass.  This  system  is  called 
the  centimetre-gramme-second,  or  C.G.S.  system,  and  units  referred  to  this 
system  are  spoken  of  as  C.G.S.  units  (61  a). 

The  manner  in  which  this  determination  is  made  in  the  case  of  magnet- 
ism, depends  essentially  on  the  observation  of  the  oscillation  of  a  horizontal 
bar  magnet  under  the  influence  of  the  earth's  magnetism  ;  and  in  the  second 
place,  on  observing  the  deflection  of  a  magnetic  needle  under  the  influence 
of  this  same  magnet. 

When  a  bar  magnet  suspended  by  a  thread  without  torsion,  free  to  oscil- 
late in  a  horizontal  plane,  is  deflected  from  its  position  of  equilibrium  and 
then  left  to  itself,  it  vibrates  backwards  and  forwards  through  its  position  of 
equilibrium,  making  oscillations  which,  if  small,  are  isochronous  like  those  of 
the  pendulum.  The  number  of  these  oscillations  in  a  given  time  depends  on  the 
mass  and  dimensions  of  the  bar,  on  its  magnetic  power,  and  on  the  intensity  of 
the  earth's  magnetism  in  the  place  of  observation.  The  time,  /,  of  a  complete 

oscillation  of  such  a  magnet  is  represented  by  the  formula  t=2,iri/ ^     ; 

where  k  is  the  moment  of  inertia  of  the  magnet  ;  that  is,  the  mass  which 
must  be  concentrated  at  the  unit  of  distance  from  the  centre  of  suspension, 
to  present  the  same  resistance  to  change  of  angular  velocity,  about  this  centre, 


648  On  Magnetism.  [709 

as  the  magnet  itself  actually  does.  The  moment  of  inertia  of  a  magnet  may 
be  determined  theoretically  if  it  be  homogeneous  in  structure,  and  of  a  regu- 
lar geometrical  shape  ;  or  it  may  be  determined  experimentally  by  first 
observing  the  time  of  oscillation  of  the  magnet  under  the  influence  of  the 
earth's  magnetism,  and  then  the  time  when  it  has  been  loaded  with  a  mass 
the  inertia  of  which  is  known,  and  which  does  not  alter  the  magnetic  moment 
of  the  bar.  M  is  the  magnetic  moment  of  the  bar  itself,  and  H  is  the  force 
of  the  earth's  magnetism.  Hence 

HM-«£*      .         .        .,..'.         (i). 

This  expression  gives  the  force  which,  applied  in  opposite  directions  at 
the  ends  of  a  lever  of  unit  length,  placed  at  right  angles  to  the  direction  of 
this  force,  would  have  the  same  effect  in  tending  to  turn  the  lever,  as  the 
magnetic  force  of  the  earth  has  in  tending  to  turn  the  magnet  about  a  vertical 
axis  when  it  is  set  at  right  angles  to  the  magnetic  meridian. 

Now  the  value  of  HM  depends  on  the  nature  of  the  bar,  and  on  the  force 
of  the  earth's  magnetism  in  the  place  in  question.  If  the  bar  were  mag- 
netised more  or  less  strongly,  or  if  the  same  bar  were  removed  to  a  different 
locality,  the  product  would  have  a  different  value.  We  must,  therefore,  find 
some  independent  relation  between  H  and  M,  which  will  give  rise  to  a  new 
equation,  and  thus  M,  the  magnetic  moment  of  the  bar,  would  be  got  rid  of, 
and  an  absolute  value  be  obtained  for  H. 

Such  a  relation  exists  in  the  deflection  from  the  magnetic  meridian,  which 
a  bar  magnet  produces  in  a  magnetic  needle. 

If,  in  the  formula  in  the  preceding  article,  we  put  M  =  2;;z/,  then        ™.  = 

the  +  or  —  force  acting  on  either  pole  of  the  magnetic  needle,  and,  as  both 
poles  are  acted  on,  the  magnet  will  be  subject  to  the  action  of  a  couple*  the 


moment  of  which  will  be  expressed  by      --    2/'  cos  a  ;  where  a  is  the  angle 

of  deflection,  lf  the  half-length  of  the  small  magnetic  needle  ;  let  M'  =  zm'l'. 
In  like  manner  the  earth's  magnetism  will  act  upon  the  magnetic  needle 
with  a  couple  the  moment  of  which  is  expressed  by  Hm'  7.1'  sin  a  =  HM' 
sin  a.  Now  when  the  needle  is  in  equilibrium  these  forces  are  equal  ;  that 
is  — 

'os  a-HM'   sin  a 


from  which  =  r3  tan  a.     .         .        .        *        .         (2). 

H 

Combining  (i)  and  (2)  we  get  the  expression 


tan  a 


an  expression  which  involves  no  other  physical  units  than  those  of  length 
(involved  in  k  and  r\  mass  (involved  in  k\  and  time  (involved  in  t\  so  that 
the  value  of  H  can  be  expressed  in  absolute  measure. 

The  value  for  H  in  this  expression   only  gives  the  horizontal   compo- 


709]        Determination  of  Magnetism  in  Absolute  Measure.      649 

nent  of  the  earth's  magnetism  ;  the  total  force  is  obtained  by  dividing  the 
value  of  H  by  the  cosine  of  the  angle  of  dip  for  the  place  and  time  of  ob- 
servation. 

The  numerical  value  of  H  will  depend,  moreover,  on  the  units  taken. 
On  the  C.G.S.  system  the  unit  of  force  is  called  a  dyne.  It  is  the  force 
which  acting  upon  a  gramme  for  a  second  generates  a  velocity  of  a  centi- 
metre per  second.  The  value  of  H  at  Greenwich  for  the  year  1877,  ex- 
pressed in  this  unit,  is  o-  18079  °f  a  dyne  ;  that  is,  the  horizontal  component 
of  the  earth's  magnetism  at  this  place  acting  on  the  unit  of  magnetism,  asso- 
ciated with  one  gramme  of  matter,  would  produce  a  velocity  of  0-18079 
centimetre  at  the  end  of  a  second.  The  angle  of  dip  at  this  time  and  place 
being  67°  37',  we  get  the  total  force  =  0-4745  unit.  If  British  units — namely, 
the  foot,  grain,  second — be  employed,  the  unit  of  force  is  that  which  by  acting 
for  a  second  on  a  grain  gives  to  it  a  velocity  of  a  foot  per  second,  and  the 
unit  magnetic  pole  is  such  that  if  placed  one  foot  from  a  second  equal  pole 
it  will  repel  it  with  a  force  equal  to  the  unit  just  defined.  To  convert  the 
value  of  H,  when  expressed  in  centimetres,  grammes,  and  seconds  into  the 
equivalent  value  referred  to  British  units,  we  must  multiply  by  21-69.  I*1  like 
manner  to  convert  magnetic  forces  referred  to  British  units  into  the  corre- 
sponding values  expressed  in  centimetres,  grammes,  and  seconds  we  must 

multiply  by  0-0461  =  — ~ 
21-69 


650  On  Magnetism.  [710- 


*  &£& 

CHAPTER    IV. 

PROCESSES   OF  MAGNETISATION. 

V       7IO«  Magnetisation. — The  various   sources  of  magnetism  are  the   in- 
fluence of  natural  or  artificial  magnets,  terrestrial  magnetism,  and  electricity. 
This  last  method  will  be  described  under  voltaic  electricity.     The  three  prin- 
cipal methods  of  magnetisation  by  magnets  are  known  by  the  technical  names 
-   of  single  touch,  separate  touch,  and  double  touch. 

711.  Method  of  single  touch. — This  consists  in  moving  the  pole  of  a 
powerful  magnet  from  one  end  to  the  other  of  the  bar  to  be  magnetised,  and 
repeating  this  operation  several  times  always  in  the  same  direction.  The 
neutral  magnetism  is  thus  gradually  decomposed  throughout  all  the  length  of 
the  bar,  and  that  end  of  the  bar  which  was  touched  last  by  the  magnet  is 
of  opposite  polarity  to  the  end  of  the  magnet  by  which  it  has  been  touched. 
This  method  only  produces  a  feeble  magnetic  power,  and  is,  accordingly,  only 
used  for  small  magnets.  It  has  further  the  disadvantage  of  frequently  de- 
'  veloping  consequent  poles. 

Y  712.  Method  of  separate  touch.— This  method,  which  was  first  used  by 

Dr.  Knight  in  1745,  consists  in  placing  the  two  opposite  poles  of  two  magnets 
of  equal  force  in  the  middle  of  the  bar  to  be  magnetised,  and  in  moving  each 
of  them  simultaneously  towards  the  opposite  ends  of  the  bar.  Each  magnet 
is  then  placed  in  its  original  position  and  the  operation  repeated.  After 
several  frictions  on  both  faces  of  the  bar  it  is  magnetised. 

In  Knight's  method  the  magnets  are  held  vertically.  Duhamel  improved 
the  method  by  inclining  the  magnets,  as  represented  in  fig.  615  ;  and  still 
more  by  placing  the  bar  to  be  magnetised  on  the  opposite  poles  of  two  fixed 
magnets,  the  action  of  which  strengthens  that  of  the  movable  magnets.  The 
relative  position  of  the  poles  of  the  magnets  is  indicated  in  the  figure.  This 
method  produces  the  most  regular  magnets. 

713.  Method  of  double  touch. — In  this  method,  which  was  invented  by 
Mitchell,  the  two  magnets  are  placed  with  their  poles  opposite  each  other 
in  the  middle  of  the  bar  to  be  magnetised.  But,  instead  of  moving  them  in 
opposite  directions  towards  the  two  ends,  as  in  the  method  of  separate  touch, 
they  are  kept  at  a  fixed  distance  by  means  of  a  piece  of  wood  placed  between 
them  (fig.  615),  and  are  simultaneously  moved  first  towards  one  end,  then 
from  this  to  the  other  end,  repeating  this  operation  several  times,  and  finish- 
ing in  the  middle,  taking  care  that  each  half  of  the  bar  receives  the  same 
number  of  frictions. 

Epinus,  in  1758,  improved  this  method  by  supporting  the  bar  to  be  mag- 
netised, as  in  the  method  of  separate  touch,  on  the  opposite  poles  of  two 
powerful  magnets,  and  by  inclining  the  bars  at  an  angle  of  15°  to  20°.  In 


-715]  Magnetism  of  Iron  SJiips.  651 

practice,  instead  of  two  bar   magnets,  it  is  usual  to  employ  a  horse-shoe 
magnet  which  has  its  poles  conveniently  close  together. 

By  this  method  of  double  touch,  powerful  magnets  are  obtained,  but  they 


Fig.  615. 

have  frequently  consequent  poles.     As  this  would  be  objectionable  in  com- 
pass needles,  these  are  best  magnetised  by  separate  touch. 

y  714.  Magnetisation  by  the  action  of  the  earth. — The  action  of  the 
earth  on  magnetic  substances  resembles  that  of  a  magnet,  and  hence  the 
terrestrial  magnetism  is  constantly  tending  to  separate  the  two  magnetisms 
in  soft  iron  and  in  steel.  But  as  the  coercive  force  is  very  considerable  in 
the  latter  substance,  the  action  of  the  earth  is  inadequate  to  produce  mag- 
netisation, except  when  continued  for  a  long  time.  This  is  not  the  case 
with  perfectly  soft  iron.  When  a  bar  of  this  metal  is  held  in  the  magnetic 
meridian  parallel  to  the  inclination,  the  bar  becomes  at  once  endowed  with 
feeble  magnetic  polarity.  The  lower  extremity  is  a  north  pole,  and  if  the 
north  pole  of  a  small  magnetic  needle  be  approached,  it  will  be  repelled. 
This  magnetism  is  of  course  unstable,  for  if  the  bar  be  turned  the  poles  are 
inverted,  as  pure  soft  iron  is  destitute  of  coercive  force. 

While  the  bar  is  in  this  position,  a  certain  amount  of  coercive  force  may 
be  imparted  to  it  by  giving  it  several  smart  blows  with  a  hammer,  and  the 
bar  retains  for  a  short  time  the  magnetism  which  it  has  thus  obtained.  But 
the  coercive  force  thus  developed  is  very  small,  and  after  a  time  the  mag- 
netism disappears. 

If  a  bar  of  soft  iron  be  twisted  while  held  vertically,  or,  better,  in  the 
plane  of  the  dip,  it  acquires  a  feeble  permanent  magnetism. 

It  is  this  magnetising  action  of  the  earth  which  develops  the  magnetism 
frequently  observed  in  steel  and  iron  instruments,  such  as  fire-irons,  rifles,, 
lamp-posts,  railings,  gates,  lightning-conductors,  &c.,  which  remain  for  some 
time  in  a  more  or  less  inclined  position.  They  become  magnetised  with  their 
north  pole  downward,  just  as  if  placed  over  the  pole  of  a  powerful  magnet. 
The  magnetism  of  native  black  oxide  of  iron  has  doubtless  been  produced  by 
the  same  causes  ;  the  very  different  magnetic  power  of  different  specimens 
being  partly  attributable  to  the  different  positions  of  the  veins  of  ore  with 
regard  to  the  line  of  dip.  The  ordinary  irons  of  commerce  are  not  quite 
pure,  and  possess  a  feeble  coercive  force  ;  hence  a  feeble  magnetic  polarity 
is  generally  found  to  be  possessed  by  the  tools  in  a  smith's  shop.  Cast  iron, 
too,  has  usually  a  great  coercive  force,  and  can  be  permanently  magnetised. 
The  turnings,  also,  of  wrought  iron  and  of  steel  produced  by  the  powerful 
lathes  of  our  ironworks  are  found  to  be  magnetised. 

V  715.  Magnetism  of  iron  ships. — The  inductive  action  of  terrestrial  mag- 
netism upon  the  masses  of  iron  always  found  in  ships  exerts  a  disturbing 
action  upon  the  compass  needle.  The  local  attraction,  as  it  is  called,  may 


652  On  Magnetism.  [715- 

be  so  considerable  as  to  render  the  indications  of  the  needle  almost  useless 
if  it  be  not  guarded  against.  A  full  account  of  the  manner  in  which  local 
attraction  is  produced,  and  in  which  it  is  compensated,  is  inconsistent  with 
the  limits  of  this  book,  but  the  most  important  points  are  the  following  : — 

i.  A  vertical  mass  of  soft  iron  in  the  vessel,  say  in  the  bows,  would 
become  magnetised  under  the  influence  of  the  earth  ;  in  the  northern  hemi- 
sphere, the  lower  end  would  be  a  north  pole,  and  the  upper  end  a  south 
pole  ;  and  as  the  latter  may  be  assumed  to  be  nearer  the  north  pole  of  the 
compass  needle,  it  would  act  upon  it.  So  long  as  the  vessel  was  sailing  in 
the  magnetic  meridian  this  would  have  no  effect  ;  but  in  any  other  direction 
the  needle  would  be  drawn  out  of  the  magnetic  meridian,  and  a  little  considera- 
tion will  show  that  when  the  ship  was  at  right  angles  to  the  magnetic  meridian 
the  effect  would  be  greatest.  This  vertical  induction  would  disappear  twice 
in  swinging  the  ship  round,  and  would  be  at  its  maximum  twice  ;  hence  the 
deviation  due  to  this  cause  is  known  as  semicircular  deviation. 

ii.  Horizontal  masses  again,  such  as  deck  beams,  are  also  acted  upon 
inductively  by  the  earth's  magnetism,  and  their  induced  magnetism  exerts 
a  disturbing  influence  upon  the  magnetic  needle.  The  effect  of  this  hori- 
zontal induction  will  disappear  when  the  ship  is  in  the  magnetic  meridian 
and  also  when  it  is  at  right  angles  thereto.  In  positions  intermediate  to  the 
above  the  disturbing  influence  will  attain  its  maximum.  Hence  in  swinging 
a  ship  round  there  would  be  four  positions  of  the  ship's  head  in  which  the 
influence  would  be  at  a  maximum,  and  four  in  which  it  would  be  at  a  mini- 
mum. The  effect  of  horizontal  induction  is  accordingly  spoken  of  as  quad- 
rantal  deviation. 

The  influence  of  both  these  causes,  vertical  and  horizontal  induction, 
may  be  remedied  in  the  process  of  *  swinging  the  ship.5  This  consists  in 
comparing  the  indications  of  the  ship's  compass  with  those  of  a  standard 
compass  placed  on  shore.  The  ship  is  then  swung  round  in  various  posi- 
tions, and  by  arranging  small  vertical  and  horizontal  masses  of  soft  iron  in 
proximity  to  the  steering  compass,  positions  are  found  for  them  in  which  the 
inductive  action  of  the  earth  upon  them  quite  neutralises  the  influence  of  the 
earth's  magnetism  upon  the  ship  ;  and  in  all  positions  of  the  ship,  the  com- 
pass points  in  the  same  direction  as  the  one  on  shore. 

iii.  The  extended  use  of  iron  in  ship-building,  more  especially  when  the 
frames  are  entirely  of  iron,  has  increased  the  difficulty.  In  the  process  of 
building  a  ship,  the  hammering  and  other  mechanical  operations  to  which 
it  is  subject,  while  under  the  influence  of  the  earth's  magnetism,  will  cause 
it  to  become  to  a  certain  extent  permanently  magnetised.  The  distribution 
of  the  magnetism,  the  direction  of  its  magnetic  axis,  will  depend  on  the 
position  in  which  it  has  been  built ;  it  may  or  may  not  coincide  with  the 
direction  of  the  keel.  The  vessel  becomes,  in  short,  a  huge  magnet,  and 
will  exert  an  influence  of  its  own  upon  the  compass  quite  independently  of 
vertical  or  horizontal  induction.  The  influence  is  semicircular ;  that  is,  it 
disappears  when  the  magnetic  axis  of  the  ship  is  in  the  magnetic  meridian, 
and  is  greatest  at  right  angles  to  it.  It  may  be  compensated  by  two  permanent 
magnets  placed  near  the  compass  in  suitable  positions  found  by  trial  during 
the  process  of  swinging  the  ship.  Supposing  the  inherent  magnetism  of  the 
ship  to  have  the  power  of  drawing  the  compass  a  point  to  the  east,  the  com- 


-717]  Magnetic  Battery.  653 

pensating  magnets  may  be  so  arranged  as  to  tend  to  draw  it  a  point  to  the 
west,  and  thus  keep  it  in  the  magnetic  meridian.  If,  however,  the  inherent 
magnetism  be  destroyed,  from  whatever  cause,  it  is  clear  that  the  magnets 
will  now  draw  it  aside  a  point  too  much  to  the  west.  This  is  the  source  of  a 
new  difficulty.  It  has  been  found  that  a  ship  which  at  the  time  of  sailing 
was  properly  compensated,  would,  on  returning  from  a  long  voyage,  have  its 
compasses  over-compensated.  The  buffeting  which  the  ship  had  experienced 
had  destroyed  its  inherent  magnetism,  and  numerous  instances  are  known 
where  the  loss  of  a  vessel  can  be  directly  traced  to  this  cause.  Fortunately, 
it  has  been  found  that  after  some  time  a  ship's  magnetic  condition  is  virtu- 
ally permanent,  and  is  unaltered  by  any  further  wear  and  tear.  The  magnet- 
ism which  it  then  retains  is  called  its  permanent  magnetism,  in  opposition 
to  the  sub-permanent  which  it  loses. 

The  difficulty  of  adequately  compensating  compasses,  which  is  greatly 
increased  by  the  armour-plated  and  turret  ships  now  in  use,  has  induced  one 
school  to  throw  over  any  attempt  at  correction  ;  but  by  careful  observation 
of  the  magnetic  condition  of  a  ship,  and  tabulating  the  errors  to  construct  a 
table,  and  comparing  this  with  the  indications  of  the  compass  at  any  one 
time,  the  true  course  can  be  made  out. 

In  the  Royal  Navy,  the  plan  now  adopted  is  to  combine  both  methods  : 
compensate  the  errors  to  a  considerable  extent,  and  then  construct  a  table 
of  the  residual  errors. 

\/7i6.  Magnetic  saturation. — Experiment  has  shown  that  with  feeble 
magnetising  power  the  magnetic  force  which,  can  be  imparted  to  a  steel  bar 
increases  with  the  magnetising  force  used.  It  depends  also  on  the  number  of 
strokes  or  movements  of  the  magnetising  magnets  or  coils  ;  on  the  form  and 
dimensions  of  the  bar,  on  its  density,  on  the  quantity  of  carbon  it  contains,  on 
its  hardness,  and  on  the  manner  in  which  it  is  tempered.  Yet  there  is  a  limit  to 
the  magnetic  force  which  can  be  imparted  to  iron  or  steel,  and  when  this  is 
attained,  the  bar  is  said  to  be  saturated  or  magnetised  to  saturation.  A  bar 
may  indeed  be  magnetised  beyond  this  point,  but  this  excess  is  temporary  ; 
it  gradually  diminishes  until  the  magnet  has  sunk  to  its  point  of  saturation. 

This  is  intelligible,  for  the  magnetisms  once  separated  tend  to  reunite, 
and  when  their  attractive  force  is  equal  to  that  which  opposes  their  separa- 
tion— that  is,  the  coercive  force  of  the  metal — equilibrium  is  attained,  and 
the  magnet  is  saturated.  Hence,  more  magnetism  ought  to  be  developed 
in  bars  than  they  can  retain,  in  order  that  they  may  decline  to  their  perma- 
nent state  of  saturation.  To  increase  the  magnetism  of  an  unsaturated  bar, 
a  less  feeble  magnet  must  not  be  used  than  that  by  which  it  was  originally 
magnetised. 

In  order  to  attain  a  stationary  condition,  the  magnet  should  be  heated  to 
boiling  for  some  time  after  being  magnetised  ;  it  should  then  be  remagnetised 
and  again  heated  to  boiling,  and  so  forth  ;  and  after  the  last  magnetisation 
it  should  be  boiled  for  six  hours  or  more.  Such  magnets  are  far  more  durable 
than  ordinary  ones. 

f  717.  Magnetic  battery. — A  magnetic  battery  or  magazine  consists  of 
a  number  of  magnets  joined  together  by  their  similar  poles.  Sometimes 
they  have  the  form  of  a  horse-shoe,  and  sometimes  a  rectilinear  form.  The 
battery  represented  in  fig.  616  consists  of  five  superposed  steel  plates.  That 


654 


On  Magnetism. 


[717- 


in  fig.  617  consists  of  twelve  plates,  arranged  in  three  layers  of  four  each. 

The  horse-shoe  form  is  best  adapted  for  supporting  a  weight,  for  then  both 

poles  are  used  at  once.     In  both  the  bars  are  magnetised  separately,  and 

then  fixed  by  screws. 

The  force  of  a  magnetic  battery  consisting  of  n  similar  plates  equally 

magnetised,  is  not  ;/  times  as  great  as  that  of  a  single  one,  but  is  somewhat 

smaller.  These  magnets  mutually  en- 
feeble each  other ;  manifestly  because, 
for  instance,  each  north  pole  evokes 
south  magnetism  in  the  adjacent  north 
pole,  and  thereby  diminishes  some  of  its 
north  polarity.  The  magnetism  of  a  plate 
which  has  formed  part  of  such  a  battery 
will  be  found  to  be  materially  less  than  it 
was  originally, 

Thus  Jamin  found  that  six  equal  plates 
which  had  each  the  portative  force  18 
kilos,  only  lifted  64  kilos  when  arranged 
as  a  battery,  instead  of  108  ;  and  when 
removed  from  the  battery,  each  of  them 
had  only  the  portative  force  9  to  10  kilos. 
The  force  is  increased  by  making  the 
lateral  plates  i  or  2  centimetres  shorter 
than  the  one  in  the  middle  (fig.  616). 

\  718.  Armatures.— When  even  a  steel 
bar  is  at  its  limit  of  saturation,  it  gradu- 
ally loses  its  magnetism.  To  prevent 
this,  armatures  or  keepers  are  used  ;  these 


Fig.  616. 


are  pieces  of  soft  iron,  A  and  B  (fig.  617),  which  are  placed  in  contact  with 
the  poles.  Acted  on  inductively,  they  become  powerful  temporary  magnets, 
possessing  opposite  polarity  to  that  of  the  inducing  pole  ;  they  thus  react 

in  turn  on  the  permanent 
magnetism  of  the  bars,  pre- 
serving and  even  increasing 
it. 

When  the  magnets  are  in 
the  form  of  bars,  they  are 
arranged  in  pairs,  as  shown 
in  fig.  618,  with  opposite 
poles  in  juxtaposition,  and 


the  circuit  is  completed  by 


Fig.  618. 

two  small  bars  of  soft  iron,  AB.  Movable  magnetic  needles,  if  not  clamped 
down,  set  spontaneously  towards  the  magnetic  poles  of  the  earth,  the  influ- 
ence of  which  acts  as  a  keeper. 

A  horse-shoe  magnet  has  a  keeper  attached  to  it,  which  is  usually  ar- 
ranged so  as  to  support  a  weight.  The  keeper  becomes  magnetised  under 
the  influence  of  the  two  poles,  and  adheres  with  great  force:  the  weight 
which  it  can  support  being  more  than  double  that  which  a  single  pole  would 
hold.  .*3 


-719]  Portative  Force.     Power  of  Magnets.  655 

In  respect  to  this  weight,  a  singular  and  hitherto  inexplicable  pheno- 
menon has  been  observed.  When  contact  is  once  made,  and  the  keeper  is 
charged  with  its  maximum  weight,  any  further  addition 
would  detach  it  ;  but  if  left  in  contact  for  a  day,  an 
additional  weight  may  be  added  without  detaching  it, 
and  by  slightly  increasing  the  weight  every  day  it 
may  ultimately  be  brought  to  support  a  far  greater 
load  than  it  would  originally.  But  if  contact  be  once 
broken,  the  weight  it  can  now  support  does  not  much 
exceed  its  original  charge. 

It  is  advantageous  that  the  surface  of  the  magnet 
and  armatures  which  are  in  contact  should  not  be 
plane  but  slightly  cylindrical,  so  that  they  touch  along 
a  line. 

In  providing  a  natural  magnet  with  a  keeper,  the 
line  joining  the  two  poles  may  first  be  approximately 
determined  by  means  of  iron  filings  ;  it  may  also  be  • 
determined  by  bringing  it  near  a  magnetic  needle,  and 
ascertaining  the  positions  in  which  its  action  is  greatest  Fis-  6l9- 

(708).  Two  poles  of  soft  iron  (fig.  619),  each  terminating  in  a  massive  shoe, 
are  then  applied  to  the  faces  corresponding  to  the  poles.  Under  the  in- 
fluence of  the  natural  magnet,  these  plates  become  magnetised,  and  if  the 
letters  A  and  B  represent  the  position  of  the  poles  of  the  natural  magnet,  the 
poles  of  the  armature  are  a  and  b. 

719.  Portative  force.  Power  of  magnets.  —  The  portative  force  is 
the  greatest  weight  which  a  magnet  can  support.  Hacker  found  that  the 
portative  force  of  a  saturated  horse-shoe  magnet,  which,  by  repeatedly  de- 
taching the  keeper,  had  become  constant,  may  be  represented  by  the  formula 


in  which  P  is  the  portative  force  of  the  magnet,  p  its  own  weight,  and  a  a 
coefficient  which  varies  with  the  nature  of  the  steel  and  the  mode  of  mag- 
netising. Hence  a  magnet  which  weighs  1,000  ounces  only  supports  25 
times  as  much  as  one  weighing  8  ounces  or  T|^  as  heavy,  and  25  such  bars 
would  support  as  much  as  a  single  one  which  is  as  heavy  as  125  of  them.  It 
appears  immaterial  whether  the  section  of  the  bar  is  quadratic  or  circular,  and 
the  distance  of  the  legs  is  of  inconsiderable  moment  ;  it  is  important,  however, 
that  the  magnet  be  suspended  vertically,  and  that  the  load  be  exactly  in  the 
middle.  In  Hacker's  magnets  the  value  of  a  was  10-33,  while  in  Logemann's 
it  was  23.  By  arranging  together  several  thin  magnetised  plates  Jamin  con- 
structed bar  magnets  which  support  1  5  times  their  own  weight. 

The  strength  of  two  bar  magnets  may  be  compared  by  the  following 
simple  method,  which  is  known  as  Kiilp's  compensation  method  \  —  A  small 
magnetic  compass  needle  is  placed  in  the  magnetic  meridian.  One  pole 
of  one  of  the  magnets  to  be  tested  is  then  placed  at  right  angles  to  the 
magnetic  meridian  in  the  same  plane  as  the  needle,  and  so  that  its  axis  pro- 
longed would  bisect  the  needle.  The  compass  needle  is  thereby  deflected 
through  a  certain  angle.  The  similar  pole  of  the  otfier  magnet  is  then 
placed  similarly  on  the  other  side  of  the  needle,  and  a  position  found  for 


656  On  Magnetism.  [719- 

it  in  which  it  exactly  neutralises  the  action  of  the  first  magnet ;  that  is, 
when  the  needle  is  again  in  the  magnetic  meridian.  If  the  magnets  are  not 
too  long,  compared  with  their  distance  from  the  needle,  their  strengths  are 
approximately  as  the  cubes  of  the  distance  of  the  acting  poles  from  the 
magnetic  needle. 

720.  Circumstances  which  influence  the  power  of  magnets. — All  bars 
do  not  attain  the  same  state  of  saturation,  for  their  coercive  force  varies. 
Twisting  or  hammering  imparts  to  iron  or  steel  a  considerable  coercive  force. 
But  the  most  powerful  of  these  influences  is  the  operation  of  tempering  (95). 
Coulomb  found  that  a  steel  bar  tempered  at  dull  redness  and  magnetised  to 
saturation,  made  ten  oscillations  in  93  seconds.  The  same  bar  tempered  at 
a  cherry-red  heat,  and  similarly  magnetised  to  saturation,  only  took  63 
seconds  to  make  ten  oscillations. 

Hence  it  would  seem,  that  the  harder  the  steel  the  greater  is  its  coercive 
force  ;  it  undergoes  magnetisation  with  much  greater  difficulty,  but  retains  it 
more  effectually.  It  appears,  however,  from  Jamin's  experiments  that  no  such 
general  rule  of  this  kind  can  be  laid  down  ;  for  each  specimen  of  steel  there 
seems,  according  to  the  proportion  of  carbon  which  it  contains,  to  be  a 
certain  degree  of  tempering  which  is  most  favourable  for  the  development 
of  permanent  magnetisation. 

Very  hard  steel  bars  have  the  disadvantage  of  being  very  brittle,  and  in 
the  case  of  long  thin  bars  a  hard  tempering  is  apt  to  produce  consequent 
poles.  Compass  needles  are  usually  tempered  at  the  blue  heat — that  is,  about 
300°  C. — by  which  a  high  coercive  force  is  obtained  without  great  fragility. 
Steel  is  magnetised  with  difficulty  even  when  placed  for  some  time  in  a  coil 
through  which  a  powerful  current  is  passing  ;  soft  iron  under  these  circum- 
stances is  magnetised  at  once.  If  a  short  coil  covering  only  a  portion  of  the 
steel  bars  be  moved  backwards  and  forwards  the  magnetisation  is  more 
complete. 

The  hardness  of  steel,  and  the  proportion  of  carbon  which  it  contains, 
exert  an  important  influence  on  the  degree  to  which  it  can  be  magnetised. 
For  the  same  degree  of  hardness,  the  magnetisation  increases  with  the  pro- 
portion of  carbon  in  the  steel,  and  more  markedly  the  smaller  this  proportion  ; 
with  the  same  proportion  of  carbon  it  increases  with  the  hardness  of  the  steel. 
It  appears  probable  that  the  compound  of  iron  and  carbon  in  steel  is  the 
carrier  of  the  permanent  magnetisation,  and  the  interjacent  particles  of  iron 
the  carriers  of  the  temporary  magnetisation.  Holtz  magnetised  plates  of 
English  corset  steel  to  saturation  and  determined  their  magnetic  moment  ; 
they  were  then  placed  in  dilute  hydrochloric  acid,  by  which  the  iron  was 
eaten  away,  and  the  magnetic  moment  determined  when  the  plate  had 
been  magnetised  to  saturation  after  each  such  treatment.  It  was  thus 
found  that,  with  a  diminution  in  the  proportion  of  iron,  there  was  an  increase 
in  the  magnetic  moment  for  the  unit  of  weight.  Holtz  found,  however, 
that  perfectly  pure  iron  prepared  by  electrolysis  can  acquire  permanent 
magnetism. 

Jamin  investigated  the  distribution  of  force  in  magnets  by  suspending 
from  one  arm  of  a  delicate  balance  a  small  iron  ball,  and  then  ascertaining 
what  force,  applied  at  the  other  arm,  was  required  to  detach  the  ball  when 
placed  in  contact  with  various  positions  of  the  magnet  to  be  investigated. 


-720]    Circumstances  which  Influence  the  Power  of  Magnets.  657 

Taking  thus  a  thin  plate  magnetised  to  saturation,  it  was  found  that  the 
magnetisation  increased  with  the  thickness,  but  did  not  materially  vary 
with  the  breadth  of  the  plate.  The  magnetic  force  was  developed  almost 
exclusively  at  the  ends.  The  curve  representing  the  magnetic  force  (721) 
was  convex  towards  the  poles  at  the  ends.  If  now  several  similar  plates  are 
superposed,  the  corresponding  curves  become  steeper  and  prolonged  towards 
the  middle  ;  the  magnetic  force  thus  becomes  increased.  When  the  curves 
run  into  each  other  in  the  middle  the  maximum  of  the  combination  is  reached  ; 
any  additional  plates  produce  no  increase  in  the  strength.  Steel  bars  may 
also  be  magnetised  so  as  to  show  the  same  curves,  and  such  bars  and  com- 
binations of  plates  are  called  by  Jamin  normal  magnets. 

Jamin  found  that  magnetisation  extends  deeper  in  a  bar  than  has  been 
usually  supposed  ;  in  soft  and  annealed  steel  it  penetrates  deeply.  The 
depth  diminishes  with  the  hardness  of  the  steel  and  the  proportion  of  carbon 
it  contains.  If  plates  of  varying  thickness  are  so  thin  that  the  magnetisation 
can  entirely  penetrate  them,  the  thicker  of  these  plates  are  more  strongly  mag- 
netised by  the  same  force,  for  the  magnetisation  extends  through  a  thicker 
layer  than  the  thinner  ones  ;  if,  however,  the  plates  are  very  thick,  they  are 
magnetised  to  the  same  extent  by  one  and  the  same  force.  With  equal  bars 
the  thickness  of  the  magnetic  layer  varies  with  the  strength  of  the  magnetising 
force.  Jamin  proved  this  by  placing  the  plates  in  dilute  sulphuric  acid  ;  he 
found  magnetisation  in  bars  which  had  been  exposed  to  the  stronger  force, 
while  those  which  had  been  more  feebly  magnetised  showed  none  when  they 
had  been  eaten  away  by  the  acid  to  the  same  extent.  He  also  showed  that 
the  magnetisation  which  had  penetrated  was  as  strong  as  that  on  the  surface. 

Holtz  has  made  some  experiments  on  the  influence  of  solid  bars  as  against 
hollow  tubes  in  the  construction  of  permanent  steel  magnets.  The  latter  are 
to  be  preferred  ;  they  are  decidedly  cheaper,  as  they  need  not  be  bored,  but 
may  be  bent  from  steel  plates.  A  bar  and  a  tube  of  the  same  steel,  125  mm. 
in  length  by  13  mm.  diameter,  the  tube  being  175  mm.  thick,  were  magnetised 
to  saturation,  and  their  magnetic  moments  determined  by  the  method  of 
oscillations  (705),  the  tube  being  loaded  with  copper.  The  magnetism  of  the 
tube  was  to  that  of  the  bar  as  r6  :  I.  The  tubes  also  retained  their  mag- 
netisation better.  After  the  lapse  of  six  months  the  ratio  of  the  magnetisation 
of  the  tube  was  to  that  of  the  bar  as  27  :  i.  A  magnetised  steel  tube  filled 
with  a  soft  iron  core  had  scarcely  any  directive  force. 

Temperature.  —  Increase  of  temperature  always  produces  a  diminution  of 
magnetic  force.  If  the  changes  of  temperature  are  small  —  those  of  the  atmo- 
sphere, for  instance  —  the  magnet  is  not  permanently  altered.  Kuppfer  allowed 
a  magnet  to  oscillate  at  different  temperatures,  and  found  a  definite  decrease  in 
its  power  with  increased  temperature,  as  indicated  by  its  slower  oscillations.  In 
the  case  of  a  magnet  2^  inches  in  length,  he  observed  that  with  an  increase  of 
each  degree  of  temperature  the  duration  of  800  oscillations  was  0-4"  longer. 
If  n  be  the  number  of  oscillations  at  zero,  and  n^  the  number  at  /,  then 


where  c  is  a  constant  depending  in  each  case  on  the  magnet  used.  This 
formula  has  an  important  application  in  the  correction  of  the  observations 
of  magnetic  force  which  are  made  at  different  places  and  at  different 

UU 


658  On  Magnetism.  [720- 

temperatures,  and  which,  in  order  to  be  comparable,  must  first  be  reduced  to 
a  uniform  temperature. 

When  a  magnet  has  been  more  strongly  heated,  it  does  not  regain  its 
original  force  on  cooling  to  its  original  temperature,  and  when  it  has  been 
heated  to  redness,  it  is  demagnetised.  This  was  first  shown  by  Coulomb, 
who  took  a  saturated  magnet,  heated  it  to  progressively  higher  temperatures, 
and  noted  the  number  of  oscillations  after  each  heating.  The  higher  the 
temperature  to  which  it  had  been  heated  the  slower  its  oscillations. 

A  magnet  heated  to  bright  redness  loses  its  magnetism  so  completely 
that  it  is  quite  indifferent,  not  only  towards  iron,  but  also  towards  another 
magnet,  and  this  holds  so  long  as  this  high  temperature  continues.  Incan- 
descent iron  also  does  not  possess  the  property  of  being  attracted  by  the 
magnet.  Hence  there  is  in  the  case  of  iron  a  magnetic  limit,  beyond  which 
it  is  unaffected  by  magnetism.  Such  a  magnetic  limit  exists  in  the  case  of 
other  magnetic  metals.  With  cobalt,  for  instance,  it  is  far  beyond  a  white 
heat,  for  at  the  highest  temperatures  hitherto  examined  it  is  still  magnetic  ; 
the  magnetic  limit  of  chromium  is  somewhat  below  red  heat  ;  that  of  nickel 
at  about  350°  C.  and  of  manganese  at  about  15°  to  20°  C. 

A  change  of  temperature  whether  from  16°  to  100°,  or  from  100°  to  16°, 
increases  the  strength  of  temporary  or  induced  magnetism  both  in  the  case 
of  iron  and  of  steel. 

Percussion  and  Torsion. — When  a  steel  bar  is  hammered  while  being 
magnetised  it  acquires  a  much  higher  degree  of  magnetisation  than  it  would 
without  this  treatment.  Conversely  when  a  magnet  is  let  fall,  or  is  otherwise 
violently  disturbed,  it  loses  much  of  its  magnetisation.  Wiedemann  has  inves- 
tigated in  a  very  complete  manner  the  relations  of  torsion  and  magnetisation. 
Torsion  exerts  a  great  influence  on  the  magnetisation  of  a  bar,  and  the  inter- 
esting phenomenon  has  been  observed  that  torsion  influences  magnetism  in 
the  same  manner  as  magnetism  does  torsion.  Thus  the  permanent  mag- 
netisation of  a  steel  bar  is  diminished  by  torsion,  but  not  proportionally  to 
the  increase  of  torsion.  In  like  manner  the  torsion  of  twisted  iron  wires  is 
diminished  by  their  being  magnetised,  though  less  so  than  in  proportion  to 
their  magnetisation.  Repeated  torsions  in  the  same  direction  scarcely 
diminish  magnetisation,  but  a  torsion  in  the  opposite  direction  produces  a 
new  diminution  of  the  magnetism.  In  a  perfectly  analogous  manner,  re- 
peated magnetisations  in  the  same  direction  scarcely  diminish  torsion,  but  a 
renewed  magnetisation  in  the  opposite  direction  does  so. 

721.  Distribution  of  free  magnetism. — Coulomb  investigated  the  dis- 
tribution of  magnetic  force  by  placing  a  large  magnet  in  a  vertical  position 
in  the  magnetic  meridian  ;  he  then  took  a  small  magnetic  needle,  and 
having  ascertained  the  number  of  its  oscillations  under  the  influence  of  the 
earth's  magnetism  alone,  he  presented  it  to  different  parts  of  the  magnet. 
The  oscillations  were  fewer  as  the  needle  was  nearer  the  middle  of  the  bar, 
and,  when  they  had  reached  that  position  their  number  was  the  same  as  under 
the  influence  of  the  earth's  magnetism  alone.  For  saturated  bars  of  more 
than  7  inches  in  length  the  distribution  could  always  be  expressed  by  a 
curve  whose  abscissae  were  the  distances  from  the  ends  of  the  magnet,  and 
whose  ordinates  were  the  force  of  magnetism  at  these  points.  With  magnets 
of  the  above  dimensions  the  poles  are  at  the  same  distance  from  the  end  ; 


-722]  Mayer's  Floating  Magnets.  659 

Coulomb  found  the  distance  to  be  i'6  inch  in  a  bar  8  inches  long.  He  also 
found  that,  with  shorter  bars,  the  distance  of  the  poles  from  the  end  is  £  of 
the  length  ;  thus  with  a  bar  of  three  inches  it  would  be  half  an  inch.  These 
results  presuppose  that  the  other  dimensions  of  the  bar  are  very  small  as 
compared  with  its  length,  that  it  has  a  regular  shape,  and  is  uniformly  mag- 
netised. When  these  conditions  are  not  fulfilled,  the  positions  of  the  poles 
can  only  be  determined  by  direct  trials  with  a  magnetic  needle.  With 
lozenge-shaped  magnets  the  poles  are  nearer  the  middle.  Coulomb  found 
that  these  lozenge-shaped  bars  have  a  greater  directive  force  than  rectangular 
bars  of  the  same  weight,  thickness,  and  hardness. 

A  short  magnet  is  defined  by  Coulomb  as  one  whose  length  is  not  less 
than  50  times  its  diameter. 

Kohlrausch  found  that  the  pole  of  a  magnet  as  far  as  its  action  at  a 
distance  is  concerned  is  T\  from  the  end. 

722.  Mayer's  floating-  mag-nets. — The  reciprocal  action  of  magnetic 
poles  may  be  conveniently  illustrated  by  an  elegant  method  devised  by 
Prof.  A.  M.  Mayer.  Steel  sewing  needles  are  magnetised  so  that  their 
points  are  north  poles,  and  their  eyes,  which  are  thus  south  poles,  just  pro- 
ject through  minute  cork  discs,  so  that  when  placed  in  water  the  magnets 
float  in  a  vertical  position.  If  the  north  pole  of  a  strong  magnet  is  brought 
near  a  number  of  these  floating  magnets  they  are  attracted  by  it,  and  take  up 
definite  positions,  forming  figures  which  depend  on  the  reciprocal  repulsion 
of  the  floating  magnets,  and  on  their  number.  Some  of  them  are  repre- 
sented in  fig.  620.  The  more  complex  produce  more  than  one  arrange- 

6  a  60 

V*  .          , 

•^  .•'        "'-^  '  .         m         *  j  V 


!»          .•- •         *._  /  .-•'       X,  '^ 

•    '^     •;'  • •  *    *         v    \    \      /    /     *     \   vx     A 

V" •/      ^ -*""        ^  /        \  *    '  ./ 

8«  8<5  8^  • * •  "•---•-"'" 

Fig.  620. 

ment  which  are  not  equally  stable,  the  letters  «,  b,  and  c  indicating  the  de- 
creasing order  of  stability.  A  slight  shock  often  causes  one  form  to  pass 
into  another  and  more  stable  form. 

These  figures  not  only  illustrate  magnetic  actions,  but  they  suggest  an 
image  of  the  manner  in  which  alteration  of  molecular  groupings  may  give 
rise  to  physical  phenomena,  such  as  those  of  superfusion  (345). 


U  U  2 


66o  Frictional  Electricity.  [723- 


BOOK   IX. 

FRICTIONAL   ELECTRICITY. 

CHAPTER    I. 
FUNDAMENTAL    PRINCIPLES. 

V  723.  Electricity.  Its  nature. — Electricity  is  a  powerful  physical  agent 
which  manifests  itself  mainly  by  attractions  and  repulsions,  but  also  by 
luminous  and  heating  effects,  by  violent  commotions,  by  chemical  decompo- 
sitions, and  many  other  phenomena.  Unlike  gravity,  it  is  not  inherent  in 
bodies,  but  it  is  evoked  in  them  by  a  variety  of  causes,  among  which  are 
friction,  pressure,  chemical  action,  heat  and  magnetism. 

Thales,  6  B.C.,  knew  that  when  amber  was  rubbed  with  silk,  it  acquired 
the  property  of  attracting  light  bodies  ;  and  from  the  Greek  form  of  this 
word  (fjXeKTpov)  the  term  electricity  has  been  derived.  This  is  nearly  all 
the  knowledge  left  by  the  ancients  ;  it  was  not  until  towards  the  end  of  the 
sixteenth  century  that  Dr.  Gilbert,  physician  to  Queen  Elizabeth,  showed 
that  this  property  was  not  limited  to  amber,  but  that  other  bodies,  such  as 
sulphur,  wax,  glass,  &c.,  also  possessed  it  in  a  greater  or  less  degree. 
Y  724.  Development  of  electricity  by  friction. — When  a  glass  rod,  or  a 

stick  of  sealing-wax,  or  shellac,  is  held  in  the  hand,  and  is  rubbed  with  a 
piece  of  flannel,  or  with  the  skin  of  a  cat,  the  parts  rubbed  will  be  found  to 
have  the  property  of  attracting  light  bodies,  such  as  pieces  of  silk,  wool, 
feathers,  paper,  bran,  gold  leaf,  &c.,  which,  after  remaining  a  short  time  in 
contact,  are  again  repelled.  They  are  then  said  to  have  become  electrified. 
In  order  to  ascertain  whether  bodies  are  electrified  or  not,  instruments  called 
electroscopes  are  used.  The  simplest  of  these,  the  electric  pendulum  (fig. 
621),  consists  of  a  pith  ball  attached  by  means  of  a  silk  thread  to  a  glass 
support.  When  an  electrified  body  is  brought  near  the  pith  ball,  the  latter 
is  instantly  attracted,  but  after  momentary  contact  is  again  repelled  (fig. 
622). 

A  solid  body  may  also  be  electrified  by  friction  with  a  liquid  or  with  a 
gas.  In  the  Torricellian  vacuum  a  movement  of  the  mercury  against  the 
sides  of  the  glass  produces  a  disengagement  of  electric  light  visible  in  the 
dark ;  a  tube  exhausted  of  air,  but  containing  a  few  drops  of  mercury,  be- 
comes also  luminous  when  agitated  in  the  dark. 

If  a  quantity  of  mercury  in  a  dry  glass  vessel  be  connected  with  a  gold- 
leaf  electroscope  by  a  wire,  and  a  dry  glass  rod  be  immersed  in  it,  no  indica- 


-725] 


Conductors  and  Nonconductors, 


66 1 


tions  are  observed  during  the  immersion,  but  on  smartly  withdrawing  the 
rod,  the  leaves  increasingly  diverge,  attaining  their  maximum  when  the  rod 
leaves  the  mercury. 

Some  substances,  particularly  metals,  do  not  seem  capable  of  receiving 
the  electric  excitement.  When  a  rod  of  metal  is  held  in  the  hand,  and 
rubbed  with  silk  or  flannel,  no  electrical  effects  are  produced  in  it ;  and  bodies 


Fig.  621. 


Fig.  622. 


were  divided  by  Gilbert  into  ideoelectrics,  or  those  which  become  electrical 
by  friction  ;  and  anelectrics,  or  those  which  do  not  possess  this  property. 
These  distinctions  no  longer  obtain  in  any  absolute  sense  \  under  appropriate 
conditions,  all  bodies  may  be  electrified  by  friction  (726). 
v  725.  Conductors  and  nonconductors. — When  a  dry  glass  rod,  rubbed 
at  one  end,  is  brought  near  an  electroscope,  that  part  only  will  be  electrified 
which  has  been  rubbed  ;  the  other  end  will  produce  neither  attraction  nor 
repulsion.  The  same  is  the  case  with  a  rod  of  shellac  or  of  sealing-wax. 
In  these  bodies  electricity  does  not  pass  from  one  part  to  another — they  do 
not  conduct  electricity.  Experiment  shows  that,  when  a  metal  has  received 
electricity  in  any  of  its  parts,  the  electricity  instantly  spreads  over  its  entire 
surface.  Metals  are  hence  said  to  be  good  conductors  of  electricity. 

Bodies  have,  accordingly,  been  divided  into  conductors  and  nonconductors 
or  insulators.  This  distinction  is  not  absolute,  and  we  may  advantageously 
consider  bodies  as  offering  a  resistance  to  the  passage  of  electricity  which 
varies  with  the  nature  of  the  substance.  Those  bodies  which  offer  little 
resistance  are  thus  conductors,  and  those  which  offer  great  resistance  are 
nonconductors  or  insulators  :  electrical  conductivity  is  accordingly  the  inverse 
of  electrical  resistance.  There  is  no  such  thing  as  an  absolute  nonconductor 
of  electricity,  any  more  than  there  is  an  absolute  nonconductor  of  heat. 
We  are  to  consider  that  between  conductors  and  nonconductors  there  is  a 
quantitative  and  not  a  qualitative  difference  ;  there  is  no  conductor  so  good 


662  Frictional  Electricity.  [725- 

but  that  it  offers  some  resistance  to  the  passage  of  electricity,  nor  is  there  any 
substance  which  insulates  so  completely  but  that  it  allows  some  electricity 
to  pass.  The  transition  from  conductors  to  nonconductors  is  gradual,  and  no 
line  of  sharp  demarcation  can  be  drawn  between  them. 

In  this  sense  we  are  to  understand  the  following  table,  in  which  bodies 
are  classed  as  conductors,  semiconductors,  and  nonconductors  ;  those  bodies 
being  conveniently  designated  as  conductors  which,  when  applied  to  a 
charged  electroscope,  discharge  it  almost  instantaneously  ;  semiconductors 
being  those  which  discharge  it  in  a  short  but  measurable  time — a  few  seconds, 
for  instance  ;  while  nonconductors  effect  no  perceptible  discharge  in  the 
course  of  a  minute. 

Conductors.  Semiconductors.  Nonconductors. 

Metals.  Alcohol  and  ether.  Dry  oxides. 

Well-burnt  charcoal.          Powdered  glass.  Ice  at- 25°  C. 

Graphite.  Flour  of  sulphur.  Lime. 

Acids.  Dry  wood.  Caoutchouc. 

Aqueous  solutions.  Paper.  Air  and  dry  gases. 

Water.  Ice  at  o°.  Dry  paper. 

Snow.  Silk. 

Vegetables.  Diamond  and  precious 

Animals.  stones. 

Soluble  salts.  Glass. 

Linen.  Wax. 

Cotton.  Sulphur. 

Resins. 

Amber. 

Shellac. 

This  list  is  arranged  in  the  order  of  decreasing  conductivity,  or,  what  is  the 
same  thing,  of  increasing  resistance.  The  arrangement,  however,  is  not  in- 
variable. Conductivity  depends  on  many  physical  conditions.  Glass,  for 
example,  which  does  not  conduct  at  any  ordinary  temperature,  does  so  at  a 
red  heat.  Shellac  and  resin  do  not  insulate  so  well  when  they  are  heated. 
Water,  which  is  a  good  conductor,  conducts  but  little  in  the  state  of  ice  at 
o°,  and  very  badly  at  —  25°.  Powdered  glass  and  flour  of  sulphur  conduct 
very  well,  while  in  large  masses  they  are  nonconductors  ;  probably  because 
in  a  state  of  powder  each  particle  becomes  covered  with  a  film  of  moisture 
that  acts  as  a  conductor.  The  nonconducting  power  of  glass  is  also  greatly 
influenced  by  its  chemical  composition. 

According  to  Said  Effendi,  if  the  conducting  power  of  water  be  taken  at 
1,000,  the  conducting  power  of  petroleum  is  72  ;  alcohol  49  ;  ether  40  ; 
turpentine  23  ;  and  benzole  16.  Domalip  obtained  the  following  numbers 
for  the  respective  conductivities:  Water  144;  ether  6-3;  turpentine  1-9; 
and  benzole  i. 

\  726.  Insulating-  bodies.  Common  reservoir. — Bad  conductors  are 
called  insulators,  for  they  are  used  as  supports  for  bodies  in  which  electricity 
is  to  be  retained.  A  conductor  remains  electrified  only  so  long  as  it  is  sur- 
rounded by  insulators.  If  this  were  not  the  case,  as  soon  as  the  electrified 


-727]  Distinction  of  the  Two  Kinds  of  Electricity.  663 

body  came  in  contact  with  the  earth,  which  is  a  good  conductor,  the  electri- 
city would  pass  into  the  earth,  and  diffuse  itself  through  its  whole  extent. 
On  this  account,  the  earth  has  been  named  the  common  reservoir.  A  body 
is  insulated,  by  being  placed  on  a  support  with  glass  feet,  or  on  a  resinous 
cake,  or  by  being  suspended  by  silk  threads.  No  bodies,  however,  insulate 
perfectly  ;  all  electrified  bodies  lose  their  electricity  more  or  less  rapidly 
by  means  of  the  supports  on  which  they  rest.  Glass  is  always  somewhat 
hygroscopic,  and  the  aqueous  vapour  which  condenses  on  it  affords  a 
passage  for  the  electricity ;  the  insulating  power  of  glass  is  materially  im- 
proved by  coating  it  with  shellac  or  copal  varnish.  Dry  air  is  a  good  insu- 
lator ;  but  when  the  air  contains  moisture  it  conducts  electricity,  and  this  is 
the  principal  source  of  the  loss  of  electricity.  Hence  it  is  necessary,  in 
electrical  experiments,  to  rub  the  supports  with  cloths  dried  at  the  fire, 
and  to  surround  electrified  bodies  by  glass  vessels,  containing  substances 
which  absorb  moisture,  such  as  chloride  of  calcium,  or  pumice  soaked  with 
sulphuric  acid. 

From  their  great  conductivity  metals  do  not  seem  to  become  electrified 
by  friction.  But  if  they  are  insulated,  and  then  rubbed,  they  give  good  indi- 
cations. This  may  be  seen  by  the  fol- 
lowing experiment  (fig.  623).  A  brass 
tube  is  provided  with  a  glass  handle  by 
which  it  is  held,  and  then  rubbed  with 

silk  or  flannel.  On  approaching  the  metal  to  an  electrical  pendulum  (fig. 
621),  the  pith  ball  will  be  attracted.  If  the  metal  is  held  in  the  hand  electri- 
city is  indeed  produced  by  friction — but  it  immediately  passes  through  the 
body  into  the  ground. 

If,  too,  the  cap  of  a  gold-leaf  electroscope  be  briskly  flapped  with  a  dry 
silk  handkerchief,  the  gold  leaves  will  diverge. 

V^  727.  Distinction  of  the  two  kinds  of  electricity. — If  electricity  be 
developed  on  a  glass  rod  by  friction  with  silk,  and  the  rod  be  brought  near 
an  electrical  pendulum,  the  ball  will  be  attracted  to  the  glass,  and  after 
momentary  contact  will  be  again  repelled.  By  this  contact  the  ball  becomes 
electrified,  and  so  long  as  the  two  bodies  retain  their  electricity,  repulsion 
follows  whenever  they  are  brought  near  each  other.  If  a  stick  of  sealing-wax 
electrified  by  friction  with  flannel  or  silk  be  approached  to  another  electrical 
pendulum,  the  same  effects  will  be  produced— the  ball  will  fly  towards  the 
wax,  and  after  contact  will  be  repelled.  Two  bodies,  which  have  been 
charged  with  electricity,  repel  one  another.  But  the  electricities  respectively 
developed  in  the  preceding  cases  are  not  the  same.  If,  after  the  pith  ball 
had  been  touched  with  an  electrified  glass  rod,  an  electrified  stick  of  stealing- 
wax,  and  then  an  electrified  glass  rod,  be  alternately  approached  to  it,  the 
pith  ball  will  be  attracted  by  the  former  and  repelled  by  the  latter.  Simi- 
larly, if  the  pendulum  be  charged  by  contact  with  the  electrified  sealing- 
wax,  it  will  be  repelled  when  this  is  approached  to  it,  but  attracted  by  the 
approach  of  the  excited  glass  rod. 

On  experiments  of  this  nature,  Dufay  first  made  the  observation  that 
there  are  two  different  electricities  :  the  one  developed  by  the  friction  of 
glass,  the  other  by  the  friction  of  resin  or  shellac.  To  the  first  the  name 
vitreous  electricity  is  given  ;  to  the  second  the  name  resinous  electricity. 


664  Frictional  Electricity.  [728- 

728.  Theories  of  electricity. — Two   theories   have   been   proposed   to 
account  for  the  different  effects  of  electricity.     Franklin  supposed  that  there 
exists  a  peculiar,  subtle,  imponderable  fluid,  which  acts  by  repulsion  on  its 
own  particles,  and  pervades  all  matter.     This  fluid  is  present  in  every  sub- 
stance in  a  quantity  peculiar  to  it,  and  when  it  contains  this  quantity  it  is  in 
the  natural  state,  or  in  a  state  of  equilibrium.     By  friction  certain  bodies 
acquire  an  additional  quantity  of  the  fluid,  and  are  said  to  be  positively 
electrified  ;  others  by  friction  lose  a  portion,  and  are  said  to  be  negatively 
electrified.      The  former  state  corresponds  to  vitreous  electricity,  and  the 
latter  to   resinous  electricity.      Positive   electricity  is   represented   by  the 
sign  + ,  and  negative  electricity  by  the  sign   — ;   a   designation   based  on 
the  algebraical  principle,  that  when  a  plus  quantity  is  added  to  an  equal 
minus  quantity  zero  is  produced.     So  when  a  body  containing  a  quantity  of 
positive  electricity  is  touched  with  a  body  possessing  an  equivalent  quantity 
of  negative  electricity,  a  neutral  or  zero  state  is  produced. 

The  theory  of  Symmer  assumes  that  every  substance  contains  an  indefinite 
quantity  of  a  subtle,  imponderable  matter,  which  is  called  the  electric  fluid. 
This  fluid  is  formed  by  the  union  of  two  fluids— the  positive  and  the  negative. 
When  they  are  combined  they  neutralise  one  another,  and  the  body  is  then 
in  the  natural  or  neutral  state.  By  friction,  and  by  several  other  means, 
the  two  fluids  may  be  separated,  but  one  of  them  can  never  be  excited 
without  a  simultaneous  production  of  the  other.  There  may,  however,  be  a 
greater  or  less  excess  of  the  one  or  the  other  in  any  body,  and  it  is  then  said 
to  be  electrified  positively  or  negatively.  As  in  Franklin's  theory,  vitreous 
corresponds  to  positive  and  resinous  to  negative  electricity.  This  distinction 
is  merely  conventional :  it  is  adopted  for  the  sake  of  convenience,  and  there 
is  no  other  reason  why  resinous  electricity  should  not  be  called  positive 
electricity. 

Electricities  of  the  same  name  repel  one  another,  and  electricities  of 
opposite  kinds  attract  each  other.  The  electricities  can  circulate  freely  on 
the  surface  of  certain  bodies,  which  are  called  conductors,  but  remain  con- 
fined to  certain  parts  of  others,  which  are  called  nonconductors. 

It  must  be  added  that  this  theory  is  quite  hypothetical  ;  but  for  purposes 
of  instruction  its  general  adoption  is  justified  by  the  convenient  explanation 
which  it  gives  of  electrical  phenomena. 

729.  Action  of  electrified  bodies  on  each  other. — Admitting  the  two- 
fluid  hypothesis,  the  phenomena  of  attraction  and  repulsion  maybe  enunciated 
in  the  following  law  : — 

Two  bodies  charged  with  the  same  electricity  repel  each  other;  two  bodies 
charged  with  opposite  electricities  attract  each  other. 

These  attractions  and  repulsions  take  place  in  virtue  of  the  action  which 
the  two  electricities  exert  on  themselves,  and  not  in  virtue  of  their  action  on 
the  particles  of  matter. 

730.  Iiaw  of  the  development  of  electricity  by  friction.— Whenever 
two  bodies  are  rubbed  together,  the  neutral  electricity  is  decomposed.     Two 
electricities  are  developed  at  the  same  time  and  in  equal  quantities — one 
body  takes  positive  and  the  other  negative  electricity.     This  may  be  proved 
by  the  following  experiment   devised   by  Faraday  :— A  small  flannel   cap 
provided  with  a  silk  thread  ('fig.  624")  is  fitted  on  the  end  of  a  stout  rod  of 


-731]    Development  of  Electricity  by  Pressure  and  Cleavage.    66$ 

shellac,  and  rubbed  round  a  few  times.  When  the  cap  is  removed  by  means 
of  the  silk  thread,  and  presented  to  a  pith  ball  pendulum  charged  with  positive 
electricity,  the  latter  will  be  repelled,  proving  that  the 
flannel  is  charged  with  positive  electricity  ;  while  if  the 
shellac  is  presented  to  the  pith  ball,  it  will  be  attracted, 
showing  that  the  shellac  is  charged  with  negative 
electricity.  Both  electricities  are  present  in  equal 
quantities  ;  for  if  the  rod  be  presented  to  the  electro- 
scopes before  removing  the  cap,  no  action  is  observed. 
The  electricity  developed  on  a  body  by  friction 
depends  on  the  rubber  as  well  as  the  body  rubbed. 
Thus  glass  becomes  negatively  electrified  when  rubbed 
with  cat's  skin,  but  positively  when  rubbed  with  silk. 

In  the  following  list,  which  is  mainly  due  to  Faraday,  the  substances  are 
arranged  in  such  an  order  that  each  becomes  positively  electrified  when 
rubbed  with  any  of  the  bodies  following,  but  negatively  when  rubbed  with 
any  of  those  which  precede  it : — 


Fig.  624. 


1.  Cat's  skin.  5.  Glass. 

2.  Flannel.  6.  Cotton. 

3.  Ivory.  7.  Silk. 

4.  Rock  crystal.  8.  The  hand. 


9.  Wood.  13.  Resin. 

10.  Metals.  14.  Sulphur. 

11.  Caoutchouc.  15.  Guttapercha. 

12.  Sealing-wax.  16.  Gun-cotton. 


The  nature  of  the  electricity  set  free  by  friction  depends  also  on  the 
degree  of  polish,  the  direction  of  the  friction,  and  the  temperature.  If  two 
glass  discs  of  different  degrees  of  polish  are  rubbed  against  each  other,  that 
which  is  most  polished  is  positively,  and  that  which  is  least  polished  is 
negatively  electrified.  If  two  silk  ribbons  of  the  same  kind  are  rubbed 
across  each  other,  that  which  is  transversely  rubbed  is  negatively  and  the 
other  positively  electrified.  If  two  bodies  of  the  same  substance,  of  the  same 
polish,  but  of  different  temperatures,  are  rubbed  together,  that  which  is  most 
heated  is  negatively  electrified.  Generally  speaking,  the  particles  which  are 
most  readily  displaced  are  negatively  electrified. 

Poggendorff  has  observed  that  many  substances  which  have  hitherto  been 
regarded  as  highly  negative,  such  as  gun-paper,  gun-cotton,  and  ebonite,  yield 
positive  electricity  when  rubbed  with  leather  coated  with  amalgam.  It 
must  be  added  that  the  results  of  experiments  on  the  kind  of  electricity  pro- 
duced by  rubbing  bodies  together  are  somewhat  uncertain,  as  slight  differences 
in  the  surfaces  of  the  bodies  rubbed  may  completely  alter  their  deportment. 

731.  Development  of  electricity  toy  pressure  and  cleavage. — 
Electrical  excitement  may  be  produced  by  other  causes  than  friction.  If  a 
disc  of  wood,  covered  with  silk,  on  which  some  amalgam  has  been  rubbed, 
and  a  metal  disc,  each  provided  with  an  insulating  handle,  be  placed  in  con- 
tact, and  then  suddenly  separated,  the  metal  disc  is  negatively  electrified. 
A  crystal  of  Iceland  spar  pressed  between  the  fingers  becomes  positively 
electrified,  and  retains  this  state  for  some  time.  The  same  property  is 
observed  in  several  other  minerals,  even  though  conductors,  provided  they 
be  insulated.  If  cork  and  caoutchouc  be  pressed  together,  the  first  becomes 
positively,  and  the  latter  negatively  electrified.  A  disc  of  wood  pressed  on 
an  orange  and  separated  carries  away  a  good  charge  of  electricity  if  the 


666 


Fractional  Electricity. 


[731- 


contact  be  rapidly  interrupted.  But  if  the  disc  is  slowly  removed  the  quan- 
tity is  smaller,  for  the  two  fluids  recombine  at  the  moment  of  their  separation. 
For  this  reason  there  is  no  apparent  effect  when  the  two  bodies  pressed 
together  are  good  conductors. 

The  contact  of  heterogeneous  bodies  is  no  doubt  the  source  of  electricity. 
Pressure  and  friction  are  but  particular  cases  ;  in  the  former  case  the  con- 
tact is  closer  and  in  the  latter  case  the  surfaces  are  being  continually  renewed, 
and  the  effect  is  the  same  as  if  there  were  a  series  of  rapidly  succeeding 
contacts. 

Cleavage  also  is  a  source  of  electricity.  If  a  plate  ol  mica  be  rapidly 
split  in  the  dark,  a  slight  phosphorescent  light  is  perceived.  Becquerel 
fixed  glass  handles  to  each  side  of  a  plate  of  mica,  and  then  rapidly  separated 
them.  On  presenting  each  of  the  plates  thus  separated  to  an  electroscope, 
he  found  that  one  was  negatively  and  the  other  positively  electrified.  If  a 
stick  of  sealing-wax  be  broken,  the  ends  exhibit  different  electricities. 

All  badly  conducting  crystalline  substances  exhibit  electrical  indications 
by  cleavage.  The  separated  plates  are  always  in  opposite  electrical  condi- 
tions, provided  they  are  not  good  conductors  :  for  if  they  were,  the  separa- 
tion would  not  be  sufficiently  rapid  to  prevent  the  recombination  of  the  two 
electricities.  To  the  phenomena  here  described  is  due  the  luminous  appear- 
ance seen  in  the  dark  when  sugar  is  broken.  If  sulphur  or  resin  be  melted 
in  glass  vessels  and  a  glass  rod  be  placed  in  the  melted  mass,  on  cooling 
the  solid  mass  can  be  lifted  out,  and  will  be  found  to  be  negatively  electrified. 
732.  Pyroelectricity. — Certain  minerals,  when  warmed,  acquire  electri- 
cal properties  :  a  phenomenon  to  which  the  name  pyroelectricity  is  given. 
It  is  best  studied  in  tourmaline,  in  which  it  was  first  discovered 
from  the  fact  that  this  mineral  has  the  power  of  first  attracting 
and  then  repelling  hot  ashes  when  placed  among  them. 

To  observe  this  phenomenon,  a  crystal  of  tourmaline 
(fig.  625)  is  suspended  horizontally  by  a  silk  thread,  in  a  glass 
cylinder  placed  on  a  heated  metal  plate,  or  in  an  ordinary  hot 
air  bath.  On  subsequently  investigating  the  electric  condition 
of  the  ends  by  approaching  to  them  successively  an  electrified 
glass  rod,  one  end  will  be  found  to  be  positively  electrified,  and 
the  other  end  negatively  electrified,  and  each  end  shows  this 
polarity  as  long  as  the  temperature  rises.  The  arrangement  of 
the  electricity  is  thus  like  that  of  the  magnetism  in  a  magnet. 
The  points  at  which  the  intensity  of  free  electricity  is  greatest 
are  called  the  poles,  and  the  line  connecting  them  is  the  electric 
axis.  When  a  tourmaline,  while  thus  electrified,  is  broken  in 
the  middle,  each  of  the  pieces  has  its  two  poles,  and  the  polarity  of  the 
broken  ends  is  opposite,  resembling  thus  the  experiment  of  the  broken 
magnets  (685).  The  quantities  of  electricity  produced  when  tourmaline 
is  heated  are  equal  as  well  as  opposite,  for  if  a  heated  crystal  be  suspended 
by  an  insulating  support  inside  an  insulated  metal  cylinder,  the  outside  of 
which  is  connected  with  an  electroscope  (745),  no  divergence  in  its  leaves  is 
produced. 

These  polar  properties  depend  on  the  change  of  temperature.  When  a 
tourmaline,  which  has  become,  electrical  by  being  warmed,  is  allowed  to  cool 


-732]  Pyroelectricity.  667 

slowly,  it  first  loses  electricity,  and  then  its  polarity  becomes  reversed  ; 
that  is,  the  end  which  was  positive  now  becomes  negative,  and  that  which 
was  negative  becomes  positive,  and  the  position  of  the  poles  now  remains 
unchanged  so  long  as  the  temperature  sinks.  Tourmaline  only  becomes 
pyroelectric  within  certain  limits  of  temperature  ;  these  vary  somewhat  with 
the  length,  but  are  usually  between  10°  and  150°  C.  Below  and  above  these 
temperatures  it  behaves  like  any  other  body,  and  shows  no  polarity. 

Tourmaline  belongs  to  the  hexagonal  system,  and  usually  crystallises  in 
hemihedral  forms  ;  those,  that  is  to  say,  which  are  differently  modified  at  the 
ends  of  their  crystallographical  principal  axis.  The  name  analogous  pole  is 
given  to  that  end  A  of  the  crystal  which  shows  positive  electricity  when  the 
temperature  is  rising,  and  negative  electricity  when  it  is  sinking ;  antilogous 
pole  to  the  end  B  which  becomes  negative  by  being  heated,  and  positive  by 
being  cooled. 

Besides  tourmaline  the  following  minerals  are  found  to  be  pyroelectric, 
though  not  so  markedly  :  boracite,  topaz,  prehnite,  silicate  of  zinc,  scolezite, 
axenite.  And  the  following  organic  bodies  are  pyroelectric  :  cane-sugar, 
Pasteur's  salt  (racemate  of  sodium  and  ammonium),  tartrate  of  potassium,  &c. 

Sir  W.  Thomson  supposes  that  every  portion  of  tourmaline  and  other 
hemihedral  crystals  possesses  a  definite  electrical  polarity,  the  intensity  of 
which  depends  on  the  temperature.  When  the  surface  is  passed  through  a 
flame  every  part  becomes  electrified  to  such  an  extent  as  to  exactly  neutralise, 
for  all  external  points,  the  effect  of  the  internal  polarity.  The  crystal  thus  has 
no  external  action,  nor  any  tendency  to  change  its  mode  of  electrification. 
But  if  it  be  heated  or  cooled  the  internal  polarisation  of  each  particle  of  the 
crystal  is  altered,  and  can  no  longer  be  balanced  by  the  superficial  electrifica- 
tion, so  that  there  is  a  resultant  external  action. 

A  very  convenient,  and  at  the  same  time  sensitive,  means  of  investigating 
the  action  of  crystals  is  to  sift  on  these,  after  having  been  warmed,  a  mixture 
of  flour  of  sulphur  and  red  lead  through  a  small  cotton  sieve.  By  the  friction 
in  sifting  the  sulphur  acquires  negative  and  the  red  lead  positive  electricity, 
and  the  powders  thus  charged  attach  themselves  to  those  parts  of  the  crystal 
which  have  the  opposite  electricity,  and  thus  by  their  different  colours  give 
at  once  an  image  of  its  distribution. 

Crystals  of  fluor  spar  are  not  only  electrified  by  heat,  but  also  when 
they  are  exposed  to  radiation  from  the  sun  and  from  the  electric  light.  This 
phenomenon  is  known  as  photo-electricity. 


668 


Fractional  Electricity. 


[733- 


CHAPTER    II. 

QUANTITATIVE   LAWS   OF   ELECTRICAL   ACTION. 

v  733.  Electrical  quantity. — In  the  experiment  with  the  flannel  cap, 
described  above  (730),  each  time  the  experiment  is  made,  the  quantity  of 
positive  electricity  produced,  which  remains  on  the  flannel,  is  equal  to  that 
of  the  negative  electricity,  which  remains  on  the  sealing-wax.  The  flannel, 
with  its  charge  of  positive  electricity,  may  be  detached,  and  if  we  work 
under  precisely  uniform  conditions,  equal  quantities  of  electricity  can  thus 
be  separated. 

If  we  fill  water  from  a  constant  source  into  a  cask  by  means  of  a  measure, 
the  quantity  added  would  be  directly  proportional  to  the  number  of  such 
measures.  Now,  although  in  the  above  experiment  the  quantities  of  elec- 
tricity produced  each  time  are  equal,  yet  when  the  flannel  cap  is  applied 
each  time  to  an  insulated  conductor  it  does  not  necessarily  follow  that  the 
quantity  of  electricity  imparted  each  time 
is  directly  proportional  to  the  number  of 
such  applications. 

On  the  C.G.S.  system  the  unit  quantity 
of  electricity  is  that  amount  which,  acting, 
at  a  distance  of  one  centimetre  across  air, 
on  a  quantity  of  electricity  of  the  same 
kind  equal  to  itself,  would  repel  it  with  a 
force  equal  to  one  dyne  (709),  and  is  called 
a  Coulomb. 

734.  Laws  of  electrical  attractions 
and  repulsions. — The  laws  which  regu- 
late the  attractions  and  repulsions  of  elec- 
trified bodies  may  be  thus  stated  : — 

I.  The  repulsions  or    attractions  be- 
tween  two   electrified  bodies  are  in    the 
inverse  ratio  of  the  sqttares  of  their  dis- 
tance. 

II.  TJie  distance  remaining  the  same, 
the  force  of  attraction  or  repulsion  between 
two  electrified  bodies  is  directly  as  the  pro- 
dttct  of  the  quantities  of  electricity  with 
which  they  are  charged. 

These  laws  were  established  by  Coulomb,  by  means  of  the  torsion 
balance,  used  in  determining  the  laws  of  magnetic  attractions  and  repul- 
sions (704),  modified  in  accordance  with  the  requirements  of  the  case.  The 


-734]         Laws  of  Electrical  Attractions  and  Repulsions.          669 

-wire,  on  the  torsion  of  which  the  method  depends,  is  so  fine  that  a  foot 
weighs  only  -^  of  a  grain.  At  its  lower  extremity  there  is  a  fine  shellac  rod, 
np  (fig.  626),  at  one  end  of  which  is  a  small  disc  of  copper-foil,  n.  Instead 
•of  the  vertical  magnetic  needle,  there  is  a  glass  rod,  /,  terminated  by  a  gilt 
pith  ball,  /«,  which  passes  through  the  aperture  r.  The  scale  oc  is  fixed 
round  the  sides  of  the  vessel,  and  during  the  experiment  the  ball,  ;/z,  is 
opposite  the  zero  point  o.  The  micrometer  consists  of  a  small  graduated 
disc,  e,  movable  independently  of  the  tube  d,  and  of  a  fixed  index,  #, 
which  shows  by  how  many  degrees  the  disc  is  turned.  In  the  centre  of 
the  disc  there  is  a  small  button,  /,  to  which  is  fixed  the  wire  which  sup- 
ports np. 

i.  The  micrometer  is  turned  until  the  zero  point  is  opposite  the  index, 
and  the  tube  d  is  turned  until  the  knob  n  is  opposite  zero  of  the  graduated 
•circle  :  the  knob;/z  is  in  the  same  position,  and  thus  presses  against  n.  The 
knob  m  is  then  removed  and  electrified,  and  replaced  in  the  apparatus, 
through  the  aperture  r.  As  soon  as  the  electrified  knob  m  touches  «,  the 
latter  becomes  electrified,  and  is  repelled,  and  after  a  few  oscillations  re- 
mains constant  at  a  distance  at  which  the  force  of  repulsion  is  equal  to  the 
force  of  torsion.  In  a  special  experiment  Coulomb  found  the  angle  of  tor- 
sion between  the  two  to  be  36°  ;  and  as  the  force  of  torsion  is  proportional 
to  the  angle  of  torsion,  this  angle  represents  the  repulsive  force  between  m 
and  n.  In  order  to  reduce  the  angle  to  18°  it  was  necessary  to  turn  the  disc 
through  126°.  The  wire  was  twisted  126°  in  the  direction  of  the  arrow  at 
Its  upper  extremity,  and  1 8°  in  the  opposite  direction  at  its  lower  extremity, 
and  hence  there  was  a  total  torsion  of  144°.  On  turning  the  micrometer  in 
the  same  direction,  until  the  angle  of  deviation  was  8^°,  567°  of  torsion  was 
necessary.  Hence  the  whole  torsion  was  575^.  Without  sensible  error 
these  angles  of  deviation  may  be  taken  at  36°,  18°,  and  9°  ;  and  on  comparing 
them  with  the  corresponding  angles  of  torsion,  36°,  144°,  and  576°,  we  see 
that  while  the  first  are  as 

i  :  f :  -J, 
the  latter  are  .as 

i   :  4  :  16; 

that  is,  that  for  a  distance  £  as  great  the  angle  of  torsion  is  4  times  as  great, 
and  that  for  a  distance  \  as  great  the  repulsive  force  is  16  times  as  great. 

In  experimenting  with  this  apparatus  the  air  must  be  thoroughly  dry,  in 
order  to  diminish,  as  far  as  possible,  loss  of  electricity.  This  is  effected  by 
placing  in  it  a  small  dish  containing  chloride  of  calcium. 

The  experiments  by  which  the  law  of  attraction  is  proved  are  made  in 
much  the  same  manner,  but  the  two  balls  are  charged  with  opposite  electri- 
cities. A  certain  quantity  of  electricity  is  imparted  to  the  movable  ball,  by 
means  of  an  insulated  pin,  and  the  micrometer  moved  until  there  is  a  certain 
angle  below.  A  charge  of  electricity  of  the  opposite  kind  is  then  imparted 
to  the  fixed  ball.  The  two  balls  tend  to  move  towards  each  other,  but  are 
prevented  by  the  torsion  of  the  wire,  and  the  movable  ball  remains  at  a 
distance  at  which  there  is  equilibrium  between  the  force  of  attraction,  which 
draws  the  balls  together,  and  that  of  torsion,  which  tends  to  separate  them 
The  micrometer  screw  is  then  turned  to  a  greater  extent,  by  which  more 


670 


Frictional  Electricity. 


[734- 


torsion  and  a  greater  angle  between  the  two  balls  are  produced.  And  it  is 
from  the  relation  which  exists  between  the  angle  of  deflection  on  the  one 
hand,  and  the  angle  which  expresses  the  force  of  torsion  on  the  other,  that 
the  law  of  attraction  has  been  deduced. 

ii.  To  prove  this  second  law  let  a  charge  be  imparted  to  m  ;  n  being  in 
contact  with  it  becomes  charged,  and  is  repelled  to  a  certain  distance.  The 
angle  of  deflection  being  noted,  let  the  ball  ni  be  touched  by  an  insulated 
but  unelectrified  ball  of  exactly  the  same  size  and  kind.  If  in  this  way  half 
the  charge  on  one  of  the  balls  is  removed  it  will  be  found  that  the  amount 
of  torsion  necessary  to  maintain  the  balls  at  their  original  angular  distance 
is  half  what  it  was  before. 

The  two  laws  are  included  in  the  formula  F   =  -  — ,  where  F  is  the  force, 

a~ 

e  and  e'  the  quantities  of  electricity  on  any  two  surfaces,  and  d  the  distance 
between  them.  If  e  and  ef  are  of  opposite  electricities  the  action  is  one  of 
attraction,  while  if  they  are  the  same  it  is  a  repulsive  action. 

Coulomb  also  established  the  law  by  the  method  of  oscillations  which  is 
particularly  applicable  to  the  case  of  attraction.  His  apparatus  consists  of 
an  insulated  metal  sphere  (fig.  627),  and  at  a  little  distance  a  short  thin  rod 


Fig.  627. 

of  shellac  hung  by  a  silk  thread  and  with  a  disc  of  metal  foil  at  one  end,  the 
whole  being  enclosed  in  a  glass  cylinder  which  rested  on  an  insulating  plate. 
If  now  the  disc  is  charged  with  the  opposite  electricity  to  that  of  the  sphere, 
and  is  removed  from  its  position  of  equilibrium,  it  will  make  a  series  of 
oscillations  before  coming  to  rest.  It  can  be  proved  that  the  charge  on  the 
sphere  acts  as  if  it  were  concentrated  at  the  centre,  and  if  the  needle  is  short, 
the  distance  at  which  the  force  acts  will  be  that  from  the  centre  of  the  sphere 
to  the  thread  of  suspension.  As  in  the  case  of  magnetic  oscillations  we  may 
use  a  formula  analogous  for  the  time  of  a  single  oscillation  to  that  of  the 


-735]  Distribution  of  Electricity.  671 

pendulum;  that  is  /  =  TTA  /  ^_,  in  which  M  is  the  moment  of  inertia  of  the 

V    FL 

needle,  L  its  length,  and  F  the  force  of  attraction.  Now,  all  other  things  being 
the  same,  it  is  found  that  when  the  sphere  is  placed  at  varying  distances, 
d  and  d,,  the  times  of  oscillations,  /  and  /,  vary,  and  therefore  the  force 
varies,  and  the  relation  is  established  that  F  :  Y/  =  dl/  :  d12. 
^735.  Distribution  of  electricity. — When  an  insulated  sphere  of  conduct- 
ing material  is  charged  with  electricity,  the  electricity  passes  to  the  surface 
of  the  sphere,  and  forms  there  an  extremely  thin  layer.  If,  in  Coulomb's 
balance,  the  fixed  ball  be  replaced  by  another  electrified  sphere,  a  certain 
repulsion  will  be  observed.  If  then  this  sphere  be  touched  with  an  insulated 
sphere  identical  with  the  first,  but  in  the  neutral  state,  the  first  ball  will  be 
found  to  have  lost  half  its  electricity,  and  only  half  the  repulsion  will  be 
observed.  By  repeating  this  experiment  with  spheres  of  various  substances 
solid  and  hollow,  but  all  having  the  same  superficies,  the  result  will  be  the 
same,  excepting  that,  with  imperfectly  conducting  materials,  the  time  required 
for  the  distribution  will  be  greater.  From  this  it  is  concluded  that  the  dis- 
tribution of  electricity  depends  on  the  extent  of  the  surface,  and  not  on  the 
mass,  and,  therefore,  that  electricity  does  not  penetrate  into  the  interior,  but 
is  confined  to  the  surface.  This  conclusion  is  further  established  by  the 
following  experiments  : — 

i.  A  thin  hollow  copper  sphere  provided  with  an  aperture  of  about  an  inch 
in  diameter  (fig.  628),  and  placed  on  an  insulating  support,  is  charged  in  the  in- 
terior with  electricity.  When  the  carrier  or  proof  plane  (a  small  disc  of  copper- 
foil  at  the  end  of  a  slender  glass  or  shellac  rod)  is  applied  to  the  interior, 
and  is  then  brought  near  an  electroscope,  no  electrical  indications  are  pro- 
duced. But  if  the  proof  plane  is  applied 
to  the  electroscope  after  having  been  in 
contact  with  the  exterior,  a  considerable 
divergence  ensues. 

The  action  of  the  proof  plane  as  a 
measure  of  the  quantity  of  electricity  is 
as  follows  : — When  it  touches  any  surface 
the  proof  plane  becomes  confounded  with 
the  element  touched  ;  it  takes  in  some 
sense  its  place  relatively  to  the  electricity, 
or  rather,  it  becomes  itself  the  element 
on  which  the  electricity  is  diffused.  Thus 
when  the  proof  plane  is  removed  from 
contact  we  have  in  effect  cut  away  from 
the  surface  an  element  of  the  same 
thickness  and  the  same  extent  as  its  own, 
and  have  transferred  it  to  the  balance 
without  its  losing  any  of  the  electricity 
which  covered  it. 

ii.  A  hollow  globe,  fixed  on  an  insu- 
lating support,  is  provided  with  two  hemispherical  envelopes  which  fit  closely, 
and  can  be  separated  by  glass  handles.  The  interior  is  now  electrified  and 
the  two  hemispheres  brought  in  contact.  On  then  rapidly  removing  them 


Fig.  628. 


6/2 


Frictional  Electricity. 


[735- 


(fig.  629),  the  coverings  will  be  found  to  be  electrified,  while  the  sphere  is 
in  its  natural  condition. 


Fig.  629. 

iii.  The  distribution  of  electricity  on  the  surface  may  also  be  shown  by 
means  of  the  following  apparatus  : — It  consists  of  a  metal  cylinder  on  in- 
sulated supports  on 
which  is  fixed  a  long 
strip  of  tin-foil  which 
can  be  rolled  up  by 
means  of  a  small  insu- 
lating handle  (fig.  630). 
A  quadrant  electro- 
meter is  fitted  in 
metallic  communica- 
tion with  the  cylinder. 
When  the  sphere  is 
rolled  up,  a  charge  is 
imparted  to  the  cylin- 
der, by  which  a  certain 
divergence  is  produced. 
On  unrolling  the  tin- 
foil this  divergence 
gradually  diminishes, 
and  increases  as  it  is 
again  rolled  up.  The  / 
quantity  of  electricity 
remaining  the  same, 
the  electrical  force,  on 
each  unit  of  surface,  is 
therefore  less  as  the  Fig.  63o. 

surface  is  greater. 

iv.  The  following  ingenious  experiment   by  Faraday  further  illustrates 


-736] 


Electric  Density. 


6/3 


this  law : — A  metal  ring  is  fitted  on  an  insulated  support,  and  a  conical 
gauze  bag,  such  as  is  used  for  catching  butterflies,  is  fitted  to  it  (ftg.  631). 

By  means  of  a  silk  thread,  the  bag  can  be 
drawn  inside  out.  After  electrifying  the  bag, 
it  is  seen  by  means  of  a  proof  plane  that  the 
electricity  is  on  the  exterior  ;  but  if  the  positions 
are  reversed  by  drawing  the  bag  inside  out, 
so  that  the  interior  has  now  become  the  ex- 
terior, the  electricity  will  still  be  found  on  the 
exterior. 

v.  The  same  point  maybe  further  illustrated 
by  an  experiment  due  to  Terquem.  A  bird-cage, 
preferably  of  metal  wire,  is  suspended  by  insu- 
lators, and  contains  either  a  gold-leaf  electro- 
scope or  pieces  of  Dutch  metal,  feathers,  pith 
balls,  &c.  When  the  cage  is  connected  with 
an  electrical  machine,  the  articles  in  the  interior 
are  quite  unaffected,  although  strong  sparks  may 
be  taken  from  the  outside.  Bands  of  paper  may 

be  fixed  to  the  inside  ;  while  those  fixed  to  the  outside  diverged  widely.  A 
bird  in  the  inside  is  quite  unaffected  by  the  charge  or  discharge  of  the 
electricity  of  the  cage. 

The  property  of  electricity,  of  accumulating  on  the  outside  of  bodies, 
is  ascribed  to  the  repulsion  which  the  particles  exert  on  each  other.  Electri- 
city tends  constantly  to  pass  to  the  surface  of  bodies,  whence  it  continually 
tends  to  escape,  but  is  prevented  by  the  resistance  of  the  feebly  conducting 
atmosphere. 

To  the  statement  that  electricity  resides  on  the  surface  of  bodies,  two 
exceptions  may  be  noted.  When  two  opposite  electricities  are  discharged 
through  a  wire — a  phenomenon  which,  when  continuous,  forms  an  electrical 
current — the  discharge  is  effected  throughout  the  whole  mass  of  the  con- 
ductor. Also  a  body  placed  inside  another  may,  if  insulated  from  it,  receive 
charges  of  electricity.  On  this  depends  the  possibility  of  electrical  experi- 
ments in  ordinary  rooms. 

\736.  Electric  density. — On  a  metal  sphere  the  distribution  of  the 
electricity  will  be  uniform  in  every  part,  simply  from  its  symmetry.  This 
can  be  demonstrated  by  means  of  the  proof  plane  and  the  torsion  balance. 
A  metal  sphere  placed  on  an  insulating  support  is  electrified,  and 
touched  at  different  parts  of  its  surface  with  the  proof  plane,  which  'each 
time  is  applied  to  the  movable  needle  of  the  torsion  balance.  As  in  all 
cases  the  torsion  observed  is  sensibly  the  same,  it  is  concluded  that  the 
proof  plane  each  time  receives  the  same  quantity  of  electricity.  In  the 
case  of  an  elongated  ellipsoid  (fig.  632)  it  is  found  that 'the  distribution 
of  electricity  is  different  at  different  points  of  the  surface.  The  electricity 
accumulates  at  the  most  acute  points.  This  is  demonstrated  by  succes- 
sively touching  the  ellipsoid  at  different  parts  with  the  proof  plane,  and 
then  bringing  this  into  the  torsion  balance.  By  this  means  Coulomb  found 
that  the  greatest  deflection  was  produced  when  the  proof  plane  had  been  in 
contact  with  the  point  a,  and  the  least  by  contact  with  the  middle  space  e. 

x  x 


6/4 


Frictional  Electricity. 


[736- 


The  electric  density  or  electric  thickness  is   the   term  used  to  express 
the  quantity  of  electricity  found  at   any  moment   on  a  given  surface.      If 

S  represents  the 
surface  and  Q  the 
quantity  of  elec- 
tricity on  that  sur- 
face, then,  assuming 
that  the  electricity 
is  equally  distri- 
buted, its  electrical 
density  is  equal 

to  -^. 

Coulomb  found, 
by  quantitative  ex- 
periments, that  in 
an  ellipsoid  the 
density  of  the  elec- 
tricity, at  the  equa- 
tor of  the  ellipsoid,  is  to  that  at  the  ends  in  the  same  ratio  as  the  length  of 
the  minor  to  the  major  axis.  On  an  insulated  cylinder,  terminated  by  two 
hemispheres,  the  density  of  the  electrical  layer  at  the  ends  is  greater  than 
in  the  middle.  In  one  case,  the  ratio  of  the  two  densities  was  found  to  be 
as  2-3  :  i.  On  a  circular  disc  the  density  is  greatest  at  the  edges. 
\  737-  Force  outside  an  electrified  body. — The  force  F  which  a  sphere, 
charged  with  a  quantity  of  electricity  Q,  exerts  on  a  point  at  a  distance  d 

from  its  centre,  is  ^  ;  this  is  equal  to  -^    if  S  is  the  area  of  the  sphere,  and 

p  the  density  of  electricity  on  the  unit  of  surface. 
Now  the  area  of  the  sphere  is  4?rR2  ;  and  if  the  distance 
d  is  equal  to  the  radius  R,  then  the  force  at  the  surface 


This  holds  also  if  the  point  considered  is  at  a  very 
small  distance  just  outside  the  sphere.     Let  a  small 
^--      segment  ab  be  cut  in  a  sphere  (fig.  633).     Then  its 
action  on  a  point  p  just  inside  the  sphere  will  be  exactly 
neutralised  by  the  action  of  the  rest  of  the  sphere  acb 

on  this  point,  since  there  is  no  electrical  force  inside  a  sphere  (735)  ;  that 
is,  the  action  of  the  two  portions  is  equal,  but  in  opposite  directions.  Now 
for  a  point/,  just  outside  the  sphere,  the  actions  will  also  be  equal,  but  in 
the  same  directions.  But  the  total  action  of  the  whole  sphere  is  4?rp  :  hence 
the  action  of  each  portion  is  half  of  this  ;  that  is,  2irp. 

It  may  be  shown  in  like  manner  that  the  whole  force  of  any  closed  con- 
ductor is  47rp. 

On  an  insulated  conductor,  where  the  electricity  is  in  equilibrium,  a 
particle  of  electricity  will  have  no  tendency  to  move  along  the  surface,  for 
otherwise  there  would  be  no  equilibrium.  But  the  electricity  does  exert  a 
pressure  on  the  external  non-conducting  medium,  which  is  always  directed 
outwards,  and  is  called  the  electrical  tension  or  pressure. 


-738]  Potential  67$ 

The  amount  of  this  pressure  is  2/rp2  for  the  unit  area,  p  being  the  elec- 
trical density  at  the  point  considered.  It  is  therefore  proportional  to  the 
square  of  the  density.  The  effect  of  this,  for  instance,  on  a  soap-bubble, 
if  electrified  with  either  kind  of  electricity,  is  to  enlarge  it.  In  any  case 
the  electrification  constitutes  a  deduction  from  the  amount  of  atmospheric 
pressure  which  the  body  experiences  when  unelectrified. 

The  term  electric  density  and  electrical  tension  are  often  confounded. 
The  latter  ought  rather  to  be  restricted,  as  Maxwell  proposed,  to  express  the 
state  of  strain  or  pressure  exerted  upon  a  dielectric  in  the  neighbourhood  of 
an  electrified  body  ;  a  strain  which,  if  continually  increased,  tends  to  disrup- 
tive discharge.  Electric  tension  may  thus  be  compared  to  the  strain  on  a 
rope  which  supports  a  weight ;  and  the  dielectric  medium  which  can  support 
a  certain  tension  and  no  more  is  said  to  have  a  certain  electrical  strength  in 
the  same  sense  as  a  rope  which  bears  a  certain  weight  without  breaking  is 
said  to  have  a  certain  strength. 

V^£38.  Potential. — In  the  experiment  (fig.  633),  instead  of  applying  the 
test  sphere  directly  to  the  large  sphere,  let  the  two  be  placed  at  a  consider- 
able distance  from  each  other,  and  let  them  be  connected  by  a  long  thin  wire, 
and  then,  detaching  the  small  sphere,  let  the  quantity  upon  it  be  measured 
by  the  torsion  balance  :  the  angle  of  deflection  will  show  that  this  quantity 
is  the  same  whatever  part  of  the  large  sphere  be  touched,  as  must  indeed  be 
the  case,  owing  to  symmetry  ;  but  the  amount  of  this  charge  will  be  mate- 
rially different  from  that  in  which  the  small  sphere  is  placed  in  direct  contact 
with  the  larger  one.  Hence  the  quantity  of  electricity  removed  differs 
according  to  the  mode  in  which  connection  is  made. 

If  now  this  experiment  be  repeated  with  the  ellipsoid,  it  will  be  found 
that  whatever  point  of  this  is  put  in  distant  connection  with  the  proof  sphere 
by  the  long  wire,  the  charge  which  the  small  sphere  acquires  is  everywhere 
the  same  ;  although,  as  we  have  seen,  the  proof  sphere  would  remove  very 
different  quantities  of  electricity  according  to  the  part  where  it  touches. 

Here,  then,  we  are  dealing  with  experimental  facts  which  our  previous 
notions  are  insufficient  to  explain.  It  is  manifest  that  the  difference  in  the 
results  depends  neither  on  the  total  charge  nor  on  the  density.  We  require 
the  introduction  of  a  new  conception,  which  is  that  of  electrical  potential. 
Introduced  originally  into  electrical  science  by  Green,  out  of  considerations 
arising  from  the  mathematical  treatment  of  the  subject,  the  use  of  the  term 
'potential'  is  justified  and  recommended  by  the  clearness  with  which  it  brings 
out  the  relations  of  electricity  to  work. 

We  have  already  seen,  that  in  order  to  lift  a  certain  mass  against  the 
attraction  of  gravitation  (59-62)  there  must  be  a  definite  expenditure  of 
work,  and  the  equivalent  of  this  work  is  met  with  in  the  energy  which  the 
lifted  mass  retains,  or  what  is  called  the  potential  energy  of  position. 

Let  us  now  suppose  that  we  have  a  large  insulated  metal  sphere  charged 
with  positive  electricity,  and  that,  at  a  distance  which  is  very  great  in  com- 
parison with  the  size  of  the  sphere,  there  is  a  small  insulated  sphere  charged 
with  the  same  kind  of  electricity.  If  now  we  move  the  small  sphere  to  any 
given  point  nearer  the  larger  one,  we  must  do  a  certain  amount  of  work  upon 
it  to  overcome  the  repulsion  of  the  two  electricities. 

The  work  required  to  be  done  against  electrical  forces,  in  order  to  move 

x  x  2 


676  Frictional  Electricity.  [738- 

the  unit  of  positive  electricity  from  an  infinite  distance  to  a  given  point  in 
the  neighbourhood  of  an  electrified  conductor,  is  called  the  potential  at  this 
point.  If,  in  the  above  case,  the  larger  sphere  were  charged  with  negative 
electricity,  then  instead  of  its  being  needful  to  do  work  in  order  to  bring  a 
unit  of  positive  electricity  towards  it,  work  would  be  done  by  electrical  at- 
traction, and  the  potential  of  the  point  near  the  charged  sphere  would  thus 
be  negative. 

The  potential  at  any  point  may  also  be  said  to  be  the  work  done  against 
electrical  force,  in  moving  unit  charge  of  negative  electricity  from  that  point 
to  an  infinite  distance. 

The  amount  of  work  required  to  move  the  unit  of  positive  electricity 
against  electrical  force,  from  any  one  position  to  any  other,  is  equal  to  the 
excess  of  the  electrical  potential  of  the  second  position  over  the  electrical 
potential  of  the  first.  This  is,  in  effect,  the  same  as  what  has  been  said 
above,  for  at  an  infinite  distance  the  potential  is  zero. 

We  cannot  speak  of  potential  in  the  abstract,  any  more  than  we  can 
speak  of  any  particular  height,  without  at  least  some  tacit  reference  to  a 
standard  of  level.  Thus,  if  we  say  that  such  and  such  a  place  is  300  feet 
high,  we  usually  imply  that  this  height  is  measured  in  reference  to  the  level 
of  the  sea.  So,  too,  we  refer  the  longitude  of  a  place  to  some  definite 
meridian,  such  as  that  of  Greenwich,  either  expressly  or  by  implication. 

In  like  manner  we  cannot  speak  of  the  potential  of  a  mass  of  electricity 
without,  at  least,  an  implied  reference  to  a  standard  of  potential.  This 
standard  is  usually  the  earth,  which  is  taken  as  being  zero  potential.  If  we 
speak  of  the  potential  at  a  given  point,  the  difference  between  the  potential 
at  this  point  and  the  earth  is  referred  to. 

If,  in  the  imaginary  experiment  described  above,  we  move  the  small  sphere 
round  the  large  electrified  one  always  at  the  same  distance,  no  work  is  done 
by  or  against  it  for  the  purpose  of  overcoming  or  of  yielding  to  electrical  at- 
tractions or  repulsions,  just  as  if  we  move  a  body  at  a  certain  constant  level 
above  the  earth's  surface,  no  work  is  done  upon  it  as  respects  gravitation. 
An  imaginary  surface  drawn  in  the  neighbourhood  of  an  electrified  body, 
such  that  a  given  charge  of  electricity  can  be  moved  from  any  one  point  of 
it  to  any  other  without  any  work  being  done  either  by  or  against  electrical 
force,  is  said  to  be  an  equipotential  surface.  Such  a  surface  may  be  described 
as  having  everywhere  the  same  electrical  level ;  and  the  notion  of  bodies  at 
different  electrical  levels,  in  reference  to  a  particular  standard,  is  analogous 
to  that  of  bodies  at  different  potentials.  In  the  case  of  an  insulated  electri- 
fied sphere  the  successive  equipotential  surfaces  would  be  successive  shells 
of  gradually  increasing  radii,  like  the  coats  of  an  onion.  The  space  about 
an  electrified  body  or  electrified  system  is  called  the  electrical  field.  The 
fall  of  potential  from  one  equipotential  surface  to  another  is  most  rapid  in 
the  direction  of  the  perpendiculars  to  the  two  surfaces.  These  perpendiculars 
represent  the  lines  of  electrical  force,  the  'lines  offeree'  of  Faraday,  or  the 
*  lines  of  induction '  of  Maxwell.  On  the  surface  of  an  insulated  electrified 
sphere  at  a  distance  from  other  conductors,  these  lines  of  force  are  perpen- 
dicular to  the  surface  of  the  sphere. 

As  water  only  flows  from  places  at  a  higher  level  to  places  at  a  lower 
level,  so  also  electricity  only  passes  from  places  at  a  higher  to  places  at  a 


-739]  Electrical  Capacity.  677 

lower  potential.  If  an  electrified  body  is  placed  in  conducting  communica- 
tion with  the  earth,  electricity  will  flow  from  the  body  to  the  earth,  if  the 
body  is  at  a  higher  potential  than  the  earth  ;  and  from  the  earth  to  the  body, 
if  the  body  is  at  a  lower  potential,  and  its  flow  will  be  proportional  to  the 
difference  of  potential.  If  the  potential  of  a  body  is  higher  than  that  of  the 
earth,  it  is  said  to  have  a  positive  potential ;  and  if  at  a  lower  potential,  a 
negative  potential.  A  body  charged  with  free  negative  electricity  is  one  at 
lower  potential  than  the  earth  ;  one  charged  with  free  positive  electricity  is 
at  z.Jh,igher  potential. 

"^739.  Electrical  capacity. — The  capacity  of  any  conductor  may  be 
measured  by  the  quantity  of  electricity  which  it  can  acquire  when  placed 
in  contact  with  a  body  which  charges  it  to  unit  electrical  potential. 

We  may  illustrate  the  relation  between  capacity  and  potential  by  refer- 
ence to  the  analogous  phenomenon  of  heat.  In  the  interchange  of  heat 
between  bodies  of  different  temperatures  the  final  result  is  that  heat  only 
passes  from  bodies  of  higher  to  bodies  of  lower  temperature.  So  also  elec- 
tricity only  passes  from  bodies  of  higher  to  bodies  of  lower  potential. 
Potential  is,  as  regards  electricity  what  temperature  is  as  regards  heat,  and 
might  indeed  be  called  electrical  temperature.  We  may  have  a  small 
quantity  of  heat  at  a  very  high  temperature.  Thus  a  short  thin  wire  heated 
to  incandescence  has  a  far  higher  heat  potential,  or  temperature,  than  a 
bucket  of  warm  water.  But  the  latter  will  have  a  far  larger  quantity.  A 
flash  of  lightning  represents  electricity  at  a  very  high  potential,  but  the 
quantity  is  small. 

The  relation  between  electrical  potential  and  density  may  be  further 
illustrated  by  reference  to  the  head  of  water  in  a  reservoir.  The  pressure 
is  proportional  to  the  depth ;  the  potential  is  everywhere  the  same.  For 
suppose  we  want  to  introduce  an  additional  pound  of  water  into  the  reservoir, 
the  same  amount  of  work  is  required  whether  the  water  be  forced  in  at  the 
bottom  or  be  poured  in  at  the  top. 

If  a  hole  be  made  very  near  the  top  of  the  reservoir,  a  quantity  of  water 
in  falling  to  the  ground  would  generate  an  amount  of  heat  proportional  to 
the  fall.  If  the  same  quantity  escaped  through  a  hole  near  the  bottom, 
it  would  not  produce  so  much  heat  by  direct  fall  ;  but  it  will  possess  a 
certain  velocity,  the  destruction  of  which  will  produce  a  quantity  of  heat 
which,  added  to  that  produced  by  the  fall,  will  give  exactly  as  much  as 
the  other. 

When  the  charge  or  quantity  of  electricity  imparted  to  a  body  increases, 
the  potential  increases  in  the  same  ratio  ;  so  that,  calling  Q  the  quantity  of 
electricity,  C  the  capacity,  and  V  the  potential,  we  have  Q  =  CV  ;  that  is  to 
say,  that  the  charge,  or  quantity  of  electricity  that  any  body  possesses,  is 
the  product  of  the  potential  into  the  capacity. 

Now  for  a  sphere  whose  radius  is  R  the  potential  V^S,  from  which  we 

R 

get  C  =  R  ;  that  is,  that  the  capacity  of  a  sphere  is  equal  to  its  radius. 

While  there  is  a  close  analogy  between  heat  and  electricity,  as  regards 
capacity,  there  are  important  differences  ;  thus  the  capacity  of  a  body  for 
heat  is  influenced  by  the  temperature  (457),  being  greater  at  higher  tem- 
peratures, while  the  capacity  of  a  body  for  electricity  does  not  depend  on 


678  Frictional  Electricity.  [739- 

the  potential.  Again,  the  calorific  capacity  depends  solely  on  the  mass  of  a 
body,  and  in  bodies  of  the  same  material  and  shape  is  proportional  to  the 
cube  of  homologous  dimensions  :  the  capacity  for  electricity  is  directly  pro- 
portional to  such  dimensions,  and  not  to  the  weight  or  volume.  Calorific 
capacity  is  proportional  to  a  specific  coefficient,  which  varies  with  the 
material,  but  is  independent  of  its  shape  ;  while  electrical  capacity  varies 
with  the  shape  of  a  body,  but  not  with  its  material,  provided  the  electricity 
can  move  freely  upon  it.  Calorific  capacity  is  unaffected  by  the  proximity 
of  other  bodies,  while  the  electrical  capacity  depends  on  the  position  and 
shape  of  all  the  adjacent  conductors. 

If  we  have  a  series  of  bodies  at  a  considerable  distance  from  each  other, 
whose  capacities  and  potentials  are  respectively  <:,  c',  c",  &c.,  and  -z/,  -z/,  T/',  &c., 
then,  if  they  are  all  connected  by  fine  wires  of  no  capacity,  they  all  instantly 
acquire  the  same  potential  V,  which  is  determined  by  the  equation 

cv  +  c'v'  +  c"v" 


The  analogy  of  this  to  the  equalisation  of  temperature  which  takes  place 
when  bodies  at  different  temperatures  are  mixed  together  is  directly  apparent 
(449).  It  may  be  further  illustrated  by  supposing  a  series  of  tubes  of  different 
diameters,  and  connected  by  very  narrow  tubes,  but  in  which  are  stopcocks 
to  cut  off  communication.  If,  while  in  this  state,  water  be  poured  into  the 
tubes  to  different  heights,  it  will  be  manifest  that  they  will  hold  very  various 
quantities  of  water.  If,  however,  the  stopcocks  are  opened,  the  tubes  will 
still  contain  quantities  of  water  proportional  to  their  capacities,  but  the  level 
or  potential  in  all  will  be  the  same. 

740.  Measurement  of  capacity  and  potential.  —  We  may  use  Cou- 
lomb's balance  for  the  purpose  of  measuring  the  capacity  C,  or  the  potential 
V,  of  a  body  charged  with  electricity.  For  this  purpose  the  body  in  question 
is  placed,  by  means  of  a  long  fine  wire  of  no  capacity,  in  distant  contact  with 
a  small  neutral  insulated  sphere  of  known  radius  r.  This  small  sphere  is 
then  applied  to  the  torsion  balance,  and  its  charge  q  =  iv  is  measured.  Now, 
since  the  original  charge  on  the  sphere  is  Q  =  CV,  after  contact  with  the 
small  sphere,  which  is  neutral,  the  system  will  have  a  new  potential  or  elec- 
trical level,  -z/,  such  that  CV=  (C  +  r)  v.  Restoring  now  the  small  sphere  to 
the  neutral  state,  and  repeating  the  experiment  and  the  measurement,  we  shall 
then  get  a  second  value  rz/,  from  which  we  have  the  equation  C-z/  =  (C  +•  r)  ?/. 

Combining  and  reducing,  we  get  the  ratio  V  -  -7,  which,  seeing  that  rv  and 

rv'  are  numerical  values,  leads  directly  to  the  desired  result. 

In  like  manner  it  is  easy  to  determine  the  capacity  by  obvious  transfor- 
mations of  these  equations. 

It  will  thus  be  seen  that  this  process  of  determining  potential  is  analogous 
to  that  of  determining  temperature  by  means  of  a  thermometer  ;  and  the 
proof  sphere  plays  the  part,  as  it  were,  of  an  electrical  thermometer.  It  may 
be  observed  that  in  the  case  of  heat  we  pass  from  the  conception  of  temperature 
to  that  of  quantity  of  heat,  while  with  electricity,  starting  with  the  fact  of 
quantity,  or  charge  of  electricity,  we  arrive  at  the  conception  of  potential  of 
electricity. 


-74:2]  Action  of  Points.  $79 

741.  Potential  of  a  sphere.—  If  q,  qf  and  q"  are  any  masses  of  electri- 
city on  the  surface  of  an  insulated  conducting  sphere,  and  d  d',  and  d"  their 

respective  distances  from  any  point  of  the  interior  of  the  sphere,  then  -  " 
and  ^  are  the  values   of  the  potentials  v,  vf,  and  v'f  which  they  would 

severally  produce  at  this  point.     Let  the  point  in  question  be  the  centre, 
and  let  Q  be  the  sum  of  the  whole  quantities  ;  then,  V,  the  potential  of  the 

sphere,  equals    ^,  R  being  the  radius. 

If  there  be  a  sphere,  or  uniform  spheroidal  shell  of  matter,  which  acts 
according  to  the  inverse  square  of  the  distance,  then  the  total  action  of  this 
sphere  is  the  same  as  if  the  whole  matter  were  concentrated  at  the  centre. 
This  was  first  proved  by  Newton  in  the  case  of  gravitation  ;  but  it  also 
applies  to  electricity,  and  hence,  in  calculating  the  potential  at  any  point  out- 
side a  sphere  possessing  a  uniform  charge,  we  need  only  consider  its  dis- 
tance from  the  centre,  and  for  such  a  case  we  may  write  the  value  of  the 

potential  V  =  -7. 

If  a  charge  of  electricity,  O,  be  imparted  to  two  insulated  conducting 
spheres  whose  radii  are  respectively  r  and  r7,  and  which  are  connected  by 
a  long  fine  wire,  the  capacity  of  which  may  be  neglected,  the  electricity 
will  distribute  itself  over  the  two  spheres,  which  will  possess  the  charges 
q  and  q'  ;  that  is,  0f  +  j7/i»Q.  (i)  The  whole  system  will  be  at  the  same 


potential  V,  such  that  V  =    =    .     (2)    Combining  these  two  equations  and 
reducing,  we  get  for  the  quantities  q  and  qf  on  each  sphere  q  =    ^—  >    and 


r+r> 

Now,  since  the  diameter  of  any  sphere  with  which  we  can  experiment  is 
infinitely  small  compared  with  that  of  the  earth,  it  follows  that  when  a  sphere 
is  connected  with  the  earth  by  a  fine  wire  the  quantity  of  electricity  which 
it  retains  is  infinitely  small. 

For  the  densities  on  the  two  spheres  we  have  d=~2-  and^  =     ^      from 

/ 


which  by  equation  (2)  it  is  readily  deduced  that  d  :  d'  =>  r'  :  r  ;  that  is,  that 
the  electrical  densities  on  two  spheres  in  distant  connection  are  inversely  as 
the  radii.  If,  for  instance,  a  fine  wire  be  connected  with  a  charged  insulated 
sphere,  the  distant  pointed  end  of  the  wire  may  be  regarded  as  a  sphere 
with  an  infinitely  small  radius,  and  thus  the  density  upon  it  would  be 
infinitely  great. 

y  742.  Action  of  points.  —  We  have  just  seen  that  on  a  point  in  connection 
with  a  conductor  charged  with  electricity  the  density  may  be  considered  to 
be  infinitely  great,  but  the  greater  the  density  the  greater  will  be  the  tendency 
of  electricity  to  overcome  the  resistance  of  the  air,  and  escape.  If  the  hand 
be  brought  near  a  point  on  an  electrified  conductor  a  slight  wind  is  felt  ;  and 
if  the  disengagement  of  electricity  takes  place  in  the  dark  a  luminous  brush 
is  seen.  If  an  electrified  conductor  is  to  retain  its  electricity  all  sharp  points 


680  Frictional  Electricity.  [742- 

and  edges  must  be  avoided  ;  on  the  other  hand,  to  facilitate  the  outflow  of 
electricity  in  apparatus  and  experiments,  frequent  use  is  made  of  this  action 
of  points. 

743.  loss  of  electricity. — Experience  shows  that  electrified  bodies 
gradually  lose  their  electricity,  even  when  placed  on  insulating  supports. 
This  loss  is  mainly  due  to  the  insulating  supports.  The  charge  is  gradually 
dissipated  in  consequence  of  the  electricity  either  passing  through  the  sup- 
ports or  creeping  over  the  surface.  All  substances  conduct  electricity  in 
.some  degree  ;  those  which  are  termed  insulators  are  simply  very  bad  con- 
ductors. An  electrified  conductor  resting  on  supports  must  therefore  lose  a 
certain  quantity  of  its  electricity — either  by  penetration  into  its  mass  or  along 
the  surface.  This  loss  of  electricity  is  a  main  cause  of  difficulty  in  experi- 
ments on  the  quantitative  laws  of  electricity. 

The  loss  varies  with  the  electric  density,  and  increases  with  the  hygro- 
metric  state. 

It  does  not  seem  that  the  loss  from  this  latter  cause  is  due  to  a  direct 
conductivity  by  even  moist  air. 

Sir  W.  Thomson  ascribes  the  greater  part  of  the  loss  ol  electricity  to  the 
conducting  layer  of  moisture  which  covers  the  supports  ;  and  he  finds  that 
in  comparison  with  this  the  direct  loss  by  moist  air  is  inconsiderable. 

Brown  shellac  or  ebonite  is  the  best  insulator  ;  glass  is  a  hygroscopic 
substance,  and  must  be  dried  with  great  care.  It  is  best  covered  with  a  thin 
layer  of  shellac  varnish,  as  has  already  been  stated. 


-744] 


Electricity  by  Influence  or  Induction. 


68 1 


CHAPTER   III. 

ACTION   OF   ELECTRIFIED   BODIES   ON   BODIES    IN   THE   NATURAL   STATE. 
INDUCED    ELECTRICITY.      ELECTRICAL  MACHINES. 

Electricity  by  influence  or  induction — An  insulated  conductor, 
charged  with  either  kind  of  electricity,  acts  on  bodies  in  a  neutral  state 
placed  near  it  in  a  manner  analogous  to  that  of  the  action  of  a  magnet  on 
-soft  iron  ;  that  is,  it  decomposes  the  neutral  fluid,  attracting  the  opposite 


Fig-  634- 

and  repelling  the  like  kind  of  'electricity.     The  action  thus  exerted  is  said  to 
take  place  by  influence  or  induction. 

The  phenomena  of  induction  may  be  demonstrated  by  means  of  a  brass 
cylinder  placed  on  an  insulating  support,  and  provided  at  its  extremities 
with  two  small  electric  pendulums,  which  consist  of  pith  balls  suspended  by 
linen  threads  (fig.  634).  If  this  apparatus  is  placed  near  an  insulated  con- 
ductor m,  charged  with  either  kind  of  electricity — for  instance,  the  conductor 
of  an  electrical  machine,  which  is  charged  with  positive  electricity — the 
natural  electricity  of  the  cylinder  is  decomposed,  free  electricity  will  be 
developed  at  each  end,  and  both  pendulums  will  diverge.  If,  while  they  still 
diverge,  a  stick  of  sealing-wax,  excited  by  friction  with  flannel,  be  approached 
to  that  end  of  the  cylinder  nearest  the  conductor,  the  corresponding  pith 
ball  will  be  repelled,  indicating  that  it  is  charged  with  the  same  kind  of 
electricity  as  the  sealing-wax — that  is,  with  negative  electricity  ;  while  if  the 
excited  sealing-wax  is  brought  near  the  other  ball  it  will  be  attracted,  showing 
that  it  is  charged  with  positive  electricity.)!  If,  further,  a  glass  rod  excited 


682  Frictional  Electricity.  [744- 

by  friction  with  silk,  and  therefore  charged  with  positive  electricity,  be  ap- 
proached to  the  end  nearest  the  conductor,  the  pendulum  will  be  attracted  ; 
while  if  brought  near  the  other  end,  the  corresponding  pendulum  will  be  re- 
pelled. If  the  influence  of  the  charged  conductor  be  suppressed,  either  by 
removing  it,  or  placing  it  in  communication  with  the  ground,  the  separated 
electricities  will  recombine,  and  the  pendulums  exhibit  no  divergence. 
^The  cause  of  this  phenomenon  is  obviously  a  decomposition  of  the  neutral 
electricity  of  the  cylinder,  by  the  free  positive  electricity  of  the  conductor  ; 
the  opposite  or  negative  electricity  being  attracted  to  that  end  of  the  cylinder 
nearest  the  conductor,  while  the  similar  electricity  is  repelled  to  the  other 
end.  Between  these  two  extremities  there  is  a  space  destitute  of  free 
electricity.  This  is  seen  by  arranging  on  the  cylinders  a  series  of  pairs  of 
pith  balls  suspended  by  threads.  The  divergence  is  greatest  at  each 
extremity,  and  there  is  a  line  at  which  there  is  no  divergence  at  all,  which  is 
called  the  neutral  line.  The  two  electricities,  although  equal  in  quantity,  are 
not  distributed  over  the  cylinder  in  a  symmetrical  manner  ;  the  attraction 
which  accumulates  the  negative  electricity  at  one  end  is,  in  consequence  of 
the  greater  nearness,  greater  than  the  repulsion  which  drives  the  positive 
electricity  to  the  other  end,  and  hence  the  neutral  line  is  nearer  one  end  than 
the  other.  Nor  is  the  electricity  induced  at  the  two  ends  of  the  cylinder 
under  the  same  conditions.  That  which  is  repelled  to  the  distant  extremity 
is  free  to  escape  if  a  communication  be  made  with  the  ground ;  whilst,  on 
the  other  hand,  the  unlike  electricity  which  is  attracted  is  held  bound  or 
captive  by  the  inducing  action  of  the  electrified  body.  Even  if  contact  be 
made  with  the  ground  on  the  face  of  the  cylinder  adjacent  to  the  inducing 
body,  the  electricity  induced  on  that  face  will  not  escape.  The  repelled 
electricity,  however,  on  the  distant  surface  is  not  thus  bound  :  it  is  free  to 
escape  by  any  conducting  channel,  and  hence  will  immediately  disappear 
wherever  contact  be  made  between  the  ground  and  the  cylinder.  Both  the  pith 
balls  will  collapse,  and  all  signs  of  electricity  on  the  cylinder  depart  with  the 
escapeof  the  repelled  or  free  electricity.  But  now,  if  communication  with 
the  ground  be  broken,  and  the  inducing  body  be  discharged  or  removed  to  a 
considerable  distance,  the  attracted  or  bound  electricity  is  itself  set  free,  and 
diffusing  over  the  whole  cylinder  causes  the  pith  balls  again  to  diverge,  but 
now  with  the  opposite  electricity  to  that  of  the  original  inducing  body.  The 
reason  for  the  escape  of  the  repelled  electricity  is  as  follows  : — If  the 
cylinder  be  placed  in  connection  with  the  ground,  by  metallic  contact  with 
the  posterior  extremity,  and  the  charged  conductor  be  still  placed  near 
the  anterior  extremity,  the  conductor  will  exert  its  inductive  action  as  before. 
But  it  is  now  no  longer  the  conductor  alone  which  is  influenced.  It  is  a 
conductor  consisting  of  the  conductor  itself,  the  metallic  wire,  and  the  whole 
earth.  The  neutral  line  will  recede  indefinitely,  and,  since  the  conductor  has 
become  infinite,  the  quantity  of  neutral  fluid  decomposed  will  be  increased. 
Hence,  when  the  posterior  extremity  is  placed  in  contact  with  the  ground, 
the  pendulum  at  the  anterior  extremity  diverges  more  widely.  If  the  con- 
necting-rod be  now  removed,  neither  the  quantity  nor  the  distribution  will 
be  altered  ;  and  if  the  conductor  be  removed,  or  be  discharged,  a  charge 
of  negative  electricity  will  be  left  on  the  cylinder.  It  will,  uin  fact,  remain 
charged  with  electricity,  the  opposite  of  that  of  the  charged  conductor.  Even 


-745]  Faraday's  Experiments.  683 

if,  instead  of  connecting  the  posterior  extremity  of  the  cylinder  with  the 
ground,  any  other  part  had  been  so  connected,  the  general  result  would  have 
been  the  same.  All  the  parts  of  the  cylinder  would  be  charged  with  nega- 
tive electricity,  and,  on  interrupting  the  communication  with  the  earth,  would 
remain  so  charged. 

Thus  a  body  can  be  charged  with  electricity  by  induction  as  well  as  by 
conduction.  But,  in  the  latter  case,  the  charging  body  loses  part  of  its 
electricity,  which  remains  unchanged  in  the  former  case.  The  electricity 
imparted  by  conduction  is  of  the  same  kind  as  that  of  the  electrified 
body,  while  that  excited  by  induction  is  of  the  opposite  kind.  To  impart 
electricity  by  conduction,  the  body 
must  be  quite  insulated  ;  while  in  the 
case  of  induction  it  must  be  in  con- 
nection with  the  earth — at  all  events 
momentarily. 

A  body  electrified  by  induction  acts 
in  turn  on  bodies  placed  near  it,  sepa- 
rating the  two  fluids  in  a  manner 
shown  by  the  signs  on  the  sphere. 

What  has  here  been  said  has  re- 
ference to  the  inductive  action  exerted 
on  good  conductors.  Bad  conductors 
are  not  so  easily  acted  upon  by  in- 
duction, owing  to  the  great  resistance 
they  present  to  the  circulation  of  elec- 
tricity ;  but,  when  once  charged,  the 
electric  state  is  more  permanent. 

This  is  analogous  to  what  is  met     j^ 
with  in  magnetism  ;  a  magnet  instan-    1| 
taneously  magnetises  a  piece  of  soft 
iron,  but  this  is  only  temporary,  and 
depends  on  the  continuance  of  the 
action  of  the  magnet ;  a  magnet  magnetises  steel  with  far  greater  difficulty,, 
but  this  magnetisation  is  permanent. 

The  fundamental  phenomena  of  induction  may  be  conveniently  investi- 
gated and  demonstrated  by  means  of  the  apparatus  represented  in  figure 
635,  which  consists  of  a  narrow  cylindrical  brass  tube  BA  supported  by  an 
insulating  glass  handle  and  held  over  the  excited  cake  of  an  electrophorus 


1 


Fig 


745.  Faraday's  experiments.  —  The  following  experiments  of  Faraday, 
known  as  f  the  ice-pail  experiments,'  are  excellent  illustrations  of  the  opera- 
tion of  induction,  and  are  of  great  theoretical  importance  :  — 

A  carefully  insulated  metal  cylinder,  A,  fig.  636,  is  connected  by  a  wire 
with  an  electroscope  E,  at  some  distance.  On  placing  inside  the  cylinder 
an  insulated  brass  ball  C,  which  is  small  in  comparison  with  the  size  of  the 
cylinder  charged  with  positive  electricity,  the  leaves  of  the  electroscope 
diverge  with  positive  electricity,  and  the  divergence  increases  until  a  certain 
depth  is  attained,  when  there  is  no  further  increase.  The  divergence  now 
remains  constant,  whatever  be  the  position  of  the  ball,  even  when  it  touches 


684 


Frictional  Electricity. 


[745- 


Fig.  636. 


the  cylinder.     On  withdrawing  the  ball  it  is  found  to  be  perfectly  discharged. 

Hence  the  charge  on  the  surface  is  equal  to  that  which  the  ball  had  originally. 

If  while  the  ball  with  its  original  charge  is  inside  the  cylinder,  the  outside 

of  the  cylinder  is  touched  with  the  finger, 
the  leaves  of  the  electroscope  collapse, 
and  whatever  be  the  position  of  the  ball 
inside  the  cylinder,  even  if  it  touches  the 
sides,  the  electroscope  does  not  alter. 
If,  however,  after  touching  the  outside 
with  the  finger  the  ball  is  removed  with- 
out having  touched  the  sides,  the  gold 

C  6  +  leaves  will  again  diverge  to  the  same  ex- 

tent as  before,  but  the  electricity  will  now 
be  found  to  be  of  the  opposite  kind. 

It  follows  from  this  experiment  that 
the  quantity  of  electricity  produced  by 
induction  is  equal  to  that  of  the  induc- 
ing body.  In  ordinary  cases  the  charge 
induced  is  less  ;  but  this  arises  from 
the  fact  that  all  the  bodies  on  which  the 
induction  is  exerted  are  not  taken  into 
account. 

Four  such  cylinders  (fig.  637)  are  placed  concentrically  within  each  other, 
and  are  insulated  from  each  other  by  discs  of  shellac,  and  the  outer  one  is 

connected  with  the  electroscope. 
On  introducing  the  charged  ball 
into  the  central  cavity  the  leaves 
diverge  just  as  if  the  intermediate 
ones  did  not  exist.  Each  of  these 
is  charged  with  equal  quantities 
of  opposite  electricities,  all  equal 
in  value  to  that  of  the  sphere. 
The  internal  charge  of  the  cylin- 
der is  the  same  as  if  all  the 
Flg-  637'  intermediate  cylinders  were  sup- 

pressed, and  the  charge  does  not  vary  even  when  the  intermediate  ones  are 
connected  with  each  other  or  are  touched  by  the  electrified  ball  C. 

If,  while  C  is  in  its  original  condition,  the  internal  cylinder,  4,  is  con- 
nected with  the  ground,  the  leaves  collapse,  and  the  other  cylinders  are  in 
the  neutral  state  ;  the  two  layers  which  remain,  positive  on  C,  and  negative 
on  the  adjacent  cylinder,  are  without  action  on  an  external  point.  If  any  other 
cylinder  be  thus  treated  the  external  ones  are  reduced  to  the  neutral  state. 
x  746.  Limit  to  the  action  of  induction. — The  inductive  action  which  an 
electrified  body  exerts  on  an  adjacent  body  in  decomposing  its  neutral  fluid 
is  limited.  On  the  surface  of  the  insulated  cylinder,  which  we  have  con- 
sidered in  the  preceding  paragraph,  let  there  be  at  n  any  small  quantity  of 
neutral  electricity  (fig.  638).  The  positive  electricity  of  the  source  m  first 
decomposes  by  induction  the  neutral  electricity  in  «,  attracting  its  negative 
towards  A,  and  repelling  its  positive  towards  B  ;  but  in  the  degree  in  which 


-747]  Faraday's  Theory  of  Induction.  685 

the  extremity  A  becomes  charged  with  negative  electricity,  and  the  extre- 
mity B  with  positive  electricity,  there  are  developed  at  A  and  B  two  forces, 
/"and  /,  which  act  in  the  opposite  direction  to  the  original  force.  For  the 
forces  /and  /  concur  in  driving  towards  B  the  negative  fluid  of  n,  and 

B 

>' 


Fig.  638. 

towards  A  its  positive  fluid.  But  as  the  inducing  force  F  which  is  exerted 
at  m  is  constant,  while  the  forces /and/  are  increasing,  a  time  arrives  at 
which  the  force  F  is  balanced  by  the  forces  /and  /.  All  decomposition  of 
the  neutral  condition  then  ceases  ;  the  inducing  action  has  attained  its  limit. 

If  the  cylinder  be  removed  from  the  source  of  electricity,  as  the  inducing 
action  decreases,  a  portion  of  the  free  electricities  at  A  and  at  B  recombine  to 
form  the  neutral  fluid  If,  on  the  other  hand,  they  are  brought  nearer,  as 
the  force  F  now  exceeds  the  forces  /  and  /,  a  new  decomposition  of  the 
neutral  fluid  takes  place,  and  fresh  quantities  of  positive  and  negative  elec- 
tricities are  respectively  accumulated  at  A  and  B. 

747.  Faraday's  theory  of  induction. — Hitherto  any  possible  influence 
of  the  medium  which  separates  the  electrified  from  the  unelectrified  body  in 
the  case  of  induction  has  been  disregarded.  It  has  been  tacitly  assumed 
that  electrical  actions  are  exerted  at  a  distance,  and  the  medium  has  been 
looked  upon  as  an  inert  mass  through  which  the  forces  can  act,  but  which 
itself  is  destitute  of  any  active  properties.  The  researches  of  Faraday,  how- 
ever, prove  that  this  is  not  the  case  ;  that  the  medium  is  of  fundamental  im- 
portance, and  that  the  action  is  not  an  action  at  a  distance,  or  at  any  rate 
at  no  greater  distance  than  that  between  any  two  molecules. 

According  to  Faraday's  views  conductors  are  in  a  certain  sense  qualita- 
tively different  from  non-conductors.  He  looked  upon  a  non-conductor  as 
consisting  of  a  number  of  molecules  which  may  be  spherical,  and  which  are 
absolute  conductors,  and  are  disseminated  in  a  non-conducting  medium. 
The  action  of  an  electrified  body  is  either  to  separate  the  electricities  within 
the  molecule  and  arrange  them  in  a  polar  chain,  or  to  impart  to  the  mole- 
cules which  are  themselves  polarised  at  the  outset  a  definite  polar  arrange- 
ment ;  those  ends  of  the  molecule  which  face  the  inducing  body  having  elec- 
tricity of  the  opposite  kind,  and  those  which  are  turned  away  from  it  having 
electricity  of  the  same  kind.  In  the  interior  of  the  medium,  where  succes- 
sively the  positive  end  of  one  molecule  faces  the  negative  end  of  the  next, 
the  two  electricities  neutralise  each  other  ;  but  where  the  non-conductor  is 
bounded  by  a  conductor  the  free  electrification  is  no  longer  neutralised,  but 
constitutes  the  charge  which  is  perceived.  The  action  is  therefore  analogous 
to  that  of  the  pole  of  a  magnet  on  a  piece  of  soft  iron  ;  and  Faraday  called  it 
dielectric  polarisation. 

The  following  experiment  was  devised  by  Faraday  to  illustrate  this 
polarisation  of  the  medium,  as  he  called  it.  He  placed  small  filaments  of 
silk  in  a  vessel  of  turpentine  (fig.  639),  and,  having  plunged  two  conductors 


686 


Frictional  Electricity. 


[747- 


in  the  liquid  on  opposite  sides,  he  charged  one  and  placed  the  other  in  con- 
nection with  the  ground.  The  particles  of  silk  immediately  arranged  them- 
selves end  to  end,  and  adhered 
closely  together,  forming  a  con- 
tinuous chain  between  the  two 
sides.  An  experiment  by  Mat- 
teucci  also  supports  Faraday's 
theory.  He  placed  several  thin 
plates  of  mica  closely  together, 
and  provided  the  outside  ones 

rig.  639. 

with    metallic    coatings,  like    a 

fulminating  pane  (769).  Having  electrified  the  system,  the  coatings  were 
removed  by  insulating  handles,  and  on  examining  the  plates  of  mica  succes- 
sively, each  was  found  charged  with  positive  electricity  on  one  side  and 
negative  electricity  on  the  other. 

748.  Specific  inductive  capacity. — Faraday  named  the  property  which 
bodies  have  of  transmitting  electrical  induction,  the  specific  inductive  capacity, 
or,  as  it  is  often  called,  the  inductive  power.  If  the  dielectric  does  play  the 
essential  part  in  the  phenomena  of  induction  it  is  not  likely  that  all  insu- 
lating bodies  possess  it  in  the  same  degree.  This  seems  to  have  been  known 
to  Cavendish.  To  determine  and  compare  the  inductive  power  Faraday 
used  the  apparatus  represented  in  fig.  640,  and  of  which  fig.  641  represents 


Fig.  640.  Fig.  641. 

a  vertical  section.  It  consists  of  a  brass  sphere  made  up  of  two  halves,  P 
and  Q,  which  fit  accurately  into  each  other,  like  the  Magdeburg  hemi- 
spheres. In  the  interior  of  this  spherical  envelope  there  is  a  smaller  brass 


-748]  Specific  Inductive  Capacity.  687 

sphere  C,  connected  with  a  metal  rod,  terminating  in  a  ball  B.  The  rod  is 
insulated  from  the  envelope  PO  by  a  thick  layer  of  shellac  A.  The  space 
mn  receives  the  substance  whose  inductive  power  is  to  be  determined.  The 
foot  of  the  apparatus  is  provided  with  a  screw  and  stopcock,  so  that  it  can 
be  screwed  on  the  air-pump,  and  the  air  in  inn  either  rarefied  or  exhausted. 

Two  such  apparatus  perfectly  identical  are  used,  and  at  first  they  only 
contain  air.  The  envelopes  PO  are  connected  with  the  ground,  and  the 
knob  B  of  one  of  them  receives  a  charge  of  electricity.  The  sphere  C  thus 
becomes  charged  like  the  inner  coating  of  a  Leydenjar  (770).  The  layer  mn 
represents  the  insulator  which  separates  the  two  coatings.  By  touching  B 
with  the  proof  plane,  which  is  then  applied  to  the  torsion  balance,  the  quantity 
of  free  electricity  is  measured.  In  one  experiment  Faraday  observed  a 
torsion  of  250°,  which  represented  the  free  electricity  on  B.  The  knob  B 
was  then  placed  in  metallic  connection  with  the  knob  B'  of  the  other  appa- 
ratus, and  the  torsion  was  now  found  to  be  125°,  showing  that  the  electricity 
had  become  equally  distributed  on  the  two  spheres,  as  might  have  been 
anticipated,  since  the  pieces  of  apparatus  were  quite  equal,  and  each  contained 
air  in  the  space  mn. 

This  experiment  having  been  made,  the  space  mn  in  the  second  appa- 
ratus was  filled  with  the  substance  whose  inductive  power  was  to  be  deter- 
mined :  for  example,  shellac.  The  other  apparatus,  in  which  mn  is  filled 
with  air,  having  been  charged,  the  density  of  the  free  electricity  on  C  was 
measured.  Let  it  be  taken  at  290°,  the  number  observed  by  Faraday  in  a 
special  case.  When  the  knob  B  of  the  first  apparatus  was  connected  with 
the  knob  W  of  the  second,  the  density  was  not  found  to  be  145°,  as  would 
be  expected.  The  apparatus  containing  air  exhibited  a  density  of  114°,  and 
that  with  shellac  of  113°.  Hence  the  former  had  lost  176°,  and  had  retained 
1 14°,  while  the  latter  ought  to  have  exhibited  a  density  of  176°  instead  of  113°. 
The  second  apparatus  had  taken  more  than  half  the  charge,  and  hence  a 
larger  quantity  of  electricity  had  been  condensed  by  the  shellac.  Of  the 
total  quantity  of  electricity,  the  shellac  had  taken  176°  and  the  air  114°; 
hence  the  specific  inductive  capacity  of  air  is  to  that  of  shellac  as  114  :  176  ; 
or  as  i  :  1-55.  That  is,  the  inductive  power  of  shellac  is  more  than  half 
as  great  again  as  air. 

By  the  following  simple  experiment  the  influence  of  the  dielectric  may  be 
shown  : — At  a  fixed  distance  above  a  gold-leaf  electroscope  let  an  electrified 
sphere  be  placed,  by  which  a  certain  divergence  of  the  leaves  is  produced. 
If,  now,  the  charges  remaining  the  same,  a  disc  of  sulphur  or  of  shellac  be 
interposed,  the  divergence  increases,  showing  that  inductive  action  takes 
place  through  the  sulphur  to  a  greater  extent  than  through  a  layer  of  air  of 
the  same  thickness. 

By  various  methods,  the  following  numbers  have  been  obtained  for  the 
specific  inductive  capacity  of  dielectrics,  as  they  are  called,  in  opposition  to 
anelectrics,  or  conductors  : — 

Air  .  -v-     ,;..;.    .  '  .     i -oo  Paraffine.        ....  .  ,  1-98 

Glass  .      r,? /.,;.-.;  .;     1-90  India-rubber   .      ,  ,  •     .  2-22 

Sulphur  .         .         .  .2-58  Gutta-percha  .  .  .    .  2-46 

Shellac  .  ;:     ,  .  .  »:  .     274 


688  Frictional  Electricity.  [748- 

These  values  are  known  as  the  dielectric  constants  ;  and  their  determination 
presents  considerable  difficulty,  owing  to  the  occurrence  of  a  phenomenon  to 
which  Faraday  gave  the  name  of  electrical  absorption,  and  which  is  due  to 
the  same  cause  as  the  residual  charge  of  condensers. 

Boltzmann  divides  dielectrics  into  two  classes  :  to  one  of  which  belong 
shellac,  paraffine,  sulphur,  and  resin,  which  act  like  perfect  insulators  ;  that 
is,  that  in  using  them  the  maximum  charge  is  attained,  if  not  instantaneously, 
at  all  events  after  a  very  short  time  :  in  others,  such  as  gutta-percha,  stearine, 
and  glass,  the  charge  increases  appreciably  with  the  time. 

A  very  interesting  relation  probably  exists  between  the  dielectric  constant 
and  the  refractive  index  of  certain  substances.  Thus  the  following  numbers 
have  been  found  : — 

D  VD  n 

Sulphur".         .         .         .     3-84  1-96  2-04 

Resin     .         .         .         .     2-55  1-59  1-54 

Paraffine        .        .         .     2-32  1-52  1-53 

where  n  is  the  refractive  index  (538),  and  >/D  the  square  root  of  the  dielectric 
constant. 

Faraday  was  not  able  to  detect  any  difference  in  the  dielectric  constants 
of  various  gases.  Boltzmann  has  shown,  however,  that  there  are  differences 
among  them,  and  that  there  is  a  very  close  agreement  between  the  square  root 
of  their  dielectric  constants  and  their  refractive  indices,  thus  : — 

Air    .,  f        .  .  .  1-00059  1-000295  i '000294 

Carbonic  acid  .  .  1-00095  1-000473  1-000449 

Hydrogen    .  .  .  1-00026  1-000132  1-000138 

Olefiant  gas  •  ,.  •  1*00131  1-000656  1-000678 

The  accurate  determination  of  the  dielectric  constant  is  a  matter  of  great 
theoretical  importance,  especially  from  its  bearing  on  Maxwell's  electro-mag- 
netic theory  of  light.  According  to  this  theory  the  medium  in  which  both 
electrical  and  luminous  actions  are  transmitted  is  the  same,  and  is  the  lumini- 
ferous  ether  (637)  ;  and  it  is  a  necessary  consequence  of  this  theory  that  the 
above  relation  must  exist  between  the  refractive  index  of  a  substance  and  its 
dielectric  constant. 

749.  Communication  of  electricity  at  a  distance. — In  the  experiment 
represented  in  fig.  640  the  opposite  electricities  of  the  conductor  and  that 
of  the  separated  cylinder  tend  to  unite,  but  are  prevented  by  the  resistance 
of  the  air.  If  the  density  is  increased,  or  if  the  distance  of  the  bodies  be 
diminished,  the  opposed  electricities  at  length  overcome  this  obstacle  ;  they 
rush  together  and  combine,  producing  a  spark,  accompanied  by  a  sharp 
sound.  The  negative  electricity  separated  on  the  cylinder,  being  thus  neu- 
tralised by  the  positive  electricity  of  the  charged  body,  a  charge  of  positive 
electricity  remains  on  the  cylinder.  The  same  phenomenon  is  observed 
when  a  finger  is  presented  to  a  strongly  electrified  conductor.  The  latter 
decomposes  by  induction  the  neutral  electricity  of  the  body,  the  opposite 
electricities  combine  with  the  production  of  a  spark,  while  the  electricity  of 
the  same  kind  as  the  electrified  conductor,  which  is  left  on  the  body,  passes 
off  into  the  ground. 

The  striking  distance  varies  with  the  density,  the  shape  of  the  bodies 


-751]  Gold  leaf  Electroscope.  689 

their  conducting  power,  and  with  the  resistance  and  pressure  of  the  inter- 
posed medium. 

750.  Motion  of  electrified  bodies. — The  various  phenomena  of  attrac- 
tion and  repulsion,  which  are  among  the  most  frequent  manifestations  of 
electrical  action,  may  all  be  explained  by  means  of  the  laws  of  induction. 
If  M  (fig.  642)  be  a  fixed  insulated  conductor  charged  with  positive  elec- 
tricity, and  N  be  a  movable  insulated  body — for  instance,  an  electrical 
pendulum — there  are  three  cases  to  be  considered  : — 

i.   The  movable  body  is  unelectrified  and  is  a  conductor. — In  this  case  M, 
acting  inductively  on  N,  attracts  the  negative  and  repels  the  positive  elec- 
tricity, so  that  the  maxima  of  density  are  respectively 
at  the  points  a  and  b.     Now  a  is  nearer  c  than  it  is  to 
b ;  and,  since  attractions  and  repulsions  are  inversely 
as  the  square  of  the  distance,  the  attraction  between 
a  and  c  is  greater  than  the  repulsion  between  b  and  c  ; 
and,  therefore,  N  will  be  attracted  to  M  by  a  force 
equal  to  the  excess  of  the  attractive  over  the  repulsive 
force. 

ii.  The  movable  body  is  a  conductor  and  is  electrified. — If  the  electricity 
of  the  movable  body  is  different  from  that  of  the  fixed  body,  there  is  always 
attraction  ;  but  if  they  are  of  the  same  kind,  there  is  at  first  repulsion 
and  afterwards  attraction.  This  anomaly  may  be  thus  explained  :  Besides 
its  charge  of  electricity,  the  neutral  electricity  is  decomposed  by  the 
induction  of  the  positive  electricity  on  M  ;  and  consequently  the  hemisphere  b 
obtains  an  additional  supply  of  positive  electricity,  while  a  becomes  charged 
with  negative  electricity.  There  is  thus  attraction  and  repulsion,  as  in 
the  foregoing  case.  The  force  of  repulsion  is  at  first  greater,  because  the 
quantity  of  positive  electricity  on  N  is  greater  than  that  of  negative ; 
but  as  the  distance  ac  diminishes,  the  attractive  force  increases  more  rapidly 
than  the  repulsive  force,  and  finally  exceeds  it. 

iii.  The  movable  body  is  a  bad  conductor. — If  N  is  charged,  repulsion  or 
attraction  takes  place,  according  as  the  electricity  is  of  the  same  or  opposite 
kind  to  that  of  the  fixed  body.  If  it  is  in  the  natural  state,  the  body  M  will 
decompose  the  neutral  electricity  of  N,  and  attraction  will  take  place  as  in 
the  first  case,  since  a  powerful  and  permanent  source  of  electricity  can  more 
or  less  decompose  the  neutral  electricity  even  of  bad  conductors. 
v75i.  Cold  leaf  electroscope. — The  name  electroscope  is  given  to  instru- 
ments for  detecting  the  presence  and  determining  the  kind  of  electricity  in 
any  body.  The  original  pith-ball  pendulum  is  an  electroscope  ;  but,  though 
sometimes  convenient,  it  is  not  sufficiently  delicate.  Many  successive  im- 
provements have  been  made  in  it,  and  have  resulted  in  the  form  now  gene- 
rally used,  which  is  due  to  Bennett. 

Bennett's,  or  the  gold  leaf  electroscope. — This  consists  of  a  tubulated  glass 
shape  B  (fig.  643),  standing  on  a  metal  foot,  which  thus  communicates  with 
the  ground.  A  metal  rod  terminating  at  its  upper  extremity  in  a  knob  C, 
and  holding  at  its  lower  end  two  narrow  strips  of  gold  leaf,  n  n,  fits  in  the 
tubulure  of  the  shade,  the  neck  of  which  is  coated  with  an  insulating 
varnish.  The  air  in  the  interior  is  dried  by  quicklime,  or  by  chloride  of 

v  Y 


690 


Frictional  Electricity. 


[751 


calcium,  and  on  the  insides  of  the  shade  there  are  two  strips  of  gold  leaf 
«,  communicating  with  the  ground. 

When  the  knob  is  touched  with  a  body  charged  with  either  kind  of 
electricity,  the  leaves  diverge  ;  usually,  however,  the  apparatus  is  charged 
by  induction  thus  : — 

If  an  electrified  body — a  stick  of  sealing-wax,  for  example — be  brought 
near  the  knob,  it  will  decompose  the  neutral  electricity  of  the  system,  at- 
tracting to  the  knob  the  electricity  of  the  opposite  kind,  and  retaining  it 
there,  and  repelling  the  electricity  of  the  same  kind  to  the  gold  leaves,  which 
consequently  diverge.  In  this  way  the  presence  of  an  electrical  charge  is 
ascertained,  but  not  its  quality. 

To  ascertain  the  kind  of  electricity  the  following  method  is  pursued  : — It 
while  the  instrument  is  under  the  influence  of  the  body  A,  which  we  will 

suppose  has  a  negative  charge,  the 
knob  be  touched  by  the  finger,  the 
negative  electricity  produced  by  in- 
duction passes  off  into  the  ground,  and 
the  previously  divergent  leaves  will 
collapse  ;  there  only  remains  positive 
electricity,  retained  in  the  knob  by  in- 
duction from  A.  If  now  the  finger  be 
first  removed,  and  then  the  electrified 
body,  the  positive  electricity  previously 
retained  by  A  will  spread  over  the  sys- 
tem, and  cause  the  leaves  to  diverge 
If  now,  while  the  system  is  charged 
with  positive  electricity,  a  positively 
electrified  body— as,  for  example,  an 
excited  glass  rod — be  approached,  the 
leaves  will  diverge  more  widely ;  for 
the  electricity  of  the  same  kind  will  be  repelled  to  the  ends.  If,  on  the 
contrary,  an  excited  shellac  rod  be  presented,  the  leaves  will  tend  to  collapse, 
the  electricity  with  which  they  are  charged  being  attracted  by  the  opposite 
electricity.  Hence  we  may  ascertain  the  kind  of  electricity,  either  by 
imparting  to  the  electroscope  electricity  from  the  body  under  examination, 
and  then  bringing  near  it  a  rod  charged  with  positive  or  negative  electricity  ; 
or  the  electroscope  may  be  charged  with  a  known  kind  of  electricity,  and  the 
electrified  body  in  question  brought  near  the  electroscope. 

It  has  been  proposed  to  use  the  gold  leaf  electroscope  as  an  electrometer. 
or  measurer  of  electricity,  by  measuring  the  angle  of  divergence  of  the 
leaves  ;  this  is  done  by  placing  behind  them  a  graduated  scale ;  for  small 
angles  the  quantity  of  electricity  is  nearly  proportional  to  the  sine  of  half  the 
angle  of  divergence.  There  are,  however,  objections  to  such  a  use,  and  the 
electroscope  is  rarely  employed  for  this  purpose. 


Fig.  643. 


-752] 


Electrophones. 


691 


ELECTRICAL   MACHINES. 

Electrophorus. — It  will  now  be  convenient  to  describe  the  various 
•electrical  machines,  or  apparatus  for  generating  and  collecting  large  supplies 
of  statical  electricity.  One  of  the  most  simple  and  inexpensive  of  these  is 
the  electrophones,  which  was  invented  by  Volta.  It  consists  of  a  cake  of 
resin  B  (fig.  645),  say  about  12  inches  in  diameter,  and  an  inch  thick,  which 
is  placed  on  a  metal  surface,  or  frequently  fits  into  a  wooden  mould  lined 


Fig.  644. 


Fig.  645. 


with  tinfoil,  which  is  called  the  form.  Besides  this  there  is  a  metal  disc  A 
(fig.  645),  of  a  diameter  somewhat  less  than  that  of  the  cake,  and  provided 
with  an  insulating  glass  handle  ;  this  is  the  cover.  The  mode  of  working  is 
as  follows  :— All  the  parts  of  the  apparatus  having  been  well  warmed,  the 
cake,  which  is  placed  in  the  form,  or  rests  on  a  metal  surface,  is  briskly 
flapped  with  silk,  or,  better,  with  catskin,  by  which  it  becomes  charged  with 
negative  electricity.  The  cover  is  then  placed  on  the  cake.  Owing,  how- 
ever, to  the  minute  rugosities  of  the  surface  of  the  resin,  the  cover  only 
comes  in  contact  with  a  few  points,  and,  from  the  non-conductivity  of  the 
resin,  the  negative  electricity  of  the  cake  does  not  pass  off  to  the  cover.  On 
the  contrary,  it  acts  by  induction  on  the  neutral  electricity  of  the  cover,  and 
decomposes  it,  attracting  the  positive  electricity  to  the  under  surface,  and 
repelling  the  negative  electricity  to  the  upper.  If  the  upper  surface  be  now 
touched  with  the  finger,  the  negative  electricity,  because  repelled  and  free, 
passes  off,  and  the  cover  remains  charged  with  positive  electricity,  held, 
however,  by  the  negative  electricity  of  the  cake  ;  the  two  electricities  do 
not  unite,  in  consequence  of  the  nonconductivity  of  the  cake  (fig.  644).  If 
now  the  cover  be  raised  by  its  insulating  handle,  the  charge  diffuses  itself 
over  the  surface  ;  and  if  a  conductor  be  brought  near  it  (fig.  645),  a  smart 
spark  passes. 

The  metal  form  on  which  the  cake  rests  plays  an  important  part  in 

Y  Y  2 


692  Frictional  Electricity.  [752- 

the  action  of  the  electrophorus,  as  it  increases  the  quantity  of  electricity,  and 
makes  it  more  permanent.  For  the  negative  electricity  of  the  upper  surface 
of  the  resin,  acting  inductively  on  the  neutral  electricity  of  the  lower,  decom- 
poses it,  retaining  on  the  under  surface  the  positive  electricity,  while  the 
negative  electricity  passes  off  into  the  ground.  The  positive  electricity  thus 
developed  on  the  under  surface  reacts  on  the  negative  electricity  of  the  upper 
surface,  binding  it,  and  causing  it  to  penetrate  into  the  badly  conducting 
mass,  on  the  surface  of  which  fresh  quantities  of  electricity  can  be  excited 
far  beyond  the  limits  possible  without  the  action  of  the  form.  It  is  for  this 
reason  that  the  electrophorus,  once  charged,  retains  its  state  for  a  consider- 
able time,  and  sparks  can  be  taken  even  after  a  long  interval.  If  the  form 
be  insulated,  the  charge  obtained  from  it  is  far  less  than  if  it  is  on  a  con- 
ducting support.  For  the  negative  electricity  developed  by  induction  on  the 
lower  surface  being  now  unable  to  escape,  the  condensing  action  referred  to 
cannot  take  place,  and  only  a  feeble  charge  can  be  given  to  the  resin.  The 
retention  of  electricity  is  greatly  promoted  by  keeping  the  cake  on  the  form, 
and  placing  the  cover  upon  it,  by  which  the  access  of  air  is  hindered. 
Instead  of  a  cake  of  resin,  a  disc  of  gutta-percha,  or  vulcanised  cloth,  or 
vulcanite  may  be  substituted  ;  and,  of  course,  if  glass,  or  any  material 
which  is  positively  electrified  by  friction,  be  used,  the  cover  acquires  a 
negative  charge. 

The  electrophorus  is  a  good  instance  of  the  conversion  of  work  into 
electropotential  energy  (63).  When  the  cover  is  lifted  from  the  excited  cake 
work  must  be  expended  in  order  to  overcome  the  attraction  of  the  electricity 
in  the  cake  for  the  opposite  electricity  developed  by  induction  on  the  cover  ; 
and  the  equivalent  of  this  work  appears  in  the  form  of  the  electricity  thus 
detached.  Thus,  when  a  Leyden  jar  is  charged  either  by  the  machine  or  by 
the  electrophorus,  the  energy  of  the  charge  is  a  transformation  of  the  work 
of  the  operator. 

753.  Plate  electrical  machine. — The  first  electrical  machine  was  in- 
vented by  Otto  von  Guericke,  the  inventor  also  of  the  air-pump.  It  con- 
sisted of  a  sphere  of  sulphur,  which  was  turned  on  an  axis  by  means  of  the 
hand,  while  the  other,  pressing  against  it,  served  as  a  rubber.  Resin  was 
afterwards  substituted  for  the  sulphur,  which,  in  turn,  Hawksbee  replaced 
by  a  glass  cylinder.  In  all  these  cases  the  hand  served  as  rubber  ;  and 
Winckler,  in  1740,  first  introduced  cushions  of  horsehair,  covered  with  silk, 
as  rubbers.  At  the  same  time  Bose  collected  electricity,  disengaged  by 
friction,  on  an  insulated  cylinder  of  tin  plate.  Lastly,.  Ramsden,  in  1760, 
replaced  the  glass  cylinder  by  a  circular  glass  plate,  which  was  rubbed  by 
cushions.  The  form  which  the  machine  has  now  is  but  a  modification  of 
Ramsden's  original  machine. 

Between  two  wooden  supports  (fig.  646)  a  circular  glass  plate  P  is  sus- 
pended by  an  axis  passing  through  the  centre,  and  which  is  turned  by  means 
of  a  handle  M.  The  plate  revolves  between  two  sets  of  cushions  or  rubbers, 
F,  of  leather  or  of  silk,  one  set  above  the  axis  and  one  below,  which,  by 
means  of  screws,  can  be  pressed  as  tightly  against  the  glass  as  may  be  desired. 
The  plate  also  passes  between  two  brass  rods,  shaped  like  a  horse-shoe,  and 
provided  with  a  series  of  points  on  the  sides  opposite  the  glass  ;  these  rods 
are  fixed  to  larger  metallic  cylinders  CC,  which  are  called  the  prime  conduc- 


-753] 


Plate  Electrical  Machine. 


693 


tors.     The  latter  are  insulated  by  being  supported  on  glass  feet,  and  are 
connected  with  each  other  by  a  smaller  rod  r. 

The  action  of  the  machine  is  thus  explained.  By  friction  with  the  rubbers, 


Fig.  646. 

the  glass  becomes  positively  and  the  rubbers  negatively  electrified.  If  now 
the  rubbers  were  insulated,  they  would  receive  a  certain  charge  of  negative 
electricity  which  it  would  be  impossible  to  exceed,  for  the  tendency  of  the 
opposed  electricities  to  reunite  would  be  equal  to  the  power  of  the  friction  to 
decompose  the  neutral  state.  But  the  rubbers  communicate  with  the  ground 
by  means  of  a  chain  ;  and,  consequently,  as  fast  as  the  negative  electricity 
is  generated,  it  is  continually  reduced  to  zero  by  contact  with  the  ground. 
The  positive  electricity  of  the  glass  acts  then  by  induction  on  the  conductor, 
attracting  the  negative  electricity.  This  negative  electricity  collects  on  the 
points  opposite  to  the  glass.  Here  its  tendency  to  discharge  becomes  so 
high  that  it  passes  across  the  intervening  space  of  air,  and  neutralises  the 
positive  electricity  on  the  glass.  The  conductors  thus  lose  their  negative 
electricity  and  remain  charged  with  positive  electricity.  The  plate  accord- 
ingly gives  up  nothing  to  the  prime  conductors  ;  in  fact,  it  only  abstracts 
from  them  their  negative  electricity. 


694  Frictional  Electricity.  [753- 

If  the  hand  be  brought  near  the  conductor  when  charged,  a  spark  follows, 
which  is  renewed  as  the  machine  is  turned.  In  this  case  the  positive  elec- 
tricity, decomposes  the  neutral  electricity  of  the  body,  attracting  its  negative 
electricity,  and  combining  with  it  when  the  two  have  a  sufficient  tension. 
Thus,  with  each  spark,  the  conductor  reverts  to  the  neutral  state,  but  becomes 
again  electrified  as  the  plate  is  turned. 

754.  Precautions  in  reference  to  the  machine. — The  glass,  of  which 
the  plate  is  made,  must  be  as  little  hygroscopic  as  possible.     Of  late  ebonite 
has   been  frequently  substituted  for  glass ;  it  has  the  advantage  of  being 
neither  hygroscopic  nor  fragile,   and  of  readily  becoming   electrified   by 
friction.     It  cannot,  however,  be  relied  on,  as  its  surface  in  time  undergoes  a 
change,  especially  if  exposed  to  the  light,  whereby  it  becomes  a  conductor. 
The  plate   is  usually  from  i  to  |  of  an  inch  in  thickness,  and  from   20 
to  30  inches  in  diameter,  though  these  dimensions  are  not  unfrequently 
exceeded. 

The  rubbers  require  great  care,  both  in  their  construction  and  their  pre- 
servation. They  are  commonly  made  of  leather,  stuffed  with  horsehair. 
Before  use  they  are  coated  either  with  powdered  aicrum  musivum  (sulphuret 
of  tin),  graphite,  or  amalgam.  The  action  of  these  substances  is  not  very 
clearly  understood.  Some  consider  that  it  merely  consists  in  promoting 
friction.  Others,  again,  believe  that  a  chemical  action  is  produced,  and 
assign,  in  support  of  this  view,  the  peculiar  smell  noticed  near  the  rubbers 
when  the  machine  is  worked.  Amalgams,  perhaps,  promote  most  power- 
fully the  disengagement  of  electricity.  Kienmayer's  amalgam  is  the  best 
of  them.  It  is  prepared  as  follows  : — One  part  of  zinc  and  one  part  of  tin 
are  melted  together  and  removed  from  the  fire,  and  two  parts  of  mercury 
stirred  in.  The  mass  is  transferred  to  a  wooden  box  containing  some  chalk, 
and  then  well  shaken.  The  amalgam,  before  it  is  cold,  is  powdered  in  an 
iron  mortar,  and  preserved  in  a  stoppered  glass  vessel.  For  use  a  little 
cacao  butter  or  lard  is  spread  over  the  cushion,  some  of  the  powdered 
amalgam  sprinkled  over  it,  and  the  surface  smoothed  by  a  ball  of  flattened 
leather. 

In  order  to  avoid  a  loss  of  electricity,  two  quadrant-shaped  pieces  of  oiled 
silk  are  fixed  to  the  rubbers,  so  as  to  cover  the  plate  on  both  sides  :  one  at  the 
upper  part  from  a  to  F,  and  the  other  in  the  corresponding  part  of  the  lower 
rubbers.  These  flaps  are  not  represented  in  the  figure.  Yellow  oiled  silk 
is  the  best,  and  there  must  be  perfect  contact  between  the  plate  and  the 
cloth. 

Ramsden's  machine,  as  represented  in  fig.  646,  only  gives  positive  elec- 
tricity. But  it  may  be  arranged  so  as  to  give  negative  electricity  by  placing 
it  on  a  table  with  insulating  supports.  The  conductor  is  connected  with  the 
ground  by  a  chain,  and  the  machine  worked  as  before.  The  positive  elec- 
tricity passes  off  by  the  chain  into  the  ground,  while  the  negative  electricity 
remains  on  the  supports  and  on  the  insulated  table.  On  bringing  the  finger 
near  the  uprights,  a  sharper  spark  than  the  ordinary  one  is  obtained. 

755.  Maximum  of  charge. — It  is  impossible  to  exceed  a  certain  limit 
of  electrical  charge  with  the  machine,  whatever  precautions  are  taken,  or 
however  rapidly  the  plate  is  turned.     This  limit  is  attained  when  the  loss  of 
electricity  equals  its  production.     The  loss  depends  on  three  causes  :  i.  The 


-757] 


Cylinder  Electrical  Machine. 


69S 


loss  by  the  atmosphere,  and  the  moisture  it  contains,    ii.  The  loss  by  the  sup- 
ports,   iii.  The  recombination  of  the  electricities  of  the  rubbers  and  the  glass. 

The  first  two  causes  have  been  already  mentioned. 
With  reference  to  the  last,  it  must  be  noticed  that  the 
electrical  charge  increases  with  the  rapidity  of  the  rota- 
tion, until  it  reaches  a  point  at  which  it  overcomes  the 
resistance  presented  by  the  non-conductivity  of  the 
glass.  At  this  point,  a  portion  of  the  two  electricities 
separated  on  the  rubbers  and  on  the  glass  recombines, 
and  the  charge  remains  constant.  It  is,  therefore,  ulti- 
mately independent  of  the  rapidity  of  rotation. 

756.  Quadrant  electrometer.  —  The  electrical 
charge  is  roughly  measured  by  the  quadrant  or  Henley's 
electrometer,  which  is  attached  to  the  conductor.  This 
is  a  small  electric  pendulum,  consisting  of  a  wooden 
rod  d,  to  which  is  attached  an  ivory  or  card-board  scale 
(fig.  647).  In  the  centre  of  this  is  a  small  index  of 
straw,  movable  on  an  axis,  and  terminating  in  a  pith  ball.  Being  attached 
to  the  conductor,  the  index  diverges  as  the  machine  is  charged,  ceasing  to 
rise  when  the  limit  is  attained.  When  the  rotation  is  discontinued  the  index 
falls  rapidly  if  the  air  is  moist ;  but  in  dry  air  it  only  falls  slowly,  showing, 
therefore,  that  the  loss  of  electricity  in  the  latter  case  is  less  than  in  the  former. 

757-  Cylinder  electrical  machine. — The  construction  of  the  cylinder 
machines,  as  ordinarily  used  in  England,  is  due  to  Nairne.  They  are  well 
adapted  for  obtaining  either  kind  of  electricity.  In  Nairne's  machine  (fig. 
648)  the  cylinder  is  rubbed  by  only  one  cushion  C,  which  is  made  of  leather 


Fig.  647. 


*=^       K 


Fig.  648. 

stuffed  with  horsehair,  and  is  screwed  to  an  insulated  conductor  A.  On  the 
opposite  side  of  the  cylinder  there  is  a  similar  insulated  conductor  B,  pro- 
vided with  a  series  of  points  on  the  sides  next  the  glass.  To  the  lower  part 
of  the  cushion  C  is  attached  a  piece  of  oiled  silk,  which  extends  over  the 


696 


Fractional  Electricity. 


[757- 


cylinder  to  just  above  the  points.  This  is  not  represented  in  the  figure. 
When  the  cylinder  is  turned,  A  becomes  charged  with  negative  and  B  with 
positive  electricity  by  the  loss  of  its  negative  from  the  points  P.  The  two 
opposite  electricities  will  now  unite  by  a  succession  of  sparks  across  D  and 
E.  If  use  is  to  be  made  of  the  electricity,  either  the  rubber  or  the  prime 
conductor  must  be  connected  with  the  ground.  In  the  former  case  positive 
electricity  is  obtained  ;  in  the  latter,  negative. 

758.  Armstrong's  hydro-electric  machine. — In  this  machine  electricity 
is  produced  by  the  disengagement  of  aqueous  vapour  through  narrow  orifices. 
The  discovery  of  the  machine  was  occasioned  by  an  accident.  A  work- 
man having  accidentally  held  one  hand  in  a  jet  of  steam,  which  was  issuing 
from  an  orifice  in  a  steam  boiler  at  high  pressure,  while  his  other  hand 
grasped  the  safety-valve,  was  astonished  at  experiencing  a  smart  shock. 
Sir  W.  Armstrong  (then  Mr.  Armstrong,  of  Newcastle),  whose  attention  was 
drawn  to  this  phenomenon,  ascertained  that  the  steam  was  charged  with 
positive  electricity,  and,  by  repeating  the  experiment  with  an  insulated  loco- 
motive, he  found  that  the  boiler  was  negatively  charged.  Armstrong  believed 
that  the  electricity  was  due  to  a  sudden  expansion  of  the  steam  ;  Faraday, 
who  afterwards  examined  the  question,  ascertained  its  true  cause,  which  will 

be  best  understood 
after  describing 
a  machine  which 
Armstrong  devised 
for  reproducing  the 
phenomenon. 

It  consists  of  a 
wrought-iron  boiler 
(fig.  649),  with  a 
central  fire,  and 
insulated  on  four 
legs.  It  is  about  5 
feet  long  by  2  feet 
in  diameter,  and 
is  provided  at  the 
side  with  a  gauge 
O,  to  show  the 
height  of  the  water 
in  the  boiler.  C  is 
the  stopcock,  which 
is  opened  when  the 
steam  has  sufficient 
pressure.  Above 
this  is  the  box  B,  in 
which  are  the  tubes 
through  which  the 
steam  is  disen- 
gaged. On  these 


Fig.  649. 


are  fitted  jets  of  a  peculiar  construction,  which  will   be   understood  from 
the  section  of  one  of  them,  M,  represented  on  a  larger  scale.     They  are 


-759] 


Holtz }s  Electrical  Machine. 


697 


lined  with  hard  wood  in  a  manner  represented  by  the  diagram.  The  box 
B  contains  cold  water.  Thus  the  steam,  before  escaping,  undergoes  partial 
condensation,  and  becomes  charged  with  vesicles  of  water — a  necessary 
condition,  for  Faraday  found  that  no  electricity  is  produced  when  the  steam 
is  perfectly  dry. 

The  development  of  electricity  in  the  machine  was  at  first  attributed  to 
the  condensation  of  the  steam  ;  but  Faraday  found  that  it  is  solely  due  to 
the  friction  of  the  globules  of  water  against  the  jet.  For  if  the  little  cylinders 
which  line  the  jets  are  changed,  the  kind  of  electricity  is  changed;  and  if 
ivory  is  substituted,  little  or  no  electricity  is  produced.  The  same  effect  is 
produced  if  any  fatty  matter  is  introduced  into  the  boiler.  In  this  case  the 
linings  are  of  no  use.  It  is  only  in  case  the  water  is  pure  that  electricity  is 
disengaged,  and  the  addition  of  acid  or  saline  solutions,  even  in  minute 
quantity,  prevents  any  disengagement  of  electricity.  If  turpentine  is  added 
to  the  boiler,  the  effect  is  reversed — the  steam  becomes  negatively,  and  the 
boiler  positively,  electrified. 

With  a  current  of  moist  air  Faraday  obtained  effects  similar  to  those  of 
this  apparatus,  but  with  dry  air  no  effect  is  produced. 

759.  Holtz's  electrical  machine. — Before  the  end  of  last  century  electrical 
machines  were  known  in  this  country  in  which  the  electricity  was  not  deve- 


Fig.  650. 


loped  by  friction,  but  by  the  continuous  inductive  action  of  a  body  already 
electrified,  as  the  electrophorus  ;  within  the  last  few  years'  such  machines 


698  Frictional  Electricity.  [759 

have  been  re-invented  and  come  into  use.  The  form  represented  in  fig.  650- 
was  invented  by  Holtz,  of  Berlin. 

It  consists  of  two  circular  plates  of  thin  glass  at  a  distance  of  3  mm.  fron> 
each  other  ;  the  larger  one,  AA,  which  is  2  feet  in  diameter,  is  fixed  by  means 
of  4  wooden  rollers  <z,  resting  on  glass  axes  and  glass  feet.  The  diameter  ot 
the  second  plate,  BB,  is  2  inches  less  ;  it  turns  on  a  horizontal  glass  axis, 
which  passes  through  a  hole  in  the  centre  of  the  large  fixed  plate  without 
touching  it.  In  the  plate  A,  on  the  same  diameter,  are  two  large  apertures, 
or  windows,  F  F'.  Along  the  lower  edge  of  the  window  F,  on  the  posterior 
face  of  the  plate,  a  band  of  paper,  p,  is  glued,  and  on  the  anterior  face  a  sort 
of  tongue  of  thin  cardboard,  ?z,  joined  to  p  by  a  thin  strip  of  paper,  and  pro- 
jecting into  the  window.  At  the  upper  edge  of  the  window,  F',  there  are 
corresponding  parts, p'  and  n'.  The  papers/  and/'  constitute  the  armatures. 
The  two  plates,  the  armatures,  and  their  tongues  are  covered  with  shellac 
varnish,  but  more  especially  the  edges  of  the  tongues. 

In  front  of  the  plate  B,  at  the  height  of  the  armatures,  are  two  brass 
combs,  O  O',  supported  by  two  conductors  of  the  same  metal,  C  Cr.  In  the 
front  end  of  these  conductors  are  two  moderately  large  brass  knobs,  through 
which  pass  two  brass  rods  terminated  by  smaller  knobs,  r  r*,  and  provided 
with  ebonite  handles,  K  K'.  These  rods,  besides  moving  with  gentle  friction 
in  the  knobs,  can  also  be  turned  so  as  to  be  more  or  less  near  and  inclined 
towards  each  other.  The  plate  B  B  is  turned  by  means  of  a  winch  M,  and  a 
series  of  pulleys  which  transmit  its  motion  to  the  axis  ;  the  velocity  which 
it  thus  receives  is  12  to  15  turns  in  a  second,  and  the  rotation  should  take 
place  in  the  direction  indicated  by  the  arrows ;  that  is,  towards  the  points  of 
the  cardboard  tongues  n  n'. 

To  work  the  machine,  the  armatures  ppf  must  be  first  primed ;  that  is, 
one  of  the  armatures  is  positively  and  the  other  negatively  electrified.  This 
is  effected  by  means  of  a  plate  of  ebonite,  which  is  excited  by  striking  it 
with  catskin  ;  the  two  knobs  rr*  having  been  connected  so  that  the  two 
conductors  C  C  only  form  one,  as  seen  in  fig.  651,  which  shows  by  a  hori- 


r  /•'  EC' 


Fig.  651. 

zontal  section,  through  the  axis  of  rotation,  the  relative  arrangement  of  the 
plates  and  of  the  conductors.  The  electrified  ebonite  is  then  brought  near 
one  of  them—/,  for  instance— and  the  plate  B  is  turned.  The  ebonite  is 
charged  with  negative  electricity,  and  this  withdraws  the  positive  electricity 
of  the  armature  and  charges  it  negatively.  This  latter  acting  by  induction 
through  the  plate  B  B,  as  it  turns  on  the  conductors  OCC'O'  (fig.  651),  attracts 
through  the  comb  O  the  positive  electricity  which  collects  on  the  front  face  of 
the  movable  plate  ;  while  at  the  same  time  negative  electricity,  repelled  on 
the  comb  O',  collects,  like  the  former,  on  the  front  face  of  the  plate  B. 
Hence,  the  two  electricities  being  carried  along  by  the  rotation,  at  the  end 


759] 


Holies  Electrical  Machine. 


699 


of  half  a  turn  all  the  lower  half  of  the  plate  B,  from^  to  F'  (fig.  652),  is  posi- 
tively electrified,  and  its  upper  surface  from^'  to  F  negatively.  But  the  two- 
opposite  electricities  above  and  below  the  window  F'  concur  in  decomposing 
the  electricity  of  the  armature  p'ri  ;  the  part  p  is  positively  electrified,  while 
negative  electricity  is  liberated  by  the  tongue  ;z',  and  is  deposited  on  the 
inner  face  of  the  plate  B  B,  which  from  its  thinness  almost  completely  neu- 
tralises the  positive  electricity  on  the  anterior  face. 

The  two  armatures  are  then  primed,  and  the  same  effect  as  at  F'  is 
produced  at  F  on  the  armature  pn ;  that  is,  that  the  opposite  electricities 
above  and  below  pn,  decomposing  a  new  quantity  of  neutral  electricity, 
the  negative  charge  of  the  part  p  increases,  while  the  positive  electricity  which 
is  liberated  by  the  tongue  n,  neutralises  the  negative  electricity  which  comes 
from  F'  towards  F  ;  and  so  forth  until,  the  machine  having  attained  its 


Fig.  652. 

maximum  charge,  there  is  equilibrium  in  all  its  parts.  From  that  point  it 
only  keeps  itself  up,  and  in  perfectly  dry  air  it  may  work  for  a  long  time 
without  its  being  necessary  to  employ  the  ebonite  plate.  If  this  be  removed, 
and  the  knobs  r  and  r'  are  moved  apart  (fig.  650)  to  a  distance  dependent 
on  the  power  of  the  machine,  on  continuing  to  turn,  a  torrent  of  sparks 
strikes  across  from  one  knob  to  the  other. 

With  plates  of  equal  dimensions  Holtz's  machine  is  far  more  powerful  than 
the  ordinary  electrical  machine  (753).  The  power  is  still  further  increased 
by  suspending  to  the  conductors  C  C'  two  condensers,  H  H'  (765),  which  con- 
sist of  two  glass  tubes  coated  with  tinfoil,  inside  and  out,  to  within  a  fifth  of 
their  height.  Each  of  them  is  closed  by  a  cork,  through  which  passes  a  rod,  - 
communicating  at  one  end  with  the  inner  coating,  and  suspended  to  one  of 
the  conductors  by  a  crook  at  the  other  end.  The  two  external  coatings  are 
connected  by  a  conductor,  G.  They  are,  in  fact,  only  two  small  Leyden 
jars  (770),  one  of  them,  H,  becoming  charged  with  positive  electricity  on  the 
inside  and  negative  on  the  outside  ;  the  other,  H',  with  negative  electricity 
on  the  inside  and  positive  on  the  outside.  Becoming  charged  by  the  play 
of  the  machine  and  being  discharged  at  the  same  rate  by  the  knobs  r  r', 
they  strengthen  the  spark,  which  may  attain  a  length  of  6  or  7  inches. 


700  Frictional  Electricity.  [759  - 

The  current  of  the  machine  is  utilised  by  placing  in  front  of  the  frame 
two  brass  uprights,  O  Q',  with  binding  screws  in  which  are  copper  wires  ;  then, 
by  means  of  the  handles  K  K',  the  rods  which  support  the  knobs  r  r  are  in- 
clined, so  that  they  are  in  contact  with  the  uprights.  The  current  being 
then  directed  by  the  wires,  a  battery  of  six  jars  can  be  charged  in  a  few 
minutes,  water  can  be  decomposed,  a  galvanometer  deflected,  and  Geissler's 
tubes  illuminated  as  with  the  voltaic  battery. 

Kohlrausch  found  that  a  Holtz's  machine  with  a  plate  16  inches  in  dia- 
meter, and  making  5  turns  in  three  seconds,  produced  a  constant  current 
capable  of  decomposing  water  at  the  rate  of  3^  millionths  of  a  milligramme 
in  a  second.  This  is  equal  to  the  effect  produced  by  a  Grove's  cell  in  a  cir- 
cuit of  45,000  ohms  resistance. 

Rossetti,  who  made  a  series  of  measurements  with  a  Holtz's  machine, 
found  that  the  strength  of  the  current  is  nearly  proportional  to  the  velocity 
of  the  rotation  ;  it  increases  a  little  more  rapidly  than  the  rotation.  The  ratio 
of  the  velocity  of  rotation  to  the  strength  of  the  current  is  greater  when  the 
hygrometric  state  increases.  The  current  produced  by  a  Holtz's  machine  is 
quite  comparable  to  that  of  a  voltaic  couple.  Its  electro-motive  force  and 
resistance  are  constant,  provided  the  velocity  of  rotation  and  the  hygrometric 
state  are  constant. 

The  electromotive  force  is  independent  of  the  velocity  of  rotation,  but 
diminishes  as  the  moisture  increases  ;  it  is  nearly  52,000  times  as  great  as 
that  of  a  DanielPs  cell. 

The  internal  resistance  is  independent  of  the  moisture,  but  diminishes 
rapidly  with  increased  velocity  of  rotation.  Thus  with  a  velocity  of  120  turns 
in  a  minute  it  is  represented  by  2,810  million  ohms,  and  with  a  velocity  of 
450  turns  it  is  646  ohms. 

Holtz's  machine  is  very  much  affected  by  the  moisture  of  the  air  ;  but 
Ruhmkorff  found  that  by  spreading  on  the  table  a  few  drops  of  petroleum, 
the  vapours  which  condense  on  the  machine  protect  it  against  the  moisture 
of  the  atmosphere. 

If  the  two  combs  of  a  Holtz's  machine  in  the  ordinary  state  are  connected 
with  the  poles  of  a  second  similar  one,  which  is  then  set  in  action,  the  combs 
of  the  first  become  luminous,  and  the  plate  begins  to  rotate,  but  in  the  oppo- 
site direction  to  its  ordinary  course  ;  the  electricity  thus  transmits  the  motion 
of  the  second  machine  to  the  first  ;  the  one  expends  what  the  other  pro- 
duces. It  may  also  be  observed  that  the  two  machines  are  connected  by 
opposite  poles,  and  the  system  constitutes  a  circuit  which  is  traversed  in  a 
definite  direction  by  a  continuous  electrical  current. 

A  very  simple  and  efficient  machine  of  this  kind  is  made  by  Voss  of 
Berlin.  One  with  a  plate  of  10  inches  diameter  produces  a  spark  of  4  to  5 
inches. 

760.  Carre's  dielectrical  machine. — This  is  a  combination  of  the  old 
form  of  frictional  machine  with  that  of  Holtz.  It  consists  of  two  plates  turning 
in  opposite  directions  (fig.  653):  one,  A,  of  glass,  and  the  other,  B,  of  ebonite. 
They  overlap  each  other,  to  about  f  to  \  of  their  radii.  The  lower  one 
is  slowly  turned  by  means  of  a  handle,  M,  while  the  upper  one  is  rapidly 
rotated  by  an  endless  cord,  which  passes  from  the  large  over  the  small 
wheel. 


-760] 


Carre 's  Dielectrical  Machine. 


701 


The  plate  A,  after  having  been  electrified  positively  between  two  rubbers 
FF',  acts  inductively  through  the  plate  B  on  a  comb  z,  withdrawing  from  it 
negative  electricity,  which  then  passes  to  the  plate  B,  the  conductor  d e 
remaining  positively  electrified;  but  as  the  plate  B  turns  very  quickly,  the 
negative  electricity,  as  it  collects  on  its  surface,  acts  inductively  on  a  second 
comb  g,  which  it  charges  with  negative  electricity,  reverting  itself  to  the 
neutral  state,  while  the  two  conductors  C  and  D,  which  are  onnected  with 
the  comb  gt  become  charged  with  negative  electricity. 


Fig.  653. 

These  conductors,  connected  as  they  are  by  two  ties,  m  and  ?z,  rest  orr 
two  columns — the  one,  #,  of  glass,  and  the  other,  £,  of  ebonite.  A  chain  in 
connection  with  the  ground  is  suspended  from  a  hook,  O,  which  can  be 
raised  at  pleasure,  but  put  in  connection  with  the  comb  z.  The  rubbers 
FFX,  moreover  are  in  connection  with  the  ground  by  means  of  two  bands 
of  tinfoil  along  the  supports. 

Lastly,  at  p  (fig.  654)  is  a  sector  of  varnished  paper  cut  in  the  form 


702 


Frictional  Electricity. 


[760- 


Fig.  654. 


of  a  comb,  and  fastened  to  an  insulating  segment,  P,  of  the  same  shape, 
which  is  used  as  support.  From  the  teeth  of  the  sector  p  positive  electricity 
flows  on  the  plate  B  as  it  moves,  and  by  induction  this  sector  p  yields  to 

the  comb  g  a  surcharge  of  negative 
electricity.  The  rod  d  and  the  knob  e 
may  be  withdrawn  at  will  from  the 
conductor  C  (fig.  653),  so  that  sparks  of 
different  lengths  may  be  taken.  At  r 
is  a  hook  to  which  can  be  attached  the 
Leyden  jars  which  are  to  be  charged. 

Owing  to  the  direct  action,  and 
when  the  inducing  plate  is  at  its  maxi- 
mum charge,  Carre's  machine  is  not 
very  much  affected  by  moisture,  and 
it  yields  a  large  supply  of  electricity. 
With  plates  whose  dimensions  are  respectively  38  and  49  centimetres,  it 
gives  sparks  of  15  to  18  centimetres,  and  more  when  a  condenser  is  added, 
as  in  Holtz's  machine. 

761.  Work  required  for  tne  production  of  electricity.  —  In  all  electrical 
machines  electricity  is  only  produced  by  the  expenditure  of  a  definite  amount 
of  force,  as  will  at  once  be  seen  by  a  perusal  of  the  preceding  descriptions. 
The  action  of  those  machines,  however,  which  work  continuously,  is  some- 
what complex.  Not  only  is  electricity  produced,  but  heat  also  ;  and  it  has 
been  hitherto  impossible  to  estimate  separately  the  work  required  for  the 
heat  from  that  required  for  the  electricity.  This  is  easily  done  in  theory,  but 
not  in  practice  :  how  difficult,  for  instance,  it  would  be  to  determine  the  tem- 
perature of  the  cushion,  or  of  the  plate  of  a  Ramsden's  machine  ! 

In  lifting  the  plate  off  a  charged  electrophorus  a  certain  expenditure  of 
force  is  needed,  though  it  be  too  slight  to  be  directly  estimated  (752).  With 
a  Holtz's  machine  it  may  be  readily  shown  by  experiment  that  there  is  a 
definite  expenditure  of  force  in  working  it.  If  such  a  machine  be  turned 
without  having  been  charged,  the  work  required  is  only  that  necessary  to 
overcome  the  passive  resistances.  If,  however,  one  of  the  sectors  be  charged 
and  the  electric  action  comes  into  play,  it  will  be  observed  that  there  must 
be  a  distinct  increase  in  the  mechanical  effort  necessary  to  work  the  machine. 
The  work  required  to  charge  an  unelectrified  conductor  to  a  given  poten- 
tial may  be  deduced  from  the  following  considerations  :  —  To  impart  to  a  body 
which  is  at  potential  V  a  quantity  of  electricity  O  would  require  an  amount 
of  work  represented  by  O  V  (739).  But  in  the  case  of  an  unelectrified  body  it 
is  neutral  at  the  outset  —  that  is,  at  zero  potential  ;  and  we  may  conceive  the 
electricity  imparted  to  it  in  a  series  of  n  very  small  charges  of  q  each,  such 
that  nq  =  Q\  and  as  the  potential  rises  proportionally  to  the  number  of 
charges,  it  may  be  assumed  that  the  work  done  is  equal  to  that  required  to 
charge  the  body  to  an  average  potential  of  £  V  ;  hence  the  work  in  question 


From  the  relation  between  the  quantity  of  heat  produced  by  the  current 
of  a  Holtz's  machine  working  under  definite  conditions,  and  the  amount  of 
work  expended  in  producing  the  rotation  of  the  plate,  Rossetti  has  made  a 
determination  of  the  mechanical  equivalent  of  heat,  which  gave  the  number 


-762] 


Spark. 


703 


1,397,  agreeing  therefore  very  well  with  the   numbers  obtained  by  other 
methods  (497). 

j6ia.  Thomson's  water-dropping1  collector. — This  may  be  given  as  an 
illustration  of  an  arrangement  by  which  a  known  charge  may  be  almost  in- 
definitely multiplied.  In  fig.  655  I  is  an  insulated  metal  cylinder  called  the 
inductor,  and  water  falls  in  drops  from  an  uninsulated  metal  tap  the  nozzle 
>of  which  is  in  the  centre  of  the  cylinder.  Directly  below  the  inductor  is  a 
second  similar  insulated  metal  cylinder  R,  with  a  funnel  the  nozzle  of  which 
is  also  in  the  centre.  This  second  cylinder  is  called 
the  receiver.  If  now  a  very  feeble  positive  charge  be 
given  to  the  inductor  I,  the  drops  of  water  as  they 
issue  will  be  charged  with  positive  electricity,  and  will 
repel  each  other  as  they  issue.  FalHng  on  the  funnel 
of  the  receiver  they  will  give  up  to  this  the  whole  of 
their  charge,  and  the  water  as  it  issues  will  be  neutral. 
The  charge  thus  imparted  to  R  will  go  on  increasing 
until  the  loss  equals  the  production,  or  until  the  drops 
issuing  from  the  inductor  are  repelled  by  the  receiver, 
so  that  they  do  not  fall  into  the  funnel. 

Suppose  two  such  apparatus  I  I'  and  R  R'  be 
arranged  near  each  other,  and  so  that  the  inductor  I 
•of  the  one  is  in  metallic  connection  with  the  receiver 
R'  of  the  other,  and  conversely  the  inductor  I'  in 
connection  with  the  receiver  R  of  the  other.  By  this 
means  they  will  act  on  each  other  and  reciprocally 
increase  their  charges.  If  a  feeble  charge  be  given 
to  one  of  the  inductors,  the  charges  will  go  on  in- 
creasing until  sparks  pass  between.  It  is  not  even 
necessary  to  give  a  charge  at  the  outset,  the  ordinary  electricity  of  the 
.atmosphere  is  sufficient. 

The  energy  in  this  apparatus  is  derived  from  that  of  the  falling  body,  and 
would  be  exactly  equivalent  to  it  if  there  were  no  loss,  and  if  the  drops 
reached  the  funnel  without  any  velocity. 


Fig.  655. 


EXPERIMENTS   WITH   THE   ELECTRICAL   MACHINE. 

762.  Spark. — One  of  the  most  curious  phenomena  observed  with  the 
electrical  machine  is  the  spark  drawn  from  the  conductor  when  a  finger  is 
presented  to  it.  The  positive  electricity  of  the  conductor,  acting  inductively 
on  the  neutral  electricity  of  the  body,  decomposes  it,  repelling  the  positive 
and  attracting  the  negative.  When  the  attraction  of  the  opposite  electricities 
is  sufficiently  great  to  overcome  the  resistance  of  the  air,  they  recombine 
with  a  smart  crack  and  a  spark.  The  spark  is  instantaneous,  and  is  accom- 
panied by  a  sharp  prickly  sensation,  more  especially  with  a  powerful  machine. 
Its  shape  varies.  When  it  strikes  at  a  short  distance  it  is  rectilinear,  as  seen 
in  fig.  656.  Beyond  two  or  three  inches  in  length  the  spark  becomes  irre- 
gular, and  has  the  form  of  a  sinuous  curve  with  branches  (fig.  657).  If  the 
discharge  is  very  powerful,  the  spark  takes  a  zigzag  shape  (fig.  658).  These 
;two  latter  appearances  are  seen  in  the  lightning  discharge. 


704 


Fractional  Electricity. 


[762- 


A  spark  may  be  taken  from  the  human  body  by  aid  of  the  insulating 
stool,  which  is  simply  a  low  stool  with  stout  glass  legs.     The  person  standing 


Fig.  656. 


Fig.  657- 


Fig.  658. 


on  this  stool  touches  the  prime  conductor,  and,  as  the  human  body  is  a  con- 
ductor, the  electricity  is  distributed  over  its  surface  as  over  an  ordinary 
insulated  metallic  conductor.  The  hair  diverges  in  consequence  of  repulsion, 
a  peculiar  sensation  is  felt  on  the  face,  and  if  another  person,  standing  on 
the  ground,  presents  his  hand  to  any  part  of  the  body,  a  smart  crack  with  a 
pricking  sensation  is  produced. 

A  person  standing  on  an  insulated  stool  may  be  positively  electrified  by 
being  struck  with  a  catskin.     If  the  person  holding  the  catskin  stands  on  an 

insulated  stool,  the  striker  becomes 
positively  and  the  person  struck  nega- 
tively electrified. 

763.  Electrical  chimes. — The  elec- 
trical chimes  is  a  piece  of  apparatus 
consisting  of  three  bells  suspended  to 
a  horizontal  metal  rod  (fig.  659).  Two 
of  them,  A  and  B,  are  in  metallic  con- 
nection with  the  conductor ;  the  middle 
bell  hangs  by  a  silk  thread,  and  is  thus 
insulated  from  the  conductor,  but  is 
connected  with  the  ground  by  means 
of  a  chain.  Between  the  bells  are 

small  copper  balls  suspended  by  silk  threads.  When  the  machine  is  worked 
the  bells  A  and  B,  being  positively  electrified,  attract  the  copper  balls,  and 


-764] 


Electrical  Whirl  or  Vane. 


70S 


after  contact  repel  them.  Being  now  positively  electrified,  they  are  in  turn 
attracted  by  the  middle  bell,  C,  which  is  charged  with  negative  electricity  by 
induction  from  A  to  B.  After  contact  they  are  again  repelled,  and  this  pro- 
cess is  repeated  as  long  as  the  machine  is  in  action. 

Fig.  660  represents  an  apparatus  originally  devised  by  Volta  for  the 
purpose  of  illustrating  what  he  supposed  to  be  the  motion  of  hail  between 
two  clouds  oppositely  electrified.  It  consists  of  a  tubulated  glass  shade, 
with  a  metal  base,  on  which  are  some  pith  balls.  The  tubulure  has  a  metal 
cap,  through  which  passes  a  brass  rod,  provided  with  a  metal  disc  or  sphere 
at  the  lower  end,  and  at  the  upper  with  a  ring,  which  touches  the  prime  con- 
ductor. 

When  the  machine  is  worked,  the  sphere  becoming  positively  electrified 
attracts  the  light  pith  balls,  which  are  then  immediately  repelled,  and,  having 
lost  their  charge  of  positive  electricity,  are  again  attracted,  again  repelled, 
and  so  on,  as  long  as  the  machine  continues  to  be  worked.  An  amusing 
modification  of  this  experiment  is  frequently  made  by  placing  between  the 
two  plates  small  pith  figures,  somewhat  loaded  at  the  base.  When  the 
machine  is  worked,  the  figures  execute  a  regular  dance. 


Fig.  660. 


Fig.  661. 


764.  Electrical  wliirl  or  vane. — The  electrical  whirl  or  vane  consists  of 
5  or  6  wires,  terminating  in  points,  all  bent  in  the  same  direction,  and  fixed 
in  a  central  cap,  which  rotates  on  a  pivot  (fig.  66 1).  When  the  apparatus  is 
placed  on  the  conductor,  and  the  machine  worked,  the  whirl  begins  to  revolve 
in  a  direction  opposite  that  of  the  points.  This  motion  is  not  analogous  to 
that  of  the  hydraulic  tourniquet  (149).  It  is  not  caused  by  a  flow  of  material 
fluid,  but  is  owing  to  a  repulsion  between  the  electricity  of  the  points  and  that 
which  they  impart  to  the  adjacent  air  by  conduction.  The  electricity,  being 
accumulated  on  the  points  in  a  high  state  of  density,  passes  into  the  air,  and, 
imparting  thus  a  charge  of  electricity,  repels  this  electricity,  while  it  is  itself 
repelled.  That  this  is  the  case  is  evident  from  the  fact  that  on  approaching 
the  hand  to  the  whirl  while  in  motion,  a  slight  draught  is  felt,  due  to  the 

z  z 


7o6 


Frictional  Electricity. 


[764- 


movement  of  the  electrified  air,  while  in  vacuo  the  apparatus  does  not  act  at 
all.  This  draught  or  wind  is  known  as  the  electrical  aura. 

If  the  experiment  be  made  in  water,  the  fly  remains  stationary,  for  water  is  a 
good  conductor  ;  but  in  olive  oil,  which  is  a  bad  conductor,  the  whirl  rotates. 

When  the  electricity  thus  escapes  by  a  point,  the  electrified  air  is  repelled 
so  strongly  as  not  only  to  be  perceptible  to  the  hand,  but  also  to  engender  a 


Fig.  663. 

current  strong  enough  to  blow  out  a  candle.  Fig.  662  shows  this  experiment. 
The  same  effect  is  produced  by  placing  a  taper  on  the  conductor  and  bring- 
ing near  it  a  pointed  wire  held  in  the  hand  (fig.  663).  The  current  arises  in 
this  case  from  the  flow  of  air  electrified  with  the  contrary  electricity  which 
escapes  by  the  point  under  the  influence  of  the  machine. 

The  electrical  orrery  and  the  electrical  inclined  plane  are  analogous  in 
their  action  to  these  pieces  of  apparatus. 


-765] 


Condensers  or  Accumulators. 


707 


CHAPTER   IV. 

CONDENSATION   OR   ACCUMULATION   OF   ELECTRICITY 

v  765.  Condensers  or  Accumulators. — A  condenser  is  an  apparatus  for 
condensing  a  large  quantity  of  electricity  on  a  comparatively  small  surface. 
The  form  may  vary  considerably,  but  in  all  cases  consists  essentially  of  two 
insulated  conductors,  separated  by  a  non-conductor,  and  the  working  depends 
on  the  action  of  induction.  When  an  insulated  conductor  is  near  other 
conductors,  and  particularly  when  these  latter  are  connected  with  the  earth, 
the  capacity  of  the  conductor  is  increased  ;  that  is  to  say,  it  requires  a 
greater  quantity  of  electricity  to  raise  it  to  a  given  potential  than  when  the 
other  conductors  are  away.  An  arrangement  of  this  kind  is  called  a  con- 
denser m  accumulator,  the  latter  term,  though  less  usual,  being  preferable,  as 
the  former  tacitly  implies  some  hypothesis  of  the  nature  of  electricity. 

Epinus's  condenser  consists  of  two  circular  brass  plates,  A  and  B  (fig.  664), 
with  a  sheet  of  glass,  C,  between  them.     The  plates,  each  provided  with  a 


Fig.  664. 

pith-ball  pendulum,  are  mounted  on  insulated  glass  legs,  and  can  be  moved 
along  a  support  and  fixed  in  any  position.  When  electricity  is  to  be  ac- 
cumulated, the  plates  are  placed  in  contact  with  the  glass,  and  then  one  of 
them,  B  for  instance,  is  connected  with  the  electrical  machine,  and  the  other 
placed  in  connection  with  the  ground,  as  shown  in  fig.  665. 

z  z  2 


708 


Frictional  Electricity. 


[765- 


In  explaining  the  action  of  the  condenser,  it  will  be  convenient  in  each 
case  to  call  that  side  of  the  metal  plate  nearest  the  glass  the  anterior  and 
the  other  the  posterior  side.  And  first  let  A  be  at  such  distance  from  B  as 
to  be  out  of  the  sphere  of  its  action.  The  plate  B,  which  is  then  connected 
with  the  conductor  of  the  electrical  machine,  takes  its  maximum  charge, 
which  is  distributed  equally  on  its  two  faces,  and  the  pendulum  diverges 


Fig.  665. 

widely.  If  the  connection  with  the  machine  be  interrupted,  nothing  would 
be  changed  ;  but  if  the  plate  A  be  slowly  approached,  its  neutral  state  being 
decomposed  by  the  influence  of  B,  negative  electricity  is  accumulated  on  its 
anterior  face,  n  (fig.  666),  and  positive  passes  into  the  ground.  But  as 
the  negative  electricity  of  the  plate  A  reacts  in  its  turn  on  the  positive  of 
the  plate  B,  the  latter  ceases  to  be  equally  distributed  on  both  faces,  and 
is  accumulated  on  its  anterior  face,  m.  The  posterior  face,  p,  having  thus 
lost  a  portion  of  its  electricity,  its  density  has  diminished,  and  is  no  longer 
equal  to  that  of  the  machine,  and  the  pendulum  b  diverges  less  widely. 
Hence  B  can  receive  a  fresh  quantity  from  the  machine,  which,  acting  as 
just  described,  decomposes  by  induction  a  second  quantity  of  neutral  fluid 
on  the  plate  A.  There  is  then  a  new  accumulation  of  negative  electricity 

on  the  face  n,  and  consequently  of  posi- 
tive electricity  on  m.  But  each  time  that 
the  machine  gives  off  electricity  to  the 
plate,  only  a  part  of  this  passes  to  the 
face  m,  the  other  remaining  on  the  face 
p  ;  the  density  here,  therefore,  continues 
to  increase  until  it  equals  that  of  the 
machine.  From  this  moment  equilibrium 
is  established,  and  a  limit  to  the  charge 
is  attained  which  cannot  be  exceeded. 
The  quantity  of  electricity  accumulated 
now  on  the  two  faces  m  and  n  is  very  considerable,  and  yet  the  pendulum 
diverges  just  as  much  as  it  did  when  A  was  absent,  and  no  more  ;  in  fact, 
the  density  at/  is  just  what  it  was  then — namely,  that  of  the  machine. 


Fig.  666. 


-766]          Slow  Discharge  and  Instantaneous  Discharge.          709 

When  the  condenser  is  charged — that  is,  when  the  opposite  electricities 
are  accumulated  on  the  anterior  faces — connection  with  the  ground  is  broken 
by  raising  the  wires.  The  plate  A  is  charged  with  negative  electricity,  but 
simply  on  its  anterior  face  (fig.  666),  the  other  side  being  neutral.  The 
plate  B,  on  the  contrary,  is  electrified  on  both  sides,  but  unequally  ;  the 
accumulation  is  only  on  its  anterior  face,  while  on  the  posterior,^,  the  den- 
sity is  simply  equal  to  that  of  the  machine  at  the  moment  the  connections 
are  interrupted.  In  fact,  the  pendulum  b  diverges,  and  a  remains  vertical. 
But  if  the  two  plates  are  removed,  the  two  pendulums  diverge  (fig.  664), 
which  is  owing  to  the  circumstance  that,  as  the  plates  no  longer  act  on  each 
•other,  the  positive  electricity  is  equally  distributed  on  the  two  faces  of  the  plate 
B,  and  the  negative  on  those  of  the  plate  A. 

'766.  Slow  discharge  and  instantaneous  discharge. — While  the  plates 
A  and  B  are  in  contact  with  the  glass  (fig.  665),  and  the  connections  inter- 
rupted, the  condenser  may  be  discharged — that  is,  restored  to  the  neutral 
state — in  two  ways  ;  either  by  a  slow  or  by  an  instantaneous  discharge.  To 
discharge  it  slowly,  the  plate  B — that  is,  the  one  containing  an  excess  of  elec- 
tricity— is  touched  with  the  finger  ;  a  spark  passes,  all  the  electricity  on  p 
passes  into  the  ground,  the  pendulum  b  falls,  but  a  diverges.  For  B,  having 
lost  part  of  its  electricity,  only  retains  on  the  face  m  that  held  by  the  inductive 
influence  of  the  negative  on  A.  But  the  quantity  thus  retained  at  B  is  less 
than  that  on  A ;  this  has  free  electricity,  which  makes  the  pendulum  a  diverge ; 
and  if  it  be  now  touched,  a  spark  passes,  the  pendulum  a  sinks  while  b  rises, 
and  so  on  by  continuing  to  touch  alternately  the  two  plates.  The  discharge 
only  takes  place  slowly  :  in  very  dry  air  it  may  require  several  hours.  If  the 
plate  A  were  touched  first,  no  electricity  would  be  removed,  for  all  it  has  is 
retained  by  that  of  the  plate  B.  To  remove  the  total  quantity  of  electricity 
by  the  method  of  alternate  contacts,  an  infinite  number  of  such  contacts  would 
theoretically  be  required. 

An  instantaneous  discharge  may  be  effected  by  means  of  the  discharging 
rod  (fig.  667).     This  consists  of  two  bent  brass  rods,  terminating  in  knobs 
and  joined  by  a  hinge.     When  provided  with  glass 
handles,  as  in  fig.  667,  it  forms  a  glass  discharging 
rod.      In  using  this  apparatus  one  of  the  knobs  is 
pressed  against  one  plate  of  the  condenser,  and  the 
other  knob  brought  near  the  other.     At  a  certain  dis- 
tance a  spark  strikes  from  the  plate  to  the  knob,  caused 
by  the  sudden  recomposition  of  the  two  opposite  elec- 
tricities. 

When  the  condenser  is  discharged  by  the  dis- 
charger no  sensation  is  experienced,  even  though  the 
latter  be  held  in  the  hand  ;  of  the  two  conductors, 
the  electricity  chooses  the  better,  and  hence  the  Fig  66? 

discharge   is    effected  through   the   metal,   and    not 

through  the  body.  But  if,  while  one  hand  is  in  contact  with  one  plate 
the  other  touches  the  second,  the  discharge  takes  place  through  the  breast 
and  arms,  and  a  considerable  shock  is  felt ;  and  the  larger  the  surface  of 
the  condenser,  and  the  greater  the  electric  density,  the  more  violent  is  the 
shock. 


Frictional  Electricity. 


[767- 


767.  Condensing:  force.  —  The  condensing  force  is  the  relation  between 
the   whole   charge,   which  the  collecting  plate  can  take  while    under  the 
influence  of  the  second  plate,  to  that  which  it  would  take  if  alone  ;  in  other 
words,  it  is  the  ratio  of  the  capacities  under  the  two  conditions. 

768.  Xiimit  of  the  charge  of  condensers.  —  The  quantity  of  electricity 
which  can  be  accumulated  on  each  plate  is  cceteris  paribus,  proportional  to 
the  potential  of  the  electricity  on  the  conductor,  and  to  the  surface  of  the 
plates  ;  it  decreases  as  the  insulating  plate  is  thicker,  and  it  differs  with  the 
specific  inductive  capacity  of  the  substance.     There  is,  however,  a  limit  in 
the  case  of  each  condenser  beyond  which  it  cannot  be  charged.     The  effect 
of  dielectric  polarisation  (747)  is  to  put  the  medium  into  a  state  of  strain 
from  which  it  is  always  trying  to  release  itself,  and  which  is  the  equivalent 
of  the  work  done  in  charging  a  condenser.     This  is,  indeed,  the  seat  of  the 
electrical  energy.     It  is  as  if  two  surfaces  were  pulled  together  by  elastic 
threads  which  repelled  each  other  laterally.     When  the  strain  exceeds  a 
certain  limit,  a  discharge  takes  place  through  the  mass  of  the  dielectric, 
generally  accompanied  by  light  and  sound,  and  with  a  temporary  or  perma- 
nent rupture  of  the  dielectric  according  as  it  is  fluid  or  solid.     This  is  what 
takes  place  when  a  substance  —  glass,  for  instance  —  is  exposed  to  a  continually 
increasing  pressure  ;  a  point  is  ultimately  reached  at  which  the  glass  gives 
way,  and  the  pressure  at  that  point  is  a  measure  of  the  resistance  to  fracture 
of  the  glass.    In  like  manner,  the  point  at  which  the  electrical  discharge  takes 
place  is  a  measure  of  the  electrical  strength  of  the  dielectric.    This  electrical 
strength  is  greater  in  dense  than  in  rarefied  air,  and  in  glass  than  in  air. 

We  may,  following  Maxwell,  further  illustrate  this  point  by  the  twisting 
of  a  wire  :  a  wire  in  which  a  small  force  produces  a  permanent  twist  corre- 
sponds to  the  case  of  the  conduction  of  electricity  in  a  good  conductor;  one 
which  having  been  twisted,  reverts  to  its  former  shape  when  the  twisting  force 

is  removed,  is  com- 
pletely elastic,  and 
corresponds  to  a 
perfect  insulator 
with  respect  to  the 
charge  employed. 
If  no  permanent 
twist  can  be  given 
to  the  wire  by  a 
force  which  does 
not  break  it,  the 
wire  is  brittle.  A 
dielectric  such  as 
air,  which  does  not 
transmit  electricity 
except  by  disruptive 
discharge,  may  be 
said  to  be  electri- 
cally  brittle. 

769.  Fulminating  pane.     Franklin's  plate.—  This  is  a  simple  form  of 
the  condenser,  and  is  more  suitable  for  giving  strong  shocks  and  sparks.     It 


-  668- 


-770] 


Leyden  Jar. 


711 


consists  of  a  glass  plate  fixed  in  a  wooden  frame  (fig.  668)  ;  on  each  side  of 
the  glass,  pieces  of  tinfoil  are  fastened  opposite  each  other,  leaving  a  space 
free  between  the  edge  and  the  frame.  It  is  well  to  cover  this  part  of  the 
glass  with  an  insulating  layer  of  shellac  varnish.  One  of  the  sheets  of  tin- 
foil is  connected  with  the  ring  on  the  frame  by  a  strip  of  tinfoil,  so  that  it  can 
be  put  in  communication  with  the  ground  by  means  of  a  chain.  To  charge 
the  pane  the  insulated  side  is  connected  with  the  machine.  As  the  other  side 
communicates  with  the  ground,  the  two  coatings  play  exactly  the  part  of  the 
condenser.  On  both  plates  there  are  accumulated  large  quantities  of  contrary 
electricities. 

The  pane  may  be  discharged  by  pressing  one  knob  of  the  discharger 
against  the  lower  surface,  while  the  other  is  brought  near  the  upper  coating. 
A  spark  ensues,  due  to  the  recombination  of  the  two  electricities  ;  but  the 
operator  experiences  no  sensation,  for  the  discharge  takes  place  through  the 
wire.  But  if  the  connection  between  the  two  coatings  be  made  by  touching 
them  with  the  hands  a  violent  shock  is  felt  in  the  hands  and  breast,  for  the 
combination  then  takes  place  through  the  body. 

J,/~77o.  leyden  jar. — The  Leyden  jar ',  so  named  from  the  town  of  Leyden, 
where  it  was  invented,  is  essentially  a  modified  condenser,  or  fulminating 
pane  rolled  up.  Fig.  669  represents  a  Leyden  jar  of  the  usual  French  shape 
in  the  process  of  being  charged.  It  consists  of  a  glass  jar  of  any  conve- 
nient size,  the  interior  of  which  is  either  coated  with  tinfoil  or  filled  with  thin 
leaves  of  copper,  or  with  gold-leaf.  Up  to  a  certain  distance  from  the  neck 
the  outside  is  coated  with  tinfoil.  The  neck  is  provided  with  a  cork,  through 
which  passes  a  brass  rod, 
which  terminates  at  one 
end  in  a  knob,  and  com- 
municates with  the  metal 
in  the  interior.  The  me- 
tallic coatings  are  called 
respectively  the  inner  and 
outer  coatings  or  arma- 
tures. Like  any  other  con- 
denser, the  jar  is  charged 
by  connecting  one  of  the 
coatings  with  the  ground, 
and  the  other  with  the 
source  of  electricity.  When  it  is  held  in  the  hand  by  the  outer  coating,  and 
the  knob  presented  to  the  positive  conductor  of  the  machine,  positive  electri- 
city is  accumulated  on  the  inner  and  negative  electricity  on  the  outer  coating. 
The  reverse  is  the  case  if  the  jar  is  held  by  the  knob,  and  the  external  coating 
presented  to  the  machine.  The  positive  charge  acting  inductively  across 
the  dielectric  glass,  decomposes  the  electricity  of  the  outer  coating,  attracting 
the  negative  and  repelling  the  positive,  which  escapes  by  the  hand  to  the 
ground.  Thus  it  will  be  seen  that  the  action  of  the  jar  is  the  same  as  that 
of  the  condenser,  and  all  that  has  been  said  of  this  applies  to  the  jar,  sub- 
stituting the  two  coatings  for  the  two  plates  A  and  B  of  fig.  665. 

Like  any  other  condenser,  the  Leyden  jar  may  be  discharged  either  slowly 
or  instantaneously.     For  the  latter  purpose  it  is  held  in  the  hand  by  the  out- 


Fig.  669. 


712 


Frictional  Electricity. 


[770- 


side  coating  (fig.  670),  and  the  two  coatings  are  then  connected  by  means  of 
the  simple  discharger.  Care  must  be  taken  to  touch  first  the  external  coat- 
ing with  the  discharger,  otherwise  a  smart  shock  will  be  felt.  To  discharge 
it  slowly  the  jar  is  placed  on  an  insulated  plate,  and  first  the  inner  and  then 
the  outer  coating  touched,  either  with  the  hand  or  with  a  metallic  conductor. 
A  slight  spark  is  seen  at  each  discharge. 

V     Fig.  671    represents  a  very  pretty  experiment  for  illustrating  the   slow 
discharge.     The  rod  terminates  in  a  small  bell,  d,  and  the  outside  coating 


Fig.  670. 


Fig.  671. 


in  connected  with  an  upright  metallic  support,  on  which  is  a  similar  bell,  e. 
Between  the  two  bells  a  light  brass  ball  is  suspended  by  a  silk  thread.  The 
jar  is  then  charged  in  the  usual  manner  and  placed  on  the  support  m.  The 
internal  coating  contains  a  quantity  of  free  electricity  ;  the  pendulum  is 
attracted  and  immediately  repelled,  striking  against  the  second  bell,  to  which 
it  imparts  its  free  electricity.  Being  now  neutralised,  it  is  again  attracted  by 


Fig.  672. 

the  first  bell,  and  so  on  for  some  time,  especially  if  the  air  be  dry,  and  the 
jar  somewhat  large. 

771.  I.eyden  jar  with  movable  coatings. — This  apparatus  (fig.  672)  is 
used  to  demonstrate  that  in  the  Leyden  jar  the  opposite  electricities  are  not 
accumulated  on  the  coatings  merely,  but  are  stored  up  in  the  state  of  strain 


-773]  Residual  Charge.  713 

into  which  the  glass  is  put.  It  consists  of  a  somewhat  conical  glass  vessel, 
B,  with  movable  coatings  of  zinc  or  tin,  C  and  D.  These  separate  pieces  placed 
one  in  the  other,  as  shown  in  figure  A,  form  a  complete  Leyden  jar.  After  hav- 
ing charged  the  jar,  it  is  placed  on  an  insulating  cake  ;  the  internal  coating  is 
first  removed  by  the  hand,  or  better  by  a  glass  rod,  and  then  the  glass  vessel. 
The  coatings  are  found  to  contain  little  or  no  electricity,  and  if  they  are 
placed  on  the  table  they  are  restored  to  the  neutral  state.  Nevertheless, 
when  the  jar  is  put  together  again,  as  represented  in  the  figure  at  A,  a  shock 
may  be  taken  from  it  almost  as  strong  as  if  the  coatings  had  not  been  re- 
moved. It  is  therefore  concluded  that  the  coatings  principally  play  the  part 
of  conductors,  distributing  the  electricity  over  the  surface  of  the  glass,  which 
thus  becomes  polarised,  and  retains  this  state  even  when  placed  on  the  table, 
owing  to  its  imperfect  conductivity. 

The  experiment  may  be  conveniently  made  without  any  special  form 
of  apparatus  by  forming  a  Leyden  jar,  of  which  the  inside  and  outside 
coatings  are  of  mercury,  charging  it ;  then  having  mixed  the  two  coatings, 
the  apparatus  is  put  together  again,  upon  which  a  discharge  may  be  once 
more  taken. 

772.  Xiichtenberg's  figures. — This  experiment  well  illustrates  the  oppo- 
site electrical  conditions  of  the  two  coatings  of  a  Leyden  jar.  Holding  a 
jar  charged  with  positive  elec- 
tricity by  the  hand,  a  series  of 
lines  are  drawn  with  the  knob 
on  a  cake  of  resin  or  vulcanite  ; 
then  having  placed  the  jar  on 
an  insulator,  it  is  held  by  the 
knob,  and  another  series  traced 
by  means  of  the  outer  coating, 
If  now  a  mixture  of  red-lead  and 
flour  of  sulphur  be  projected  on 
the  cake,  the  sulphur  will  attach 
itself  to  the  positive  lines,  and 
the  red  lead  to  the  negative 
lines ;  the  reason  being  that  in 
mixing  the  powders  the  sulphur 
has  become  negatively  electri- 
iied,  and  the  red  lead  positively. 
The  sulphur  will  arrange  itself 
in  tufts  with  numerous  diverging  Fig-  673' 

branches,  while  the  red  lead  will  take  the  form  of  small  circular  spots,  in- 
dicating a  difference  in  the  two  electricities  on  the  surface  of  the  resin. 
These  figures  form,  in  short,  a  very  sensitive  electroscope  for  investigating 
the  distribution  of  electricity  on  an  insulating  surface. 

Fig.  673  represents  the  appearance  of  a  plate  of  resin,  which  has  been 
touched  by  the  knob  of  a  Leyden  jar  charged  with  positive  electricity,  and 
lias  then  been  dusted  with  lycopodium  powder. 

Y^~773-  Residual  charge. — Not  only  do  the  electricities  adhere  to  the  two 
surfaces  of  the  insulating  medium  which  separates  them,  but  they  penetrate 
to  a  certain  extent  into  the  interior,  as  is  shown  by  the  following  experi- 


Frictional  Electricity. 


[773- 


ment  : — A  condenser  is  formed  of  a  plate  of  shellac  and  movable  metal 
plates.  It  is  then  charged,  retained  in  that  state  for  some  time,  and  after- 
wards discharged.  On  removing  the  metal  coatings  and  examining  both 
surfaces  of  the  insulator,  they  show  no  signs  of  electricity.  After  some  time, 
however,  each  face  exhibits  the  presence  of  some  electricity  of  the  same 
kind  as  that  of  the  plate  with  which  it  was  in  contact  while  the  apparatus 
was  charged.  This  is  explained,  by  some,  as  a  kind  of  electrical  absorp- 
tion. 

A  phenomenon  frequently  observed  in  Leyden  jars  is  of  the  same  nature. 
When  a  jar  has  been  discharged  and  allowed  to  stand  a  short  time,  it 
exhibits  a  second  charge,  which  is  called  the  electric  residue.  The  jar  may 
be  again  discharged,  and  a  second  residue  will  be  left,  feebler  than  the  first,, 
and  so  on,  for  three  or  four  times.  Indeed,  with  a  delicate  electroscope  a 
long  succession  of  such  residues  may  be  demonstrated.  The  residue  is 
greater  the  longer  the  jar  has  remained  charged.  The  magnitude  of  the 
residue  further  depends  on  the  amount  of  the  charge,  and  also  on  the 
degree  in  which  the  metal  plates  are  in  contact  with  the  insulator.  It 
varies  with  the  nature  of  the  substance,  but  there  is  no  residue  with 
either  liquids  or  gaseous  insulators.  Faraday  found  that  with  paraffine 
the  residue  was  greatest,  then  with  shellac,  while  with  glass  and  sulphur  it 
was  least  of  all.  Kohlrausch  has  found  that  the  residue  is  nearly  proportional 
to  the  thickness  of  the  insulator.  If  successive  small  charges,  alternately 
positive  and  negative,  be  imparted  to  the  jar,  it  is  found  that  the  residual 
charges  come  out  in  the  reverse  order  in  which  the  original  charges 
go  in. 

Maxwell  proved  that  a  dielectric  composed  of  strata  of  different  materials 
may  exhibit  the  phenomena  of  the  residual  charge,  even  though  none  of  the 
substances  composing  it  exhibit  it  when  alone. 

From  what  has  been  said  as  to  the  state  of  mechanical  strain  in  which 
the  dielectric  of  a  condenser  is  thrown  when  charged  with  electricity,  it  is 
not  difficult  to  account  for  the  phenomenon  of  the  residual  charge.  An 
elastic  body,  such  as  a  steel  plate,  which  has  been 
twisted  or  bent,  reverts  to  its  original  state  when  the 
force  which  brought  about  the  deformation  ceases  to- 
act,  but  not  quite  completely.  A  certain  length  of 
time  is  required  for  this  alteration  to  take  place,  but 
the  change  is  promoted  by  any  gentle  mechanical 
action,  such  as  tapping,  which  gives  the  molecules  a 
certain  freedom  of  motion.  Hopkinson  has  made 
an  experiment  with  a  Leyden  jar  which  is  quite  ana- 
logous to  this.  A  glass  vessel  (fig.  674)  contains  sul- 
phuric acid,  and  in  it  is  placed  a  thinner  one,  about  half 
full  of  the  same  liquid.  Platinum  wires  dip  in  the  two  liquids,  one  of  which 
is  in  connection  with  the  prime  conductor  of  an  electrical  machine,  while  the 
other  is  connected  with  the  earth.  The  arrangement  forms,  in  short,  a  con- 
denser, the  coatings  of  which  are  sulphuric  acid.  When,  after  being  thus 
charged,  the  jar  is  discharged,  after  some  time  a  residual  discharge  may  be 
taken  by  again  connecting  the  wires  ;  if,  however,  the  inner  jar  be  gently 
struck  with  a  piece  of  wood,  the  residue  makes  its  appearance  much  more 


Fig.  674. 


-775] 


The  Universal  Discharger. 


71$ 


rapidly.  The  same  observer  draws  a  parallel  between  the  phenomena  of  the 
residual  charge  and  those  of  residual  magnetism  (715). 

V^74.  Electric  batteries. — The  charge  which  a  Leyden  jar  can  take 
depends  on  the  extent  of  the  coated  surface,  and  for  small  thicknesses  is 
inversely  proportional  to  the  thickness  of  the  insulator.  Hence,  the  larger 
and  thinner  the  jar  the  more  powerful  the  charge.  But  very  large  jars  are 
expensive,  and  liable  to  break  ;  and  when  too  thin,  the  accumulated  elec- 
tricities are  apt  to  discharge  themselves  through  the  glass,  especially  if 
it  is  not  quite  homogeneous.  Leyden  jars  have  usually  from  £  to  3  square 
feet  of  coated  surface.  For  more  powerful  charges  electric  batteries  are 
used. 

An  electric  battery  consists  of  a  series  of  Leyden  jars,  whose  internal 
and  external  coatings  are  respectively  connected  with  each  other  (fig.  675). 
They  are  usually  placed  in  a  wooden  box  lined  on  the  bottom  with  tinfoil. 
This  lining  is  connected  with  two  metal  handles  in  the  sides  of  the 
box.  The  inner  coatings  are  connected  with  each  other  by  metal  rods, 
and  the  battery  is  charged  by  placing  the  inner  coatings  in  connection 
with  the  prime  conductor,  while  the  outer  coatings  are  connected  with 
the  ground  by  means  of  a  chain  fixed  to  the  handles.  A  quadrant  electro- 
meter fixed  to  one  jar  indicates  the  charge  of  the  battery.  Although 
there  is  a  large 
quantity  of  elec- 
tricity accumulated 
in  the  apparatus 
the  divergence  is 
not  great,  for  it  is 
simply  due  to  the 
free  electricity  on 
the  inner  coating. 
The  larger  and 
more  numerous 
they  are,  the  longer 
is  the  time  required 
to  charge  the  bat- 
tery, but  the  effects 
are  so  much  the 
more  powerful 

(784). 

When  a  battery 

is  to  be  discharged,  the  coatings  are  connected  by  means  of  thejdischarging- 
rod,  the  outside  coating  being  touched  first.  Great  care  is  required,  for  with 
large  batteries  serious  and  even  fatal  accidents  may  occur. 

775.  The  universal  discharger. — This  is  an  almost  indispensable  ap- 
paratus in  experiments  with  the  electric  battery.  On  a  wooden  stand  (fig, 
676)  are  two  glass  legs,  each  provided  with  universal  joints,  in  which  movable 
brass  rods  are  fitted.  Between  these  legs  is  a  small  ivory  table,  on  which  is 
placed  the  object  under  experiment.  The  two  metal  knobs  being  directed 
towards  the  objects,  one  of  them  is  connected  with  the  outer  coating  of 
the  battery,  and  the  moment  communication  is  made  between  the  outer  and 


Frictional  Electricity. 


[775- 


the  inner  coating  by  means  of  the  glass  discharging  rod,  a  violent  shock 
passes  through  the  object  on  the  table. 

y*776.  Charging  by  cascade. — A  series  of  Leyden  jars  are  placed  each 
separately  on  insulating  supports.  The  knob  of  the  first  is  in  connection 
with  the  prime  conductor  of  the  machine,  and  its  outer  coating  joined  to  the 
knob  of  the  second,  the  outer  coating  of  the  second  to  the  knob  of  the  third, 
and  so  on,  the  outer  coating  of  the  last  communicating  with  the  ground. 
The  inner  coating  of  the  first  receives  a  charge  of  positive  electricity  from 
the  machine,  and  the  corresponding  positive  electricity  set  free  by  induction 
on  its  outer  coating,  instead  of  passing  to  the  ground,  gives  a  positive  charge 
to  the  inner  coating  of  the  second,  which,  acting  in  like  manner,  develops  a 


Fig.  676. 

charge  in  the  third  jar,  and  so  on  to  the  last,  where  the  positive  electricity 
developed  by  induction  on  the  outer  coating  passes  to  the  ground.  The  jars 
may  be  discharged  either  singly  by  connecting  the  inner  and  outer  coatings 
of  each  jar,  or  simultaneously  by  connecting  the  inner  coating  of  the  first 
with  the  outer  of  the  last.  In  this  way  the  quantity  of  electricity  necessary 
to  cjiarge  one  jar  is  available  for  charging  a  series  of  jars. 
V  777-  Measurement  of  the  charge  of  a  battery.  Kane's  electro- 
meter.— When  the  outer  and  inner  coatings  of  a  charged  Leyden  jar  are 
gradually  brought  nearer  each  other,  at  a  certain  distance  a  spontaneous  dis- 
charge ensues..  The  distance  is  called  the  striking  or  sparking  distance. 
For  the  same  charge  it  is  inversely  proportional  to  the  pressure  of  the  air, 


-778] 


Harris's  Unit  Jar. 


717 

and,  with  the  same  jar  but  different  charges,  directly  proportional  to  the 
electric  density  of  that  point  of  the  inner  coating  at  which  the  discharge 
takes  place.  As  the  density  of  any  point  of  the  inner  coating,  other  things 
remaining  the  same,  is  proportional  to  the  entire  charge,  the  striking  distance 
is  proportional  to  the  quantity  of  electricity  in  a  jar.  The  measurement  of 
the  charge  of  a  battery,  however,  by  means  of  the  striking  distance,  can  only 
take  place  when  the  charge  dis- 
appears. 

By  means  of  Lane's  electro- 
meter, which  depends  on  an 
application  of  this  principle,  the 
charge  of  a  jar  or  battery  may 
be  measured.  This  apparatus, 
c  (fig.  677),  consists  of  an  ordi- 
nary Leyden  jar,  near  which 
there  is  a  vertical  metallic  sup- 
port. At  the  upper  end  is  a 
brass  rod,  with  a  knob  at  one 


Fig.  677. 


end,  which  can  be  placed  in  metallic  connection  with  the  outside  of  the  jar  : 
the  rod  being  movable,  the  knob  can  be  kept  at  a  measured  distance  from 
the  knob  of  the  inner  coating.  Fig.  677  represents  the  operation  of  measur- 
ing the  charge  of  a  jar  by  means  of  this  apparatus.  The  jar  £,  whose  charge 
is  to  be  measured,  is  placed  on  an  insulated  stool  with  its  outer  coating  in 
metallic  connection  with  the  inner  coating  of  Lane's  jar  c,  the  outer  coating 
of  which  is  in  connection  with  the  ground,  or  still  better  with  a  system  of  gas 
or  water  pipes  ',  a  is  the  conductor  of  the  machine.  When  the  machine  is 
worked,  positive  electricity  passes  into  the  jar  b  ;  a  proportionate  quantity  of 
positive  electricity  is  repelled  from  its  outer  coating,  passes  into  the  inner 
coating  of  the  electrometer,  and  there  produces  a  charge.  When  this  has 
reached  a  certain  limit,  it  discharges  itself  between  the  two  knobs,  and  as 
often  as  such  a  discharge  takes  place,  the  same  quantity  of  positive  electricity 
will  have  passed  from  the  machine  into  the  battery  ;  hence  its  charge  is  pro- 
portional to  the  number  of  discharges  of  the  electrometer. 

778.  Harris's  unit  jar. — Harris's  unit  jar  (fig.  678)  is  an  application 
of  the  same  principle,  and  is  often  convenient  for  measuring  quantities 
of  electricity.  It  consists  of  a  small 
Leyden  phial,  4  inches  in  length  and  f 
of  an  inch  in  diameter,  coated  to  about 
an  inch  from  the  end,  so  as  to  expose 
about  6  inches  of  coated  surface.  It  is 
fixed  horizontally  on  a  long  insulator, 
and  the  charging  rod  connected  at  P 
with  the  conductor  of  the  machine, 
while  the  outer  coating  is  connected 
with  the  jar  or  battery  by  the  rod  /  p. 
When  the  accumulation  of  electricity  in  the  interior  has  reached  a  certain 
height  depending  on  the  distance  of  the  two  balls  m  and  «,  a  discharge  ensues, 
and  marks  a  certain  quantity  of  electricity  received  as  a  charge  by  the: 
battery,  in  terms  of  the  small  jar. 


Fig.  678. 


718 


Frictional  Electricity. 


[778- 


Harris,  by  means  of  experiments  with  the  unit  jar  suitably  modified,  and 
Riess,  by  analogous  arrangements,  found,  by  independent  researches,  that 
for  small  distances  the  striking  distance  m  is  directly  proportional  to  the 
quantity  of  electricity,  and  inversely  proportional  to  the  extent  of  coated 
surface  ;  in  other  words,  it  is  proportional  to  the  potential.  Thus,  taking  the 
surface  of  one  jar  as  unity,  if  a  battery  of  six  Leyden  jars  charged  by  100 
turns  of  the  machine  has  a  striking  distance  of  9  millimetres,  a  battery  of 
four  similar  jars  charged  by  120  turns  will  have  the  striking  distance  of  l6'2 

millimetres.     For 

x:       =  I6.2 


As  the  striking  distance  increases  this  proportionality  ceases  to  hold,  owing 
probably  to  the  greater  loss  of  electricity  at  high  potentials,  and  also  to  the 
increased  duration  of  the  discharge.  Riess  also  found  that  when  a  battery  or 
jar  is  discharged  at  the  greatest  striking  distance,  the  residual  charge,  when 
the  discharge  takes  place  at  the  greatest  striking  distance,  is  always  in  the 
same  proportion  to  the  entire  charge.  In  Riess's  experiments,  0*846  or  ~ 
of  the  total  charge  disappeared  and  only  -^  remained. 

y^779.  Volta's  condensing  electroscope.  —  The  condensing  electroscope 
invented  by  Volta  is  a  modification  of  the  ordinary  gold-leaf  electroscope 


Fig.  680. 


(751)-  The  rod  to  which  the  gold-leaves  are  affixed  terminates  in  a  disc 
instead  of  in  a  knob,  and  there  is  another  disc  of  the  same  size  provided  with 
an  insulating  glass  handle.  The  discs  are  covered  with  a  layer  of  insulating 
shellac  varnish  (fig.  679). 


-780] 


TJiomsorfs  Quadrant  Electrometer. 


719 


To  render  very  small  quantities  of  electricity  perceptible  by  this  apparatus 
one  of  the  plates,  which  thus  becomes  the  collecting  plate,  is  touched  with 
the  body  under  examination.  The  other  plate,  the  condensing  plate,  is  con- 
nected with  the  ground  by  touching  it  with  the  finger.  The  electricity  of 
the  body,  being  diffused  over  the  collecting  plate,  acts  inductively  through 
the  varnish  on  the  other  plate,  attracting  the  opposite  electricity,  but 
repelling  that  of  like  kind.  The  two  electricities  thus  become  accumulated 
on  the  two  plates  just  as  in  a  condenser,  but  there  is  no  divergence  of  the 
leaves,  for  the  opposite  electricities  counteract  each  other.  The  finger  is 
now  removed,  and  then  the  source  of  electricity,  and  still  there  is  no  diver- 
gence ;  but  if  the  upper  plate  be  raised  (fig.  680)  the  neutralisation  ceases, 
and  the  electricity  being  free  to  move  diffuses  itself  over  the  rod  and  the 
leaves,  which  then  diverge  widely.  The  delicacy  of  this  electroscope  is  in- 
creased by  adapting  to  the  foot  of  the  apparatus  two  metal  rods,  terminat- 
ing in  knobs  ;  for  these  knobs,  being  excited  by  induction  from  the  gold 
leaves,  react  upon  them. 

A  still  further  degree  of  delicacy  is  attained  if  the  rods  be  replaced  by  two 
Bohnenberger's  dry  piles,  one  of  which  presents  its  positive  and  the  other  its 
negative  pole.  Instead  of  two  gold  leaves  there  is  only  one  ;  the  least  trace 
of  electricity  causes  it  to  oscillate  either  to  one  side  or  to  the  other,  and  at 
the^same  time  shows  the  kind  of  electricity. 

V/So.   Thomson's  quadrant  electrometer. — Sir  William    Thomson  has 
devised  a  new  and  delicate  form  of  electrometer,  by  which  accurate  measure- 
ments of  the  amount  of  electrical 
charge  may  be  made.     The  prin- 
ciple of  this    instrument   may  be 
understood  from  the  following  de- 
scription of  a  form  of  it  constructed 
for   lecture   purposes    by   Messrs. 
Elliott. 

A  light  flat  broad  aluminium 
needle  (fig.  68 1)  hangs  by  a  very  fine 
wire  from  the  inner  coating  of  a 
charged  Leyden  jar,  the  outer  coat- 
ing being  in  conducting  communi- 
cation with  the  earth.  The  whole 
apparatus  is  enclosed  within  a  glass 
shade,  and  the  air  is  kept  dry  by 
means  of  a  dish  of  sulphuric  acid  ; 
there  is,  therefore,  very  little  loss  of 
electricity,  and  the  needle  remains 
at  a  virtually  constant  charge. 

The  needle  is  suspended  over 
four  quadrantal  metal  plates,  insu- 
lated from  each  other  and  from  the 
ground  by  resting  on  glass  rods. 


Fig.  681. 


The  alternate  quadrants  are  in  conducting  communication  with  each  other 
by  means  of  wires.  If  now  all  the  quadrants  are  in  the  same  electrical  con- 
dition; the  needle  will  be  at  rest  when  it  is  directly  over  one  of  the  diametrical 


720 


Frictional  Electricity. 


[780- 


slits.  But  if  the  two  pairs  of  quadrants  are  charged  with  opposite  kinds 
of  electricity,  as  when,  for  instance,  they  are  connected  with  the  two  poles  of 
an  insulated  voltaic  cell  by  means  of  the  knobs,  then  each  end  of  the  needle 
will  be  repelled  by  the  pair  of  quadrants  which  are  electrified  like  itself,  and 
will  be  attracted  by  the  other  pair.  It  will  thus  be  subject  to  the  action  of  a 
couple  tending  to  set  it  obliquely  to  the  slit. 

In  order  to  render  the  slightest  motion  of  the  needle  visible,  a  small  silver 
concave  mirror  with  a  radius  of  about  a  metre  is  fixed  above  it.  The 
light  of  a  petroleum  lamp,  not  represented  in  the  figure,  strikes  against  this, 
and  is  reflected  as  a  spot  on  a  horizontal  scale.  Any  deflection  of  the  needle, 
either  on  one  side  or  the  other,  is  indicated  by  the  motion  of  the  spot  of 
lighj^pn  the  scale  (520). 

\  781.  Thomson's  absolute  electrometer. — Another  class  of  electro- 
meters, also  invented  by  Sir  W.  Thomson,  have  the  advantage  of  furnishing 
a  direct  measure  of  electrical  constants  in  absolute  measure.  Fig.  682 
represents  the  essential  features  of  a  modified  form  of  the  electrometer,, 
which  has  been  devised  by  Professor  Foster  for  class  experiments. 

Two  plane  metal  discs  A  and  B,  about  10  cm.  in  diameter,  are  kept  at  a 
distance  from  each  other,  which  is  small  in  proportion  to  their  diameters, 
but  which  can  be  very  accurately  measured.  Out  of  the  centre  of  the  upper 
one  is  cut  a  disc  c  ;  this  is  suspended  by  insulating  threads  from  one  end  of 
the  arm  a  b  of  a  balance,  at  the  other  end  of  which  is  a  counterpoise,  or  a 
scale  pan  p.  At  the  end  of  the  arm  is  a  fork,  across  which  is  stretched  a 
fine  wire  ;  when  the  disc  is  exactly  in  the  plane  of  the  circular  band  or  ring 
which  surrounds  it,  and  which 
is  called  the  guard  ring,  this 
fine  wire  is  exactly  across  the 
interval  between  two  marks 
in  the  upright,  and  the  posi- 
tion of  which  can  be  accu- 
rately determined  by  means 
of  the  lens  C.  The  disc  and 
the  guard  ring  are  kept  at  a 
constant  potential,  being  con- 
nected by  a  wire  with  a  con- 
stant source  of  electricity, 
while  the  other  can  be  kept 
at  any  potential. 

Suppose    now    that  the 
whole  system  is  at  the  same 

potential,  and  that  the  disc  is  exactly  balanced  so  as  to  be  in  the  plane  of  the 
guard  ring.  If  now  A  be  electrified  to  a  given  potential,  while  the  plate  B 
is  connected  with  the  earth,  then  the  body  charged  with  electricity  of  higher 
potential—that  is,  the  disc— will  be  urged  towards  the  body  of  lower  potential, 
the  fixed  plate  ;  and  in  order  to  retain  it  exactly  in  the  plane  of  the  guard 
ring  the  force  applied  at  the  other  end  of  the  lever  must  be  increased.  This 
may  be  done  by  altering  the  distance  of  the  counterpoise,  or  by  adding  weights 
to  a  scale  pan,  and  the  additional  weight  thus  applied  is  a  measure  of  the 
attractive  force. 


-782]  Potential  and  Capacity  of  a  Ley  den  Jar.  721 

Now,  it  can  be  shown  that  the  attractive  force  between  any  two  plates 
electrified  to  different  potentials  is  proportional  to  the  square  of  the  differ- 
ence of  potentials,  provided  the  distance  between  them  is  small  in  comparison 
with  their  area,  and  that  the  portions  of  the  plates  opposite  each  other  are 
at  some  distance  from  the  edge.  These  conditions  are  fulfilled  in  the  above 
case.  If  S  is  the  area  of  the  disc,  dfthe  distance  of  the  plates,  V  —  V\  the 
difference  of  potentials,  and  F  the  force  required  to  balance  a  certain  attrac- 
tion, then 


^A    /^k 


for  V  =  O  ;  this  is  ^!?  and  V 

Now  as  F  is  expressed  by  a  weight  and  S  and  d  depend  on  measures  of 
length,  we  have  a  means  of  expressing  difference  of  potentials  in  absolute 
measure  (709). 

It  is  also  clear  that  the  experiments  may  be  modified  by  making  the 
weight  constant,  and  the  distance  variable.  By  means  of  micrometric 
arrangements  the  distance  of  the  plates  may  be  varied  and  measured  with 
very  great  accuracy. 

782.  Potential  and  capacity  of  a  Leyden  jar. — Let  us  suppose  A  (fig. 
683)  to  represent  an  insulated  metal  sphere,  and  let  us  consider  it  placed 
in  conducting  communication  with  a  source  of,  say,  positive  electricity, 
which  is  supposed  to  be  at  a  constant  potential  V.  Then  its  potential  V  is 

3  ,  and  its  charge  q  =  VR,  R  being  the  radius  of  the  sphere  A. 

Suppose  now  it  be  possible  to  surround  this  sphere  by  an  external  conduct- 
ing shell  or  envelope  B,  which  is  in  connection  with  the  ground  ;  movements  of 
electricity  will  take  place  ;  a  new  equilibrium 
will  be  established,  and  there  will  now  be  two 
electrical  layers — one  on  the  sphere  A,  and 
the  other  on  the  sphere  B.     These  will  have 
no  action  on  any  external  point,  which  is  only 
possible  provided  the  charges  are  equal  and 
contrary.     If  +  Q  is  the  charge  on  the  inner, 
then  —  Q  is  that  on  the  outer  sphere  (745). 

The  charge  of  the  original  sphere  is  at 
first  not  altered  by  this  operation,  but  its 
potential  is  less,  its  capacity  being  now 
greater ;  but,  as  it  is  in  contact  with  the 
source,  which  is  constant,  it  receives  fresh 
charges  of  electricity  until  it  is  again  at  the 
potential  of  the  source  V. 

Now  let  us  suppose  that  the  insulating  layer  which  separates  the  inner 
from  the  outer  coating  is  air,  and  that  its  thickness  is  /  ;  then  the  potential 
V  of  the  whole  system  is  made  up  of  two  parts,  the  first  due  to  the  elec- 
trical charge  of  the  inner  sphere  V  =  +  5s,  and  the  second  due  to  the  charge 
Q  .  A.*:.  ^_Q  Q  _Q(R'-R)  .:  rt  VRR' 


Fig.  683. 


of  the  outer  sphere 


-*  •  thatis  V-2     Q_Q(R/-R) 

R"   thatlS'V-R-R>-         RR,        ' 


or  Q 


R'-R' 
3  A 


722  Frictional  Electricity.  [782- 

Now,  the  charge  of  the  insulated  sphere  q  =  VR  ;  hence  ?  =  —  ~  —    But 


R'  —  R  is  the  thickness  of  the  dielectric,  which,  for  the  sake  of  simplicity,  we 

O 

^ 


O 
will  suppose  is  air,  and,  calling   this   t,  we   have  ^  =  —  ;  that  is,  that  the 


charge  is  inversely  as  the  thickness  of  the  dielectric. 

It  is  to  be  observed  that  the  results  here  obtained  apply  strictly  only  to 
the  supposed  case  in  which  the  inner  conductor  is  completely  surrounded  by 
the  outer  one  (745),  which  is  not  the  case  with  the  ordinary  form  of  a  Leyden 
jar.  It  may,  however,  be  applied  to  them  if  we  compare  homologous  jars  ; 


in  the  above  formula  Q  =  ^7—  -fr>  if  R  and  R/  are  nearly  equal,  then  O  =  _  -  = 
5  js  the  surface  and  /  the  thickness  of  the  dielectric. 


In  this  formula  —  is  a  constant  for  a  Leyden  jar  of  given  dimensions,  and 

47T/ 

represents  the  capacity  of  the  jar. 

If  instead  of  air  there  be  a  solid  or  liquid  dielectric,  whose  specific  induc- 
tive capacity  is  K,  the  formula  becomes  O  =  —  ,= — ~.     If  the  dielectric  be 

K 

partly  air  and  partly  some  other  material  such  as  glass,  then  if  the  thick- 

VS 
ness  of  this  latter  is  0,  Q  =  — ~. —      —^•.      The  expression  6  is   sometimes 


written  /',  and  represents  the  thickness  of  the  layer  of  air  equivalent  to  it  in 
specific  inductive  capacity.     It  is  also  called  the  reduced  thickness. 

"\7T?  T?  '  T?  T?  ' 

From  the  expression  Q  =  _  - — _.  we  get  the  capacity  C  =  — - — — ;  or  as  above 
K.  —  K  K.  —  K 

ss.^:1::,  so  that  the  presence  of  the  envelope  multiplies  the  capacity  of  the 

sphere   by  -— . 

If  Rr  is  so  great  that  the  value  of  R  in  the  denominator  may  be  disre- 
garded, we  get  C  =  R  which  is  the  expression  for  the  capacity  of  an  insulated 
sphere  (739)  ;  such  a  sphere  may  indeed  be  regarded  as  a  condenser,  in 
which  the  layer  of  air,  between  it  and  the  sides  of  the  room,  represents  the 
dielectric. 

If  a  series  of  n  identical  jars  are  joined  in  surface,  we  have  a  condenser 
whose  capacity  is  equal  to  the  w-fold  capacity  of  a  single  jar. 

If  these  n  jars  are  joined  in  cascade,  the  capacity  of  the  system  is  that  of 
a  single  jar,  the  dielectric  of  which  is  n  times  as  thick. 


-784]       Work  Effected  by  the  Discharge  of  a  Ley  den  Jar.         723 


THE   ELECTRIC   DISCHARGE. 

783.  Effects  of  the  electric  discharge. — The  recombination  of  the  two 
electricities  which  constitutes  the  electrical  discharge  may  be  either  con- 
tinuous or  sudden  :  continuous,  or  of  the  nature  of  a  current,  as  when  the 
two  conductors  of  a  Holtz's  machine  are  joined  by  a  chain  or  a  wire  ;  and 
sudden,  as  when  the  opposite  electricities  accumulate  on  the  surface  of  two 
adjacent  conductors,  till  their  mutual  attraction  is  strong  enough  to  over- 
come the  intervening  resistances,  whatever  they  may  be.  But  the  difference 
between  a  sudden  and  a  continuous  discharge  is  one  of  degree,  and  not  of 
kind,  for  there  is  rrb  such  thing  as  an  absolute  non-conductor,  and  the  very 
best  conductors,  the  metals,  offer  an  appreciable  resistance  to  the  passage  of 
electricity.  Still  the  difference  at  the  two  extremes  of  the  scale  is  sufficiently 
great  to  give  rise  to  a  wide  range  of  phenomena. 

Riess  has  shown  that  the  discharge  of  a  battery  does  not  consist  in  a 
simple  union  of  the  positive  with  the  negative  electricity,  but  that  it  consists 
of  a  series  of  successive  partial  discharges.  The  direction  of  the  discharge 
depends  mainly  on  the  length  and  nature  of  the  circuit.  By  observations  of 
the  image  of  the  spark  in  a  rotating  mirror,  and  of  the  luminous  phenomena 
at  the  positive  and  negative  poles  when  the  discharge  takes  place  in  highly 
rarefied  gases,  as  well  as  by  the  manner  in  which  a  magnet  affects  the  pheno- 
mena of  discharge,  Feddersen  and  Paalzow  have  shown  that  the  discharge 
consists  of  a  series  of  oscillating  currents  alternating  in  opposite  directions. 
Helmholtz  had  already  deduced  the  necessity  of  such  an  oscillating  motion 
from  the  laws  of  the  conservation  of  energy,  and  Thomson  and  Kirchhoff 
had  deduced  the  conditions  under  which  it  occurs.  As  the  resistance  of  the 
circuit  increases,  the  number  of  these  alternating  discharges  decreases,  but 
at  the  same  time  their  duration  is  greater.  With  very  great  resistance — as, 
for  instance,  when  a  wet  thread  is  interposed — the  alternating  discharge 
becomes  a  single  one. 

The  phenomena  of  the  discharge  are  conveniently  divided  into  \htphysto- 
logicaj^luminous,  mechanical,  magnetical,  and  chemical  effects. 

784.  Work  effected  by  the  discharge  of  a  Key  den  jar. — The  work 

required   to   charge   a   Leyden  jar   is  W  =  \  OV  = =  ^  and  from  the 

principle  of  the  conservation  of  energy,  this  stored-up  energy  reappears  when 
the  jar  is  discharged.  This  occurs  partly  in  the  form  of  a  spark,  partly  in  the 
heating  effect  of  the  whole  system  of  conductors  through  which  the  discharge 
takes  place.  When  the  armatures  are  connected  by  a  thick  short  wire,  the 
spark  is  strong  and  the  heating  effect  small :  if,  on  th<e  contrary,  the  jar  is 
discharged  through  a  long  fine  wire,  this  becomes  more  heated,  but  the  spark 
is  weaker. 

If  a  series  of  identical  jars  are  each  separately  charged  from  the  same 
source,  they  will  each  acquire  the  same  potential,  which  will  not  be  altered  if 
all  the  jars  are  connected  by  their  inner  and  outer  coatings  respectively. 
The  total  charge  will  be  the  same  as  if  the  battery  had  been  charged  directly 
from  the  source,  and  its  energy  will  be  W  =  |  Vnq  =  £  VO  ;  that  is,  the  energy 

3A2 


724  Frictional  Electricity.  [784- 

of  a  battery  of  n  equal  jars  is  the  same  as  that  of  a  single  jar  of  the  same 
thickness  but  of  n  times  the  surface. 

Let  us  consider  two  similar  Leyden  jars  having  respectively  the  capaci- 
ties c  and  c',  and  let  one  of  them  be  charged  to  potential  V  and  let  the  other 
remain  uncharged.  Suppose  now  that  the  inner  and  outer  coatings  of  the 
jars  are  respectively  connected  with  each  other.  Then  the  energy  of  the 

Q2 

charged  jar  alone  is  W  =  |  ~~,  and  when  it  is  connected  with  the  other,  the 
original  charge  will  spread  itself  over  the  two,  so  that  the  energy  of  the 
charge  in  the  two  jars  is  W  =  —^ — — .  Hence  W  :  W  =  c  +  c' :  c\  and  there- 
fore, since  c  +  c'  is  always  greater  than  £•,  there  must  be  a  loss  of  energy.  In 
point  of  fact,  when  a  charged  jar  is  connected  with  an  uncharged  one,  a  spark 
passes  which  is  the  equivalent  of  this  loss  of  energy. 

It  follows,  further,  that  when  two  jars  at  different  potentials  are  united 
there  is  always  a  loss  of  energy. 

If  a  series  of  n  similar  jars  are  joined  in  surface,  and  a  given  charge  of 
electricity  is  imparted  to  them,  the  energy  is  inversely  as  the  number  of  jars  ; 
but,  when  they  are  charged  from  a  source  of  constant  potential,  the  energy 
is  proportional  to  the  number  of  jars.  If,  however,  the  jars  are  arranged  in 
cascade,  then  for  a  given  charge  the  energy  is  n  times  that  of  a  single  jar 
while  for  a  given  potential  it  is  n  times  smaller.  It  is  sometimes  convenient 
to  arrange  the  jars  in  a  combination  of  the  two  systems. 

785.  Physiological  effects. — The  physiological  effects  are  those  pro- 
duced on  living  beings,  or  on  those  recently  deprived  of  life.  In  the  first 
case  they  consist  of  a  violent  excitement  which  the  electricity  exerts  on 
the  sensibility  and  contractility  of  the  organic  tissues  through  which  it  passes  ; 
and  in  the  latter,  of  violent  muscular  convulsions  which  resemble  a  return 
to  life. 

The  shock  from  the  electrical  machine  has  been  already  noticed  (770), 
The  shock  taken  from  a  charged  Leyden  jar  by  grasping  the  outer  coating 
with  one  hand  and  touching  the  inner  with  the  other,  is  much  more  violent, 
and  has  a  peculiar  character.  With  a  small  jar  the  shock  is  felt  in  the  elbow  ; 
with  a  jar  of  about  a  quart  capacity  it  is  felt  across  the  chest,  and  with  jars 
of  still  larger  dimensions  in  the  stomach. 

A  shock  may  be  given  to  a  large  number  of  persons  simultaneously'by 
means  of  the  Leyden  jar.  For  this  purpose  they  must  form  a  chain  by  join- 
ing hands.  If  then  the  first  touches  the  outside  coating  of  a  charged  jarr 
while  the  last  at  the  same  time  touches  the  knob,  all  receive  a  simultaneous 
shock,  the  intensity  of  which  depends  on  the  charge,  and  on  the  number  of 
persons  receiving  it.  Those  in  the  centre  of  the  chain  are  found  to  receive 
a  less  violent  shock  than  those  near  the  extremities.  The  Abbe  Nollet  dis- 
charged a  Leyden  jar  through  an  entire  regiment  of  1,500  men,  who  all 
received  a  violent  shock  in  the  arms  and  shoulders. 

With  large  Leyden  jars  and  batteries  the  shock  is  sometimes  very  dan- 
gerous. Priestley  killed  rats  with  batteries  of  7  square  feet  coated  surface., 
and^ts  with  a  batteiy  of  about  4^  square  yards  coating. 

\r~/Jf786.  luminous  effects. — The  recombination  of  two  electricities  of  high 
potential  (738)  is  always  accompanied  by  a  disengagement  of  light,  as  is  seen 


-787]  Spark  and  Brush  Discharge.  725 

when  sparks  are  taken  from  a  machine,  or  when  a  Leyden  jar  is  discharged. 
The  better  the  conductors  on  which  the  electricities  are  accumulated,  the 
more  brilliant  is  the  spark  :  its  colour  varies  not  only  with  the  nature  of  the 
bodies,  but  also  with  the  nature  of  the  surrounding  medium  and  with  the 
pressure.  The  spark  between  two  charcoal  points  is  yellow,  between  two 
balls  of  silvered  copper  it  is  green,  between  knobs  of  wood  or  ivory  it  is 
crimson.  In  atmospheric  air  at  the  ordinary  pressure  the  electric  spark  is 
white  and  brilliant ;  in  rarefied  air  it  is  reddish ;  and  in  vacuo  it  is  violet. 
In  oxygen,  as  in  air,  the  spark  is  white  ;  in  hydrogen  it  is  reddish,  and  green 
in  the  vapour  of  mercury ;  in  carbonic  acid  it  is  also  green,  while  in  nitrogen 
it  is  blue  or  purple,  and  accompanied  by  a  peculiar  sound.  Generally 
speaking,  the  higher  the  potential  the  greater  is  the  lustre  of  the  spark. 
It  is  asserted  by  Fusinieri  that  in  the  electric  spark  there  is  always  a 
transfer  of  material  particles  in  a  state  of  extreme  tenuity,  in  which  case 
the  modifications  in  colour  must  be  due  to  the  transport  of  ponderable 
matter. 

When  the  spark  is  viewed  through  a  prism,  the  spectrum  obtained  is  full 
•of  dark  lines  (578),  the  number  and  arrangement  of  which  depend  on  the 
material  of  which  the  poles  are  made. 

787.  Spark  and  brush  discharge. — The  shapes  which  luminous  electric 
phenomena  assume  may  be  classed  under  two  heads — the  spark  and  the 
.brush.  The  brush  forms  when  the  electricity  leaves  the  conductor  in  a 
continuous  flow ;  the  spark,  when  the  discharge  is  discontinuous.  The 
formation  of  one  or  the  other  of  these  depends  on  the  nature  of  the  con- 
ductor and  on  the  nature  of  the  conductors  in  its  vicinity  ;  and  small  altera- 
tions in  the  position  of  the  surrounding  conductors  transform  the  one  into 
the  other. 

The  spark  which  at  short  distances  appears  straight,  at  longer  distances 
has  a  zigzag  shape  with  diverging  branches.  Its  length  depends  on  the 
density  at  the  part  of  the  conductor  from  which  it  is  taken  ;  and  to  obtain 
the  longest  sparks  the  electricity  must  be  of  as  high  a  density  as  possible,  but 
not  so  high  as  to  discharge  spontaneously.  With  long  sparks  the  luminosity 
is  different  in  different  parts  of  the  spark. 

The  brush  derives  its  name  from  the  radiating  divergent  arrangement 
•of  the  light,  and  presents  the  appearance  of  a  luminous  cone,  whose  apex 
touches  the  conductor.  Its  size  and  colour  differ  with  the  nature  and  form  of 
the  conductor  ;  it  is  accompanied  by  a  peculiar  hissing  noise,  very  different 
from  the  sharp -crack  of  the  spark.  Its  luminosity  is  far  less  than  that  of 
the  spark  ;  for  while  the  latter  can  easily  be  seen  by  daylight,  the  former  is 
only  visible  in  a  darkened  room.  The  brush  discharge  may  be  obtained  by 
placing  on  the  conductor  a  wire  filed  round  at  the  end,  or,  with  a  powerful 
machine,  by  placing  a  small  bullet  on  the  conductor.  The  brush  from  a 
negative  conductor  is  less  than  from  a  positive  conductor  ;  the  cause  of 
this  difference  has  not  been  satisfactorily  made  out,  but  may  originate  in  the 
fact,  which  Faraday  has  observed,  that  negative  electricity  discharges  into 
the  air  at  a  somewhat  lower  density  than  positive  electricity  ;  so  that  a  nega- 
tively charged  knob  sooner  attains  that  density  at  which  spontaneous  dis- 
charge takes  place,  than  does  a  positively  charged  one,  and  therefore  dis- 
charges the  electricity  at  smaller  intervals  and  in  less  quantities. 


726 


Frictional  Electricity. 


[787- 


When  electricity,  in  virtue  of  its  high  density,  issues  from  a  conductor,  no 
other  conductor  being  near,  the  discharge  takes  place  without  noise,  and  at 
the  places  at  which  it  appears  there  is  a  pale  blue  luminosity  called  the 
electrical  glow,  or  on  points,  a  star-like  centre  of  light.  It  is  seen  in  the  dark 
by  placing  a  point  on  the  conductor  of  the  machine. 

788.  Electric  egg. — The  influence  of  the  pressure  of  the  air  on  the  elec- 
tric light  may  be  studied  by  means  of  the  electric  egg.  This  consists  of  an 
ellipsoidal  glass  vessel  (fig.  684),  with  metal  caps  at 
each  end.  The  lower  cap  is  provided  with  a  stopcock, 
so  that  it  can  be  screwed  into  an  air-pump,  and  also 
into  a  heavy  'metallic  foot.  The  upper  metal  rod 
moves  up  and  down  in  a  leather  stuffing-box;  the 
lower  one  is  fixed  to  the  cap.  A  vacuum  having  been 
made,  the  stopcock  is  turned,  and  the  vessel  screwed 
into  its  foot ;  the  upper  part  is  then  connected  with  a 
powerful  electrical  machine,  and  the  lower  one  with 
the  ground.  On  working  the  machine,  the  globe 
becomes  filled  with  a  feeble  violet  light  continuous  from 
one  end  to  the  other,  and  resulting  from  the  recompo- 
sition  of  the  positive  electricity  of  the  upper  cap  with  the 
negative  of  the  lower.  If  the  air  be  gradually  allowed 
to  enter  by  opening  the  stopcock,  the  light  now  appears 
white  and  brilliant,  and  is  only  seen  as  an  ordinary  in- 
termittent spark. 

Some  beautiful  effects  of  the  electric  light  are  ob- 
tained by  means  of  Geissler's  tubes,  which  will  be 
noticed  under  Dynamical  Electricity. 

789.  luminous  tube,  square,  and  bottle. — The 
luminous  tube  (fig.  685)  is  a  glass  tube  about  a  yard 
long,  round  which  are  arranged  in  a  spiral  form  a  series 
of  lozenge- shaped  pieces  of  tinfoil,  between  which  are 

very  short  intervals.  There  is  a  brass  cap  with  hooks  at  each  end,  in  which 
the  spiral  terminates.  If  one  end  be  presented  to  a  machine  in  action,  while 
the  other  is  held  in  the  hand,  sparks  appear  simultaneously  at  each  interval, 
and  produce  a  brilliant  luminous  appearance,  especially  in  the  dark. 


Fig.  685. 


The  luminous  pane  (fig.  686)  is  constructed  on  the  same  principle,  and 
consists  of  a  square  of  ordinary  glass,  on  which  is  fastened  a  narrow  strip  of 
tinfoil  folded  parallel  to  itself  for  a  great  number  of  times.  Spaces  are  cut 


-790J 


Heating  Effects  of  the  Electric  Discharge. 


727 


out  of  this  strip  so  as  to  represent  any  figure,  a  portico  for  example. 
The  pane  being  fixed  between  two  insulating  supports,  the  upper  extre- 
mity of  the  strip  is  connected  with 
the  electrical  machine,  and  the 
lower  part  with  the  ground.  When 
the  machine  is  in  operation,  a  spark 
appears  at  each  interval,  and  repro- 
duces in  luminous  flashes  the  ob- 
ject represented  on  the  glass. 

790.  Heating:  effects. — Besides 
being  luminous,  the  electric  spark 
is  a  source  of  intense  heat.  When  it 
passes  through  inflammable  liquids, 
as  ether  or  alcohol,  it  inflames  them. 
An  arrangement  for  effecting  this  is 
represented  in  fig  687.  It  is  a  small 
glass  cup  through  the  bottom  of 
which  passes  a  metal  rod,  termi- 
nating in  a  knob  and  fixed  to  a 
metal  foot.  A  quantity  of  liquid 
sufficient  to  cover  the  knob  is 
placed  in  the  vessel.  The  outer 
coating  of  the  jar  having  been 
connected  with  the  foot  by  means  of  a  chain,  the  spark  which  passes  when 
the  two  knobs  are  brought  near  each  other  inflames  the  liquid.  With 
ether  the  experiment  succeeds  very  well,  but  alcohol  requires  to  be  first 
warmed. 

Coal  gas  may  also  be  ignited  by  means  of  the  electric  spark.  A  person 
standing  on  an  insulated  stool  places  one  hand  on  the  conductor  of  a 
machine  which  is  then  worked,  while 
he  presents  the  other  to  the  jet  of  gas 
issuing  from  a  metallic  burner.  The 
spark  which  passes  ignites  the  gas. 
When  a  battery  is  discharged  through 
an  iron  or  steel  wire  it  becomes 
heated,  and  even  made  incandescent 
or  melted  if  the  discharge  is  very 
powerful. 

If,  in  discharging  a  jar,  the  dis- 
charge does  no  other  work,  then  the 
whole  of  the  energy  of  the  charge 
(784)  appears  in  the  form  of  heat ;  and 
if  we  divide  this  by  Joule's  equivalent 
(497),  we  have  the  total  heating  due 
to  any  charge. 


Fig.  686. 


Fig.  687. 


The  laws  of  this  heating  effect  were  investigated  independently  by 
Harris  and  by  Riess  by  means  of  the  electric  thermometer.  This  consists  of 
a  glass  bulb,  fig.  688,  closed  by  a  stopper  V,  and  to  which  is  fixed  a  capillary 
tube  bent  twice,  and  terminating  in  an  enlargement ;  this  contains  coloured 


728 


Frictional  Electricity. 


[790- 


Fig.  688. 


liquid.  The  whole  apparatus  is  fixed  on  a  hinged  support  A,  which  works 
on  the  base  B,  so  that  it  can  be  inclined  and  fixed  at  any  given  angle.  The 
diameter  of  the  tube  being  very  small  compared  with  that  of  the  enlarge- 
ment, a  consider- 
able displacement 
of  the  liquid  may 
take  place  along 
the  scale  without 
any  material  alter- 
ation in  pressure, 
and  before  making 
the  experiment  the 
stopper  c  is  opened 
so  as  to  equalise 
the  pressure.  Be- 
tween the  binding 
screws  a  and  b 
a  fine  platinum 
wire  is  stretched. 
When  a  Leyden 
jar  is  discharged 
through  the  wire  this  becomes  heated,  expands  the  air  in  the  bulb,  and  the 
expansion  is  indicated  by  the  motion  of  the  liquid  along  the  graduated  stem 
of  the  thermometer.  In  this  way  it  has  been  found  that  the  increase  in 
temperature  in  the  wire  is  proportional  to  the  square  of  the  quantity  of 
electricity  divided  by  the  surface — a  result  which  follows  from  the  formula 
already  given  (784).  Riess  has  also  found  that  with  the  same  charge,  but 
with  wires  of  different  dimensions,  the  rise  of  temperature  is  inversely  as  the 
fourth  power  of  the  diameter.  Thus,  compared  with  a  given  wire  as  unity, 
the  rise  of  temperature  in  a  wire  of  double  or  treble  the  diameter  would  be 
~  or  ~  as  small ;  but  as  the  masses  of  these  wires  are  four  and  nine  times 
as  great,  the  heat  produced  would  be  respectively  \  and  |  as  great  as  in  a 
wire  of  unit  thickness. 

If  a  jar  charged  to  a  given  potential  be  discharged  through  the  electrical 
thermometer,  the  discharge  will  take  place  at  a  certain  striking  distance, 
and  a  certain  depression  will  be  produced  which  is  a  measure  of  the  heating 
effect  in  the  thermometer.  If  now  a  card  be  interposed  in  the  path  of 
the  discharge,  a  certain  proportion  of  its  energy  will  be  expended  in 
the  mechanical  perforation  of  the  card,  and  the  proportion  in  the  thermo- 
meter will  be  less.  Thus  Riess  found  that  that  charge  which  when  passed 
through  air  produced  a  depression  of  15-9,  when  passed  in  addition 
through  one  card,  two  cards,  and  a  plate  of  mica,  produced  depressions 
of  117,  8-0  and  6*8  respectively;  showing  then  that  the  heating  effect  was 
less  according  as  more  of  the  energy  of  the  discharge  was  used  for  other 
purposes. 

When  an  electric  discharge  is  sent  through  gunpowder  placed  on  the 
table  of  a  Henley's  discharger,  it  is  not  ignited,  but  is  projected  in  all  direc- 
tions. But  if  a  wet  string  be  interposed  in  the  circuit,  a  spark  passes  which 
ignites  the  powder.  This  arises  from  the  retardation  which  electricity 


-792]          Mechanical  Effects  of  the  Electrical  Discharge.  729 

'experiences  in  traversing  a  semi-conductor,  such  as  a  wet  string ;  for  the 
heating  effect  is  proportional  to  the  duration  of  the  discharge. 

When  a  charge  is  passed  through  sugar,  heavy  spar,  fluor-spar,  and  other 
substances,  they  afterwards  become  phosphorescent  in  the  dark.  Eggs, 
fruit,  £c.,  may  be  made  luminous  in  the  dark  in  this  way. 

When  a  battery  is  discharged  through  a  gold  leaf  pressed  between  two 
glass  plates  or  between  two  silk  ribbons,  the  gold  is  volatilised  in  a  violet 
powder  which  is  finely  divided  gold.  In  this  way  what  are  called  electric 
'portraits  are  obtained. 

Siemens  has  shown  that  when  a  jar  is  charged  and  discharged  several 
times  in  succession  the  glass  becomes  heated.  Hence  during  the  discharge 
there  must  be  movements  of  the  molecules  of  the  glass,  as  Faraday  sup- 
posed (747) ;  we  have  here,  probably,  something  analogous  to  the  heating 
produced  in  iron  when  it  is  rapidly  magnetised  and  demagnetised. 

,  791.  Magnetic  effects. — By  the  discharge  of  a  large  Leyden  jar  or 
battery,  a  steel  wire  may  be  magnetised  if  it  is  laid  at  right  angles  to  a  con- 
ducting wire  through  which  the  discharge  is 
effected,  either  in  contact  with  the  wire  or  at 
some  distance.  And  even  a  steel  bar  or  needle 
may  be  magnetised  by  placing  it  inside  a  spiral 
of  insulated  copper  wire  A  (fig.  689),  and  passing 
one  or  more  discharges  through  it.  The  polarity 
depends  on  the  direction  in  which  the  electricity 
enters  the  coil,  and  the  way  in  which  the  wire 
is  coiled.  Thus  if  the  jar  is  charged  in  the  in- 
-side  with  positive  electricity,  and  the  direction 
in  which  the  wire  is  coiled  is  that  in  which  the 
hands  of  a  watch  move,  that  end  at  which  the  positive  electricity  enters  will 
be  a  south  pole. 

To  effect  a  deflection  of  the  magnetic  needle  by  the  electric  current  pro- 
duced by  frictional  electricity  is  more  difficult.  It  may  be  accomplished 
by  making  use  of  a 'galvanometer  consisting  of  400  or  500  turns  of  fine  silk- 
covered  wire,  which  is  further  insulated  by  being  coated  with  shellac  varnish, 
and  by  separating  the  layers  by  means  of  oiled  silk.  When  the  prime  con- 
ductor of  a  machine  in  action  is  connected  with  one  end  of  the  galvanometer 
wire^and  the  other  with  the  ground,  a  deflection  of  the  needle  is  produced. 
V~792.  Mechanical  effects. — The  mechanical  effects  are  the  violent  lacera- 
tions, fractures,  and  sudden  expansions  which  ensue  when  a  powerful  dis- 
charge is  passed  through  a  badly  conducting  substance.  Glass  is  perforated, 
wood  and  stones  are  fractured,  and  gases  and  liquids  are  violently  disturbed. 
The  mechanical  effects  of  the  electric  spark  may  be  demonstrated  by  a 
variety  of  experiments. 

Fig.  690  represents  an  arrangement  for  perforating  a  piece  of  glass  or 
card.  It  consists  of  two  glass  columns,  with  a  horizontal  cross-piece,  in 
which  is  a  pointed  conductor,  B.  The  piece  of  glass,  A,  is  placed  on  an 
insulating  glass  support,  in  which  is  placed  a  second  conductor,  terminating 
.also  in  a  point,  which  is  connected  with  the  outside  of  the  battery,  while 
the  knob  of  the  inner  coating  is  brought  near  the  knob  of  B.  When  the 
discharge  passes  between  the  two  conductors  the  glass  is  perforated.  The 


Fig.  689. 


730 


Frictional  Electricity. 


[792 


Fig.  690. 


experiment  only  succeeds  with   a  single  jar  when  the  glass  is  very  thin  ; 
otherwise  a  battery  must  be  used. 

When  the  discharge  takes  place  through  a  piece  of  cardboard  be- 
tween two  points  exactly 
opposite  each  other  the 
line  of  perforation  is  quite 
straight ;  but  if  not  exactly 
opposite  a  slight  hole  is 
seen  near  the  negative 
point.  This  phenomenon, 
which  is  known  as  Lulliris 
experiment,  is  probably 
connected  with  the  greater 
facility  with  which  elec- 
tricity discharges  into  air 
according  as  it  is  negative 
or  positive  (787). 

The  perturbation  and 
sudden  expansion  -which 
the  discharge  produces 
may  be  illustrated  by 
means  of  what  is  known 
as  Kinnersley's  thermo- 
meter. This  consists  of 
two  glass  tubes  (fig.  691),  which  fit  into  metallic  caps  and  communicate  with 
each  other.  At  the  top  of  the  large  tube  is  a  rod  terminating  in  a  knob,  and 

moving  in  a  stuffing-box,  and  at 
the  bottom  there  is  a  similar  rod 
with  a  knob.  The  apparatus  con- 
tains water  up  to  the  level  of  the 
lower  knob.  When  the  electric 
discharge  passes  between  the 
two  knobs,  the  water  is  driven 
out  of  the  larger  tube  and  rises 
to  a  slight  extent  in  the  small 
one.  The  level  is  immediately 
re-established,  and  therefore  the 
phenomenon  is  not  due  to  a  rise 
of  temperature. 

If  the  upper  knob  inside  a 
Kinnersley's  thermometer  be 
replaced  by  a  point,  and  the 
outside  knob  is  connected  with 
the  prime  conductor  of  a  ma- 
chine at  work,  the  electricity 
discharges  itself  in  the  form  of 
a  brush,  and  a  permanent  dis- 
placement of  the  liquid  in  the 


Fig.  691. 


stem  shows' that  this  is  due  to  the  heating  effect  of  the  brush  discharge. 


Fig.  692. 


-793]          Chemical  Effects  of  the  Electrical  Discharge.  731 

For  the  production  of  mechanical  effects  the  universal  discharger 
(fig.  676)  is  of  great  service.  A  piece  of  wood,  for  instance,  placed  on  the 
table  between  the  two  conductors,  is  split  when  the  discharge  passes. 

When  a  Leyden  jar  is  charged  it  undergoes  a  true 
expansion  which  is  not  that  due  to  heat.  This  was 
shown  by  Ouincke,  one  of  whose  experiments  is  repre- 
sented in  fig.  692.  It  consists  of  a  glass  bulb  A  about 
2  inches  in  diameter  at  the  end  of  a  narrow  capillary 
tube  K,  on  an  enlargement  in  which  a  platinum  wire  B 
is  fused.  The  bulb  and  a  portion  of  the  stem  contains 
a  conducting  liquid,  such  as  water  or  sulphuric  acid, 
and  it  is  placed  in  a  vessel  of  ice-cold  water,  K,  which 
can  be  connected  with  the  earth  by  a  conducting  wire, 
G  If  now  this  condenser  is  charged  by  connecting 
the  wire  B  with  an  electrical  machine,  while  G  is  in 
connection  with  the  earth,  there  is  a  distinct  depres- 
sion of  the  liquid  in  the  tube.  When  the  jar  is  dis- 
charged the  liquid  resumes  its  original  level.  Hence 
this  cannot  have  been  due  to  heat,  apart  from  the 
fact  that  the  temperature  was  kept  constant ;  nor  is 
it  due  to  a  contraction  of  the  thickness  of  the  glass. 
The  same  results  are  obtained  if  the  outer  coating  is  insulated  by  resting 
it  on  shellac  T,  which  in  turn  is  insulated  by  resting  on  a  slab  of  india- 
rubber,  the  inner  coating  being  put  to  earth.  Similar  effects  are  observed 
with  solid  condensers  of  other  materials,  and  also  with  liquids. 
^  793-  Chemical  effects. — The  chemical  effects  are  the  decompositions 
and  recombinations  effected  by  the  passage  of  the  electric  discharge.  When 
two  gases  which  act  on  each  other  are  mixed  in  the  proportions  in  which 
.they  combine,  a  single  spark  is  often  sufficient  to  determine  their  combina- 
tion ;  but  when  either  of  them  is  in  great  excess,  a  succession  of  sparks  is 
necessary.  Priestley  found  that  when  a  series  of  electric  sparks  was  passed 
through  moist  air,  its  volume  diminished,  and  blue  litmus  introduced  into 
the  vessel  was  reddened.  This,  Cavendish  discovered,  was  due  to  the  for- 
mation of  nitric  acid. 

Several  compound  gases  are  decomposed  by  the  continued  action  of  the 
electric  spark.  With  olefiant  gas,  sulphuretted  hydrogen,  and  ammonia,  the 
decomposition  is  complete ;  while  carbonic  acid  is  partially  decomposed 
into  oxygen  and  carbonic  oxide.  The  electric  discharge  also  by  suitable 
means  can  feebly  decompose  water,  oxides,  and  salts  ;  but,  though  the  same 
in  kind,  the  chemical  effects  of  statical  electricity  are  by  no  means  so  powerful 
and  varied  as  those  of  dynamical  electricity.  The  chemical  action  of  the 
spark  is  easily  demonstrated  by  means  of  a  solution  of  iodide  of  potassium. 
A  small  lozenge-shaped  piece  of  filtering  paper,  impregnated  with  iodide  of 
potassium,  is  placed  on  a  glass  plate,  and  one  corner  connected  with  the 
ground.  When  a  few  sparks  from  a  conductor  charged  with  positive  elec- 
tricity are  taken  at  the  other  corner,  brown  spots  are  produced,  due  to  the 
separation  of  iodine. 

The  electric  piston  is  a  small  apparatus  which  serves  to  demonstrate  the 
chemical  effects  of  the  spark.  It  consists  of  a  brass  vessel  (fig.  693),  in 


732 


Frictional  Electricity. 


[793- 


which  is  introduced  a  detonating  mixture  of  two  volumes  of  hydrogen  and 
one  of  oxygen,  and  which  is  then  closed  with  a  cork.  In  a  tubulure  in  the 
side  there  is  a  glass  tube,  in  which  fits  a  metal  rod,  terminated  by  the 


A 


Fig.  693. 

Imobs  A  and  B.  The  vessel  is  held  as  represented  in  fig.  694,  and  brought 
near  the  machine.  The  knob  A  becomes  negatively,  and  B  positively,  elec- 
trified by  induction  from  the  machine  and  a  spark  passes  between  the  con- 
ductor and  A.  Another  spark  passes  at 
the  same  time  between  the  knob  B  and 
the  side  ;  this  determines  the  combina- 
tion of  the  gases,  which  is  accompanied 
by  a  great  disengagement  of  heat,  and  the 
vapour  of  water  formed  acquires  such  an 
expansive  force,  that  the  cork  is  pro- 
jected with  a  report  like  that  of  a  pistol. 
Among  the  chemical  effects  must  be 
enumerated  the  formation  of  ozone,  which 
is  recognised  by  its  peculiar  odour,  and 
by  certain  chemical  properties.  The 
odour  is  perceived  when  electricity  issues 
from  a  conductor  into  the  air  through 
a  series  of  points.  It  has  been  estab- 
lished that  ozone  is  an  allotropic  modi- 
fication of  oxygen. 

With  these  effects  may  be  associated 
a  certain  class  of  phenomena  observed 
when  gases  are  made  to  act  as  the  dielec- 
tric in  a  charged  Leyden  jar.  An  appa- 
ratus by  which  this  is  effected  is  repre- 
sented in  fig.  695  ;  it  is  a  modification  of 
one  invented  by  Siemens.  It  consists 
of  a  glass  cylinder  E,  containing  dilute 
sulphuric  acid  ;  a  is  a  glass  tube  closed  at  the  bottom,  and  also  containing 
sulphuric  acid,  in  an  enlargement  of  which  at  the  top  the  inner  tube  ec  fits. 
There  is  a  tube  /,  by  which  gas  enters,  and  one  d  f  by  which  it  emerges. 
When  the  acids  in  E  and  e  are  respectively  connected  with  the  two  combs  of 
a  Holtz  machine,  or  with  the  two  terminals  of  a  Ruhmkorft's  coil,  a  certain 
condition  or  strain  (747)  is  produced  in  the  dielectric,  which  is  known  as  the 


Fig.  695. 


—794]    Application  of  Electrical  DiscJtarge  to  Firing  Mines.     733 

silent  discharge  or  the  electric  effluvium.  What  that  condition  is  cannot  be 
definitely  stated  ;  but  it  gives  rise  to  powerful  and  characteristic  chemical 
actions,  often  differing  from  those  produced  by  the  spark. 

By  this  apparatus  large  quantities  of  ozone  may  be  produced. 

794.  Application  of  tne  electrical  discharge  to  firing-  mines. — By  the 
labours  of  Sir  F.  Abel  in  this  country,  and  of  Baron  von  Ebner  in  Austria,  the 
electrical  discharge  has  been  applied  to  firing  mines  for  military  purposes,, 
and  the  methods  have  acquired  a  high  degree  of  perfection.  The  principle 
on  which  the  method  is  based  may  be  understood  from  the  following  state- 
ment : — 

One  end  of  an  insulated  wire  in  which  is  a  small  break  is  placed  in  con- 
tact with  the  outside  of  a  charged  Leyden  jar,  the  other  end  being  placed 
near  the  inner  coating.  If  now  this  end  be  brought  in  contact  with  the  inner 
coating  the  jar  is  discharged,  and  a  spark  strikes  across  the  break  ;  and 
if  there  be  here  some  explosive  compound  it  is  ignited,  and  this  ignition 
may  of  course  be  communicated  to  any  gunpowder  in  which  it  is  placed. 
If  on  one  side  of  the  break,  instead  of  having  an  insulated  wire  direct 
back  to  the  outer  coating  of  the  Leyden  jar,  an  uncovered  wire  be  led 
into  the  ground,  the  out- 
side of  the  jar  being  also 
connected  with  the 
ground,  the  result  is  un- 
changed, the  earth  acting 
as  a  return  wire.  More- 
over, if  there  be  several 
breaks,  the  explosion  will 
still  ensue  at  each  of  them, 
provided  the  charge  be 
sufficiently  powerful. 

In  the  actual  applica- 
tion it  is  of  course  neces- 
sary to  have  an  arrange- 
ment for  generating 
frictional  electricity  which 
shall  be  simple,  portable, 
powerful,  and  capable  of 
working  in  any  weather. 
Fig.  696  represents  a  view 
of  Von  Ebner's  instrument 
as  constructed  by  Messrs. 
Elliott,  part  of  the  case 
being  removed  to  show 
the  internal  construction. 

1 1  consists  of  two  circu-  Fis-  696- 

lar  plates  of  ebonite,  <2,  mounted  on  an  axis  so  that  they  are  turned  by  a 
handle,  b,  between  rubbers,  which  are  so  arranged  as  to  be  easily  removed 
for  the  purposes  of  amalgamation,  &c.  Fastened  to  a  knob  on  the  base  of 
the  apparatus  and  projecting  between  the  plates  is  a  pointed  brass  rod, 
which  acts  as  a  collector  of  the  electricity.  The  condenser  or  Leyden  jar- 


734 


Fractional  Electricity. 


[794- 


arrangement  is  inside  the  case,  part  of  which  has  been  removed  to  show  the 
arrangement.  It  consists  of  india-rubber  cloth,  coated  on  each  side  with 
tinfoil,  and  formed  into  a  roll  for  the  purpose  of  greater  compactness. 
By  means  of  a  metal  button  the  knob  is  in  contact  with  one  tinfoil  coating, 
which  thus  receives  the  electricity  of  the  machine,  and  corresponds  to  the 
inner  coating  of  the  Leyden  jar.  Another  button,  connected  with  the 
other  tinfoil  coating,  rests  on  a  brass  band  at  the  base  of  the  apparatus 
which  is  in  metallic  contact  with  the  cushions,  the  knob  d,  and  the  per- 
forated knob  in  which  slides  a  rod  at  the  front  of  the 
apparatus.  These  are  all  in  connection  with  the  earth. 
The  knob  e  is  in  metallic  connection  with  a  disc  g,  pro- 
vided with  a  light  arm.  By  means  of  a  flexible  chain 
this  is  so  connected  with  a  trigger  on  the  side  of  the 
apparatus  not  represented  in  the  figure,  that  when  the 
trigger  is  depressed,  the  arm,  and  therewith  the  knob  <?, 
is  brought  into  contact  with  the  inner  coating  of  the 
condenser. 

On  depressing  the  trigger,  after  a  certain  number  of 
turns,  a  spark  passes  between  the  knob  e  and  the  sliding 
rod,  and  the  striking  distance  is  a  measure  of  the 
working  condition  of  the  instrument. 

The  fuse  used  is  known  as  Abel's  electrical  fuse,  and 
has  the  following  construction  : — The  ends  of  two  fine 
copper  wires  (fig.  697)  are  imbedded  in  a  thin  solid 
gutta-percha  rod,  parallel  to  each  other,  but  at  a  dis- 
tance of  about  1*5  mm.  At  one  end  of  the  gutta-percha 
a  small  cap  of  paper  c  c,  is  fastened,  in  which  is  placed 
a  small  quantity  of  the  priming  composition,  which  con- 
sists of  an  intimate  mixture  of  subsulphide  of  copper, 
subphosphide  of  copper,  and  chlorate  of  potassium. 
The  paper  is  fastened  down  so  that  the  exposed  ends  of 
the  wires  are  in  close  contact  with  the  powder. 
This  is  the  actual  fuse  ;  for  service  the  capped  end  of  the  fuse  is  placed 
in  a  perforation  in  the  rounded  head  of  a  wooden  cylinder,  so  as  to  project 
slightly  into  the  cavity  g  of  the  cylinder.  This  cavity  is  filled  with  meal 
powder,  which  is  well  rammed  down,  so  that  the  fuse  is 
firmly  imbedded.  It  is  afterwards  closed  by  a  plug  of 
gutta-percha,  and  the  whole  is  finally  coated  with  black 
varnish. 

The  free  ends  of  the  wire  a  a  are  pressed  into  small 
grooves  in  the  head  of  the  cylinder  (fig.  698),  and  each 
end  is  bent  into  one  of  the  small  channels  with  which  the 
cylinder  is  provided,  and  which  are  at  right  angles  to 
the  central  perforation.  They  are  wedged  in  here  by 
driving  in  small  copper  tubes,  the  ends  of  which  are 
then  filed  flush  with  the  surface  of  the  cylinder.  The 
bared  ends  of  two  insulated  conducting  wires  are  then 
pressed  into  one  of  the  small  copper  tubes  or  eyes,  and 
fixed  there  by  bending  the  wire  round  on  to  the  wood,  as  shown  at  e. 


Fig.  697. 


-795]  Duration  of  the  Electric  Spark.  735 

The  conducting  wire  used  in  firing  may  be  thin,  but  it  must  be  well 
insulated.  One  end  which  is  bared,  having  been  pressed  into  the  hole  d 
of  the  fuse  (fig.  697),  the  other  is  placed  near  the  exploder.  In  the  other 
hole  d'  of  the  fuse  a  wire  is  placed  which  serves  as  earth  wire,  care  being 
taken  that  there  is  no  connection  between  the  two  wires.  The  fuse  having 
been  introduced  into  the  charge,  the  earth  wire  is  placed  in  good  connection 
with  the  ground.  The  knob  f  of  the  exploder  is  also  connected  with  the 
earth  by  leading  the  bare  wire  into  water  or  moist  earth,  and  the  condi- 
tion of  the  machine  tested.  The  end  of  the  insulated  wire  is  then  connected 
with  the  knob  e  and  the  rod  drawn  down  ;  at  the  proper  signal  the  handle 
is  turned  the  requisite  number  of  times,  and  when  the  signal  is  given  the 
trigger  is  depressed,  and  the  explosion  ensues. 

When  a  number  of  charges  are  to  be  fired  they  are  best  placed  in  a  single 
circuit,  care  being  taken  that  the  insulation  is  good. 

795.  Duration  of  the  electric  spark. — Wheatstone  measured  the  dura- 
tion of  the  electric  spark  by  means  of  the  rotating  mirror  which  he  invented 
for  this  purpose.  At  some  distance  from  this  instrument,  which  can  be  made 
to  rotate  with  a  measured  velocity,  a  Leyden  jar  is  so  arranged  that  the  spark 
of  its  discharge  is  reflected  from  the  mirror.  Now,  from  the  laws  of  reflec- 
tion (520)  the  image  of  the  luminous  point  describes  an  arc  of  double  the 
number  of  degrees  which  the  mirror  describes,  in  the  time  in  which  the 
mirror  passes  from  the  position  in  which  the  image  is  visible  to  that  in  which 
it  ceases  to  be  so.  If  the  duration  of  the  image  were  absolutely  instanta- 
neous the  arc  would  be  reduced  to  a  mere  point.  Knowing  the  number  of 
turns  which  the  mirror  makes  in  a  second,  and  measuring,  by  means  of  a 
divided  circle,  the  number  of  degrees  occupied  by  the  image,  the  duration  of 
the  spark  would  be  determined.  In  one  experiment  Wheatstone  found  that 
this  arc  was  24°.  Now,  in  the  time  in  which  the  mirror  traverses  360°  the 
image  traverses  720°  ;  but  in  the  experiment  the  mirror  made  800  turns  in  a 
second,  and  therefore  the  image  traversed  576,000°  in  this  time  ;  and  as  the 
arc  was  24°,  the  image  must  have  lasted  the  time  expressed  by  -^~Q  or  -^—-^ 
of  a  second.  Thus  the  discharge  is  not  instantaneous,  but  has  a  certain 
duration,  which,  however,  is  excessively  short. 

Feddersen  found  that  when  greater  resistances  were  interposed  in  the 
circuit  through  which  the  discharge  was  effected,  the  duration  of  the  spark 
was  increased.  With  a  tube  of  water  9  mm.  in  length,  the  spark  lasted  0-0014 
second  ;  and  with  one  of  180  mm.  its  duration  was  0-0183  second.  The 
duration  increased  also  with  the  striking  distance,  and  with  the  dimensions 
of  the  battery. 

To  determine  the  duration  of  the  electric  spark  Lucas  and  Cazin  used  a 
method  by  which  it  may  be  measured  in  millionths  of  a  second.  The  method 
is  an  application  of  the  vernier  (10).  A  disc  of  mica  15  centimetres  in  dia- 
meter is  blackened  on  one  face,  and  at  the  edge  are  traced  180  equal  divi- 
sions in  very  fine  transparent  lines.  The  disc  is  mounted  on  a  horizontal 
axis,  and  by  means  of  a  gas  engine  it  may  be  made  to  turn  with  a  velocity 
of  loo  to  300  turns  in  a  second.  A  second  disc  of  silvered  glass  of  the  same 
radius  is  mounted  on  the  same  axis  as  the  other  and  very  close  to  it ;  at  its 
upper  edge  six  equidistant  transparent  lines  are  traced,  forming  a  vernier 
with  the  lines  on  the  mica.  For  this,  the  distance  between  two  consecutive 


736 


Frictional  Electricity. 


[795 


lines  on  the  two  discs  is  such  that  five  divisions  of  the  mica  disc  DC  corre- 
spond to  six  divisions  of  the  glass  disc  AB,  as  seen  in  fig.  699.  Thus  the 
vernier  gives  the  sixths  of  a  division  of  the  mica  disc  (10).  In  the  apparatus 

the  lines  AB  are  not  above  the  lines  C  D,  but 
are  at  the  same  distance  from  the  axis,  so* 
that  the  latter  coincide  successively  with 
the  former. 

The  mica  disc  is  contained  in  a  brass 
box  D  (fig.  700),  on  the  hinder  face  of 
which  is  fixed  the  vernier.  In  the  front 
face  is  a  glass  window  O,  through  which  the  coincidence  of  the  two  sets  of 
lines  can  be  observed  by  means  of  a  magnifying  lens  L. 

The  source  of  electricity  is  a  battery  of  2  to  8  jars,  each  having  a  coated 
surface  of  1,243  square  centimetres,  and  charged  continuously  by  a  Holtz's 
machine.  The  spark  strikes  between  two  metal  balls  a  and  b,  1 1  millimetres 


Fig.  699. 


in  diameter.  Their  distance  can  be  varied,  and  at  the  same  time  measured^ 
by  means  of  a  micrometric  screw,  r.  The  two  opposite  electricities  arrive 
by  wires  m  and  «,  and  the  sparks  strike  at  the  principal  focus  of  a  condensing 
lens  placed  in  the  collimator  C,  so  that  the  rays  which  fall  on  the  vernier  are 
parallel. 


-796]  Velocity  of  Electricity.  737 

The  motion  is  transmitted  to  the  toothed  wheels  and  to  the  mica  disc  by 
means  of  an  endless  band,  which  can  be  placed  on  any  one  of  three  pulleys 
P,  so  that  the  velocity  may  be  varied.  At  the  end  of  the  axis  of  the  pulleys 
is  a  bent  wire  which  moves  a  counter,  V,  that  marks  on  three  dials  the 
number  of  turns  of  the  disc. 

These  details  being  premised,  suppose  the  velocity  of  the  disc  is  400 
turns  in  a  second.  In  each  second  400+  180  or  72,000  lines  pass  before  the 
observer's  eye  in  each  second  ;  hence  an  interval  of  y^o  °f  a  second  elapses 
between  two  consecutive  lines.  But  as  the  spark  is  only  seen  when 
one  of  the  lines  of  the  disc  coincides  with  one  of  the  six  lines  of  the  ver- 
nier ;  and  as  this  gives  sixths  of  a  division  of  the  movable  disc,  when  the 
latter  has  turned  through  a  sixth  of  a  division,  a  second  coincidence  is 
produced ;  so  that  the  interval  between  two  successive  coincidences  is 

— 5-  =  0*0000023  of  a  second. 

72000x6 

That  being  the  case,  let  the  duration  of  a  spark  be  something  between 
23  and  46  ten-millionths  of  a  second  ;  if  it  strikes  exactly  at  the  moment  of 
a  coincidence,  it  will  last  until  the  next  coincidence  ;  and  owing  to  the  per- 
sistence of  impressions  on  the  retina  (625)  the  observer  will  see  two  luminous 
lines.  But  if  the  spark  strikes  between  two  coincidences  and  has  ceased 
when  the  third  is  produced,  only  one  brilliant  line  is  seen.  Thus  if,  with  the 
above  velocity  sometimes  I  and  sometimes  2  bright  lines  are  seen,  the  dura- 
tion of  the  spark  is  comprised  between  23  and  46  ten-millionths  of  a  second. 

By  experiments  of  this  kind,  with  a  striking  distance  of  5  millimetres 
between  the  balls  a  and  b,  and  varying  the  number  of  the  jars,  MM.  Lucas 
and  Cazin  obtained  the  following  results  : — 

Duration  in  millionths 
Number  of  jars  of  a  second. 

2  .  :  J;  '     .'-  ''"  >     •'  ".  .  .26 

4  .  '.  1'-    V'r-    '  .  41 

6  .  -'/';:;   V   '-v":r::.  .  .  45 

8  .  ,_    .,    ^.    .  ;  .  .  .47 

It  will  thus  be  seen  that  the  duration  of  the  spark  increases  with  the 
number  of  jars.  It  also  increases  with  the  striking  distance  ;  but  it  is  inde- 
pendent of  the  diameter  of  the  balls  between  which 
the  spark  strikes. 

The  spark  of  electrical  machines  has  so  short  a 
duration  that  it  could  not  be  measured  with  the 
chronoscope. 

V"796.  Velocity  of  electricity. — To  determine  the 
velocity  of  electricity  Wheatstone  constructed  an 
apparatus  the  principle  of  which  will  be  understood 
from  fig.  701.  Six  insulated  metal  knobs  were  ar- 
ranged in  a  horizontal  line  on  a  piece  of  wood  called 
a  spark  board;  of  these  the  knob  i  was  connected  Fi 

with  the  outer,  while  6  could  be  connected  with  the 
inner  coating  of  a  charged  Ley  den  jar  ;  the  knob  I  was  a  tenth  of  an  inch 
distant  from  the  knob  2  ;  while  between  2  and  3  a  quarter  of  a  mile  of 
insulated  wire  was  interposed  :  3  was  likewise  a  tenth  of  an  inch  from  4,  and 

3B 


738  Frictional  Electricity.  [796- 

there  was  a  quarter  of  a  mile  of  wire  between  4  and  5  ;  lastly,  5  was  a  tenth 
of  an  inch  from  6,  from  which  a  wire  led  directly  to  the  outer  coating  of  the 
Leyden  jar.  Hence,  when  the  jar  was  discharged  by  connecting  the  wire 
from  6  with  the  inner  coating  of  the  jar,  sparks  would  pass  between  i  and  2, 
between  3  and  4,  and  between  5  and  6.  Thus  the  discharge,  supposing  it  to 
proceed  from  the  inner  coating,  has  to  pass  in  its  course  through  a  quarter  of 
a  mile  of  wire  between  the  first  and  second  spark,  and  through  the  same 
distance  between  the  second  and  third. 

The  spark  board  was  arranged  at  a  distance  of  10  feet  from  the  rotating 
mirror,  and  at  the  same  height,  both  being  horizontal ;  and  the  observer 
looked  down  on  the  mirror.  Thus  the  sparks  were  visible  when  the  mirror 
made  an  angle  of  45°  with  the  horizon. 

Now,  if  the  mirror  were  at  rest  or  had  only  a  small  velocity,  the  images 
of  the  three  spots  would  be  seen  as  three  dots  • ,  but  when  the  mirror  had 
a  certain  velocity  these  dots  appeared  as  lines,  which  were  longer  as  the 
rotation  was  more  rapid.  The  greatest  length  observed  was  24°,  which, 
with  800  revolutions  in  a  second,  can  be  shown  to  correspond  to  a  duration 
of  —1^  of  a  second.  With  a  slow  rotation  the  lines  present  the  appearance 
ZHZZZ ')  they  are  quite  parallel,  and  the  ends  in  the  same  line.  But  with 
greater  velocity,  and  when  the  rotation  took  place  from  left  to  right,  they 
presented  the  appearance  "~,  and  when  it  turned  from  right  to  left 

the  appearance  ~  ,  because  the  image  of  the  centre  spark  was  formed 

after  the  lateral  ones.  Wheatstone  found  that  this  displacement  amounted 
to  half  a  degree  before  or  behind  the  others.  This  arc  corresponds  to  a 

duration  of  -  -  or  ^looo  °f  a  second ;  the  space  traversed  in  this 

time  being  a  quarter  of  a  mile,  gives  for  the  velocity  of  electricity  288,000 
miles  in  a  second,  which  is  greater  than  that  of  light.  The  velocity  obtained 
from  experiments  with  dynamical  electricity  is  far  less  ;  and,  owing  to  induc- 
tion, the  transmission  of  a  current  through  submarine  wires  is  comparatively 
slow. 

In  the  above  experiment  the  images  of  the  two  outer  sparks  appear 
simultaneously  in  the  mirror,  from  which  it  follows  that  the  electric  current 
issues  simultaneously  from  the  two  coatings  of  the  Leyden  jar. 

From  theoretical  considerations  based  upon  measurements  of  constant 
electrical  currents  Kirchoff  concluded  that  the  motion  of  electricity  in  a  wire 
in  which  it  meets  with  no  resistance  is  like  that  of  a  wave  in  a  stretched 
string,  and  has  the  velocity  of  192,924  miles  in  a  second,  which  is  about  that 
of  light  in  vacuo  (507). 

According  to  Walker,  the  velocity  of  electricity  is  18,400  miles,  and  ac- 
cording to  Fizeau  and  Gounelle,  it  is  62,100  miles  in  iron,  and  111,780  in 
copper  wire.  These  measurements,  htiwever,  were  made  with  telegraph  wires, 
which  induce  opposite  electricities  in  the  surrounding  media  ;  there  is  thus 
produced  a  resistance  which  diminishes  the  velocity.  The  velocity  is  less 
in  insulated  wires  in  water  than  in  air.  The  nature  of  the  conductor  appears 
to  have  some  influence  on  the  velocity  ;  but  not  the  thickness  of  the  wire, 
nor  the  potential  of  the  electricity. 

For  atmospheric  electricity,  reference  must  be  made  to  the  chapter  on 
Meteorology. 


-797J 


Galvani' s  Experiment  and  Theory 


739 


BOOK   X. 

DYNAMICAL   ELECTRICITY. 


CHAPTER    I. 


VOLTAIC  PILE.      ITS   MODIFICATIONS. 


V  797.  Galvani's  experiment  and  tneory. — The  fundamental  experiment 
which  led  to  the  discovery  of  dynamical  electricity  is  due  to  Galvani,  pro- 
fessor of  anatomy  in  Bologna.  Occupied  with  investigations  on  the  in- 
fluence of  electricity  on  the  nervous  excitability  of  animals,  and  especially  of 
the  frog,  he  observed 
that  when  the  lum- 
bar nerves  of  a  dead 
frog  were  connected 
with  the  crural  mus- 
cles by  a  metallic 
circuit,  the  latter  be- 
came briskly  con- 
tracted. 

To  repeat  this 
celebrated  experi- 
ment, the  legs  of  a 
recently  killed  frog 
are  prepared,  and 
the  lumbar  nerves 
on  each  side  of  the 
vertebral  column  are 
exposed  in  the  form 
of  white  threads. 
A  metal  conductor, 
composed  of  zinc  Fig.  702. 

and  copper,   is  then 

taken  (fig.  702),  and  one  end  introduced  between  the  nerves  and  the  vertebral 
column,  while  the  other  touches  one  of  the  muscles  of  the  thighs  or  legs  ; 
at  each  contact  a  smart  contraction  of  the  muscles  ensues. 

Galvani  had  some  time  before  observed  that  the  electricity  of  machines 
produced  in  dead  frogs  analogous  contractions,  and  he  attributed  the  pheno- 
mena first  described  to  an  electricity  inherent  in  the  animal.  He  assumed 

3B2 


740  Dynamical  Electricity.  [797- 

that  this  electricity,  which  he  called  vital  fluid,  passed  from  the  nerves  to 
the  muscles  by  the  metallic  arc,  and  was  thus  the  cause  of  contraction 
This  theory  met  with  great  support,  especially  among  physiologists,  but  it 
was  not  without  opponents.  The  most  considerable  of  these  was  Alexander 
Volta,  professor  of  physics  in  Pavia. 

r  798.  Volta's  fundamental  experiment. — Galvani's  attention  had  been 
exclusively  devoted  to  the  nerves  and  muscles  of  the  frog  ;  Volta's  was 
directed  upon  the  connecting  metal.  Resting  on  the  observation,  which 
Galvani  had  also  made,  that  the  contraction  is  more  energetic  when  the  con- 
necting arc  is  composed  of  two  metals,  than  when  there  is  only  one,  Volta 
attributed  to  the  metals  the  active  part  in  the  phenomenon  of  contraction. 
He  assumed  that  the  disengagement  of  electricity  was  due  to  their  contact, 
and  that  the  animal  parts  only  officiated  as  conductors,  and  at  the  same  time 
as  a  very  sensitive  electroscope. 

By  means  of  the  condensing  electroscope,  which  he  had  then  recently 
invented,  Volta  devised  several  modes  of  showing  the  disengagement  of  elec- 
tricity on  the  contact  of  metals,  of  which  the  following  is  the  easiest  to  per- 
form : — 

The  moistened  finger  being  placed  on  the  upper  plate  of  a  condensing 
electroscope  (fig.  679),  the  lower  plate  is  touched  with  a  plate  of  copper,  ^, 
soldered  to  a  plate  of  zinc,  #,  which  is  held  in  the  other  hand.  On  breaking 
the  connection  and  lifting  the  upper  plate  (fig.  680),  the  gold  leaves  diverge, 
and,  as  may  be  proved,  with  negative  electricity.  Hence,  when  soldered 
together,  the  copper  is  charged  with  negative  electricity,  and  the  zinc  with 
positive  electricity.  The  electricity  could  not  be  due  either  to  friction  or 
pressure  ;  for  if  the  condensing  plate,  which  is  of  copper,  is  touched  with 
the  zinc  plate  #,  the  copper  plate  to  which  it  is  soldered  being  held  in  the 
hand,  no  trace  of  electricity  is  observed. 

A  memorable  controversy  arose  between  Galvani  and  Volta.  The  latter 
was  led  to  give  greater  extension  to  his  contact  theory,  and  propounded  the 
principle  that  when  two  heterogeneous  substances  are  placed  in  contact^  one 
of  them  always  assumes  the  positive  and  the  other  the  negative  electrical 
condition.  In  this  form  Volta's  theory  obtained  the  assent  of  the  principal 
philosophers  of  his  time.  Galvani,  however,  made  a  number  of  highly  in- 
teresting experiments  with  animal  tissues.  In  some  of  these  he  obtained 
indications  of  contraction,  even  though  the  substances  in  contact  were  quite 
homogeneous. 

799.  Disengagement  of  electricity  in  chemical  actions. — The  contact 
theory  which  Volta  had  propounded,  and  by  which  he  explained  the  action  of 
the  pile,  soon  encountered  objectors.  Fabroni,  a  countryman  of  Volta,  having 
observed  that,  in  the  pile,  the  discs  of  zinc  became  oxidised  in  contact  with 
the  acidulated  water,  thought  that  this  oxidation  was  the  principal  cause  of 
the  disengagement  of  electricity.  In  England  Wollaston  soon  advanced  the 
same  opinion,  and  Davy  supported  it  by  many  ingenious  experiments. 

It  is  true  that  in  the  fundamental  experiment  of  the  contact  theory  (798) 
Volta  obtained  signs  of  electricity.  But  De  la  Rive  showed  that  if  the  zinc 
be  held  in  a  wooden  clamp,  all  signs  of  electricity  disappear,  and  that  the 
same  is  the  case  if  the  zinc  be  placed  in  gases,  such  as  hydrogen  or  nitrogen, 
which  exert  upon  it  no  chemical  action.  De  la  Rive  accordingly  concluded 


-799]      Disengagement  of  Electricity  in  Chemical  Actions.       741 

that  in  Volta's  original  experiment  the  disengagement  of  electricity  is  due  to 
the  chemical  actions  which  result  from  the  perspiration  and  from  the  oxygen 
of  the  atmosphere. 

The  development  of  electricity  in  chemical  actions  may  be  demonstrated 
in  the  following  manner  by  means  of  the  condensing  electroscope  (786)  : — A 
disc  of  moistened  paper  is  placed  on  the  upper  plate  of  the  condenser,  and 
on  this  a  zinc  capsule,  in  which  some  very  dilute  sulphuric  acid  is  poured.  A 
platinum  wire,  communicating  with  the  ground,  but  insulated  from  the  sides 
of  the  vessel,  is  immersed  in  the  liquid,  and  at  the  same  time  the  lower  plate 
of  the  condenser  is  also  connected  with  the  ground  by  touching  it  with  the 
moistened  finger.  On  breaking  contact  and  removing  the  upper  plate,  the 
gold  leaves  are  found  to  be  positively  electrified,  proving  that  the  upper 
plate  has  received  a  charge  of  negative  electricity. 

By  a  variety  of  analogous  experiments  it  may  be  shown  that  various 
chemical  actions  are  accompanied  by  a  disturbance  of  the  electrical  equili- 
brium ;  though  of  all  chemical  actions  those  between  metals  and  liquids  are 
the  most  productive  of  electricity.  All  the  various  resultant  effects  are  in 
accordance  with  the  general  rule,  that  when  a  liquid  acts  chemically  on  a 
metal  the  liquid  assumes  the  positive,  and  the  metal  the  negative,  con- 
dition. In  the  above  experiment  the  sulphuric  acid,  by  its  action  on 
zinc,  becomes  positively  electrified,  and  its  electricity  passes  off  through 
the  platinum  wire  into  the  ground,  while  the  negative  electricity  excited 
on  the  zine  acts  on  the  condenser  just  as  an  excited  rod  of  sealing-wax 
would  do. 

In  many  cases  the  electrical  indications  accompanying  chemical  actions 
are  but  feeble,  and  require  the  use  of  a  very  delicate  electroscope  to  render 
them  apparent.  Thus,  one  of  the  most  energetic  chemical  actions,  that  of 
sulphuric  acid  upon  zinc,  gives  no  more  free  electricity  than  water  alone  does 
with  zinc. 

Opinion — which  in  this  country,  at  least,  had,  mainly  by  the  influence  of 
Faraday's  experiments,  tended  in  favour  of  the  purely  chemical  origin  of 
the  electricity  produced  in  voltaic  action — has  of  late  inclined  more  and  more 
towards  the  contact  theory.  The  following  experiments,  due  to  Sir  W. 
Thomson,  afford  perhaps  the  most  conclusive  arguments  hitherto  adduced 
in  favour  of  the  latter  view  : — 

A  very  light  metal  bar  is  suspended  by  fine  wire,  so  as  to  be  movable 
about  an  axis  perpendicular  to  the  plane  of  a  disc  made  up  of  two  half  discs 
one  of  zinc,  Z,  and  the  other  of  copper,  C,  (fig. 
703).  The  light  bar  is  counterpoised  so  as  to 
be  exactly  over  one  half  of  the  line  of  separa- 
tion of  the  two  discs.  When  the  discs  are 
placed  in  connection  and  the  bar  is  charged 
positively  by  being  connected  with  a  Leyden 
jar,  the  bar  moves  from  the  zinc  towards  the 
copper  ;  if  the  jar,  and  therefore  the  bar,  is 

charged  negatively,  its  motion  is  in  the  opposite  direction.  The  same  results 
are  obtained  when  the  discs  are  connected  by  a  wire,  thus  showing  that  the 
contact  of  the  two  metals  causes  them  to  assume  different  electrical  con- 
ditions, the  zinc  taking  the  positive,  and  the  copper  the  negative  electricity. 


742  Dynamical  Electricity.  [799- 

When,  however,  the  two  halves,  instead  of  being  in  metallic  contact,  are 
connected  by  a  drop  of  water,  no  change  is  produced  in  the  position  of  the 
bar  by  altering  its  electrification,  provided  it  hang  quite  symmetrically  re- 
lative  to  the  two  halves  of  the  ring.  This  result  shows  that,  under  the  cir- 
cumstances, nientioned,  no  difference  is  produced  in  the  electrical  condition 
of  the  two  metals.  Hence  the  conclusion  has  been  drawn  by  Sir  W.  Thom- 
son and  others,  that  the  movement  of  electricity  in  the  galvanic  circuit  is 
entirely  due  to  the  electrical  difference  produced  at  the  surfaces  of  contact  of 
the  dissimilar  metals.  These  results  have  been  confirmed  by  some  recent 
very  careful  experiments  by  Professor  Clifton. 

There  are,  however,  other  facts  which  are  not  easily  harmonised  with 
this  view  ;  and  indeed  the  last-mentioned  experiment  can  hardly  be  regarded 
as  proving  that  in  all  cases  two  different  metals  connected  by  an  electrolytic 
(8 1 6)  liquid  assume  the  same  electrical  condition.  It  may,  therefore,  still 
be  regarded  as  possible,  or  even  probable,  that  the  contact  between  the 
metals  and  the  liquids  of  a  cell  contributes,  at  least  in  some  cases,  to  the 
production  of  the  current. 

A  most  complete  discussion  of  the  question  as  to   the   seat  of  electro- 
motive forces  in  the  voltaic  cell  is  published  in  a  series  of  papers  by  Prof. 
Lodge  in  the  nineteenth  volume  of  the  '  Philosophical  Magazine.' 
\   800.  Current  electricity. — When  a  plate  of  zinc  and  a  plate  of  copper  are 
partially  immersed  in  dilute  sulphuric  acid,  no  electrical  or  chemical  change 
is  apparent  beyond  perhaps  a  slight  disengagement  of  hydrogen  from  the 
surface  of  the  zinc  plate.     If  now  the  plates  are 
placed  in  direct  contact,  or,  more  conveniently, 
are  connected  by  a  metal   wire,  the  chemical 
action  sets  in,  a  large  quantity  of  hydrogen  is 
disengaged ;  but  this  hydrogen  is  no  longer  dis- 
engaged at  the  surface  of  the  zinc,  but  at  the 
surface  of  the  copper  plate.     Here  then  we  have 
to  deal  with  something  more  than  mere  chemical 
action,  for  chemical  action  would  be  unable  to 
explain  either  the   increase  in  the   quantity  of 
hydrogen  disengaged  when  the  metals  touch,  or 
the  fact  that  this  hydrogen  is  now  given  off  at 
Fls'  7°4'  the  surface  of  the  copper  plate.     At  the  same 

time,  if  the  wire  is  examined  it  will  be  found  to  possess  many  remarkable 
thermal,  magnetic,  and  other  properties  which  will  be  afterwards  described. 
In  order  to  understand  what  here  takes  place,  let  us  suppose  that  we  have 
two  insulated  metal  spheres,  and  that  one  is  charged  with  positive  and  the 
other  with  negative  electricity,  and  that  they  are  momentarily  connected  by 
means  of  a  wire.  Electricity  will  pass  from  a  place  of  higher  to  a  place  of 
lower  potential — that  is,  from  the  positive  along  the  wire  to  the  negative — 
and  the  potentials  become  equal.  This  is,  indeed,  nothing  more  than  an 
electrical  discharge  taking  place  through  the  wire  ;  and  during  the  infinitely 
short  time  in  which  this  is  accomplished,  it  can  be  shown  that  the  wire 
exhibits  certain  heating  and  magnetising  effects,  of  which  the  increase  of 
temperature  is  perhaps  the  easiest  to  observe.  If  now  we  can  imagine  some 
agency  by  which  the  different  electrical  conditions  of  the  two  spheres  are 


-801]  Voltaic  Couple.     Electromotive  Series.  743 

renewed  as  fast  as  they  are  discharged,  which  is  what  very  nearly  takes 
place  when  the  two  spheres  are  respectively  connected  with  the  two  con- 
ductors r  and  r±  of  a  Holtz's  machine  (figs.  650,  651),  this  equalisation  of 
potentials,  thus  taking  place,  is  virtually  continuous,  and  the  phenomena 
above  mentioned  are  also  continuous. 

Now  this  is  what  takes  place  when  the  two  metals  are  in  contact  in  a 
liquid  which  acts  upon  them  unequally.  This  is  independent  of  hypothesis 
as  to  the  cause  of  the  phenomena — whether  the  electrical  difference  is  only 
produced  at  the  moment  of  contact  of  the  metals,  or  whether  it  is  due  to  the 
chemical  action,  or  tendency  to  chemical  action,  between  the  metal  and  the 
liquid.  The  rapidly  succeeding  series  of  equalisations  of  potential  which 
takes  place  in  the  wire  being  continuous,  so  long  as  the  chemical  action 
continues,  is  what  is  ordinarily  spoken  of  as  the  electrical  current. 

If  we  represent  by  +^the  potential  of  the  copperplate,  and  by  —  <?  the 
potential  of  the  zinc,  then  the  electrical  difference — that  is,  the  difference  of 
potentials — is  +  e  —  (  —  e]  =  T.B.  And  this  is  general ;  the  essential  point  of  any 
such  combination  as  the  above  is,  that  it  maintains,  or  tends  to  maintain,  a 
difference  of  potentials,  which  difference  is  constant.  If,  for  instance,  the 
zinc  plate  be  connected  with  the  earth  which  is  at  zero  potential,  its  potential 
also  becomes  zero  ;  and  since  the  electrical  difference  remains  constant,  we 
have  for  the  potential  of  the  copper  plate  +  ie.  Similarly,  if  the  copper  be 
connected  with  the  earth  the  potential  of  the  zinc  plate  is  negative  and  is  —  ie. 

The  conditions  under  which  a  current  of  electricity  is  formed  in  the  above 
experiment  may  be  further  illustrated  by  reference  to  the  conditions  which 
determine  the  flow  of  water  between  two  reservoirs  containing  water  at  dif- 
ferent levels.  If  they  are  connected  by  a  pipe,  water  will  flow  from  the 
one  at  a  higher  level  to  the  one  at  a  lower  level  until  the  water  in  the  two 
is  at  the  same  level,  when  of  course  the  flow  ceases.  If  we  imagine  the 
lower  reservoir  so  large  that  any  water  added  to  it  would  not  affect  its  level — 
if  it  were  the  sea,  for  example — that  would  represent  zero  level,  and  if  the 
higher  reservoir  could  be  kept  at  a  constant  level  there  would  be  a  constant 
flow  in  the  pipe. 

We  must  here  be  careful  not  to  dwell  too  much  on  this  analogy.  It  is  not 
to  be  supposed  that  in  speaking  of  current  of  electricity  we  mean  that  any- 
thing actually  flows — that  there  is  any  actual  transfer  of  matter.  We  say 
'  electricity  flows '  or  '  a  current  is  produced,'  in  much  the  same  sense  as  that 
in  wjiich  we  say  *  sound  or  light  travels.' 

y  801.  Voltaic  couple.  Electromotive  series. — The  arrangement  just 
described,  consisting  of  two  metals  in  metallic  contact,  and  a  conducting 
liquid  in  which  they  are  placed,  constitutes  a  simple  voltaic  element  or  couple. 
So  long  as  the  metals  are  not  in  contact,  the  couple  is  said  to  be  open,  and 
when  connected  it  is  closed. 

According  to  the  chemical  view,  to  which  we  shall  for  the  present  pro- 
visionally adhere,  it  is  not  necessary  that,  for  the  production  of  a  current,  one 
of  the  metals  be  unaffected  by  the  liquid,  but  merely  that  the  chemical  action 
upon  the  one  be  greater  than  upon  the  other.  For  then  we  may  assume 
that  the  current  produced  would  be  due  to  the  difference  between  the  differ- 
ences of  potential  which  each  of  the  metals  separately  produces  by  its  con- 
tact with  the  liquid.  If  the  differences  of  potentials  were  absolutely  equal — 


744  Dynamical  Electricity.  [801- 

a  condition,  however,  impossible  of  realisation  with  two  distinct  metals — we 
must  assume  that  when  the  metals  are  joined  no  current  would  be  produced. 
The  metal  which  is  most  attacked  is  called  the  positive  or  generating  plate, 
and  that  which  is  least  attacked  the  negative  or  collecting  plate.  The  posi- 
tive metal  determines  the  direction  of  the  current,  which  proceeds  in  the 
liquid  from  the  positive  to  the  negative  plate,  and  out  of  the  liquid  through 
the  connecting  wire  from  the  negative  to  the  positive  plate. 

In  speaking  of  the  direction  of  the  current  the  direction  of  the  positive 
electricity  is  always  understood. 

In  the  fundamental  experiment,  not  only  the  connecting  wire  but  also  the 
liquid  and  the  plates  are  traversed  by  the  electrical  current — are  the  scene 
of  electrical  actions. 

The  mere  immersion  of  two  different  metals  in  a  liquid  is  not  alone 
sufficient  to  produce  a  current ;  there  must  be  chemical  action.  When  a 
platinum  and  a  gold  plate  are  connected  with  a  delicate  galvanometer,  and 
immersed  in  pure  nitric  acid,  no  current  is  produced  ;  but  on  adding  a  drop 
of  hydrochloric  acid  a  strong  current  is  excited,  which  proceeds  in  the  liquid 
from  the  gold  to  the  platinum,  because  the  gold  is  attacked  by  the  nitro- 
hydrochloric  acid,  while  the  platinum  is  less  so,  if  at  all. 

As  a  voltaic  current  is  produced  whenever  two  metals  are  placed  in 
metallic  contact  in  a  liquid  which  acts  more  powerfully  upon  one  than  upon 
the  other,  there  is  a  great  choice  in  the  mode  of  producing  such  currents. 
In  reference  to  their  electrical  deportment,  the  metals  have  been  arranged  in 
what  is  called  an  electromotive  series,  in  which  the  most  electropositive  are 
at  one  end,  and  the  most  electronegative  at  the  other.  Hence  when  any  two  of 
these  are  placed  in  contact  in  dilute  acid,  the  current  in  the  connecting  wire 
proceeds  from  the  one  lower  in  the  list  to  the  one  higher.  The  principal 
metals  are  as  follows  : — 

1.  Zinc  5.  Iron  10.  Silver 

2.  Cadmium  6.  Nickel  n.  Gold 

3.  Tin  7.  Bismuth  12.  Platinum 

4.  Lead  8.  Antimony  13.  Graphite 

9.  Copper 

It  will  be  seen  that  the  electrical  deportment  of  any  metal  depends  on  the 
metal  with  which  it  is  associated.  Iron,  for  example,  in  dilute  sulphuric  acid 
is  electronegative  towards  zinc,  but  is  electropositive  towards  copper  ;  copper 
in  turn  is  electronegative  towards  iron  and  zinc,  but  is  electropositive  towards 
silver,  platinum,  or  graphite. 

-  "802.  Electromotive  force. — The  force  in  virtue  of  which  continuous 
electrical  effects  are  produced  throughout  a  circuit  consisting  of  two  metals 
in  metallic  contact  in  a  liquid  which  acts  unequally  upon  them,  is  usually 
called  the  electromotive  force.  Electromotive  force  and  difference  of  potentials 
are  commonly  used  in  the  same  sense.  It  is,  however,  more  correct  to  regard 
difference  of  potentials  as  a  particular  case  of  electromotive  force  ;  for  as  we 
shall  afterwards  see,  there  are  cases  in  which  electrical  currents  are  pro- 
duced without  the  occurrence  of  that  particular  condition  which  we  have  called 
difference  of  potentials.  The  electromotive  force  is  greater  in  proportion  to 
the  distance  of  the  two  metals  from  one  another  in  the  series.  That  is  to 


-802]  Electromotive  Force.  745 

say,  it  is  greater  the  greater  the  difference  between  the  chemical  action  upon 
the  two  metals  immersed.  Thus  the  electromotive  force  between  zinc  and 
platinum  is  greater  than  that  between  zinc  and  iron,  or  between  zinc  and 
copper.  The  law  established  by  experiment  is,  that  the  electromotive  force 
between  any  two  metals  is  equal  to  the  sum  of  the  electromotive  forces  between 
all  the  intervening  metals.  Thus  the  electromotive  force  between  zinc  and 
platinum  is  equal  to  the  sum  of  the  electromotive  forces  between  zinc  and 
iron,  iron  and  copper,  and  copper  and  platinum. 

The  electromotive  force  is  influenced  by  the  condition  of  the  metal  ; 
rolled  zinc,  for  instance,  is  negative  towards  cast  zinc.  It  also  depends  on 
the  degree  of  concentration  of  the  liquid  ;  in  dilute  nitric  acid  zinc  is  positive 
towards  tin,  and  mercury  positive  towards  lead  ;  while  in  concentrated  nitric 
acid  the  reverse  is  the  case,  mercury  and  zinc  being  respectively  electronega- 
tive towards  lead  and  tin. 

The  nature  of  the  liquid  also  influences  the  direction  of  the  current.  If 
two  plates,  one  of  copper  and  one  of  iron,  are  immersed  in  dilute  sulphuric 
acid,  a  current  is  set  up  proceeding  through  the  liquid  from  the  iron  to  the 
copper  ;  but  if  the  plates,  after  being  washed,  are  placed  in  solution  of 
potassium  sulphide,  a  current  is  produced  in  the  opposite  direction — the 
copper  is  now  the  positive  metal.  Other  examples  may  be  drawn  from  the 
following  table,  which  shows  the  electric  deportment  of  the  principal  metals 
with  three  different  liquids.  It  is  arranged  like  the  preceding  one  ;  each 
metal  being  electropositive  towards  any  one  lower  in  the  list,  and  electro- 
negative towards  any  one  higher. 

Caustic  potass  Hydrochloric  acid 

Zinc  Zinc 

Tin  Cadmium 

Cadmium  Tin 

Antimony  Lead 

Lead  Iron 

Bismuth  Copper 

Iron  Bismuth 

Copper  Nickel 

Nickel  Silver 

Silver  Antimony 


Sulphide  of 
potassium 

Zinc 

Copper 

Cadmium 

Tin 

Silver 

Antimony 

Lead 

Bismuth 

Nickel 

Iron 


A  voltaic  current  may  also  be  produced  by  means  of  two  liquids  and 
one  metal.  This  may  be  shown  by  the  following 
experiment  : — In  a  beaker  containing  strong  nitric 
acid  is  placed  a  small  porous  pot  (fig.  705),  con- 
taining strong  solution  of  caustic  potass.  If  now 
two  platinum  wires  connected  with  the  two  ends 
of  a  galvanometer  (821)  are  immersed  respectively 
in  the  alkali  and  in  the  acid,  a  voltaic  current  is 
produced,  proceeding  in  the  wire  from  the  nitric 
acid  to  the  potass,  which  thus  correspond  re- 
spectively to  the  negative  and  positive  plates  in 
ordinary  couples. 

A  metal  which  is  acted  upon  by  a  liquid  can  be  protected  from  solution 


Fig.  705. 


746 


Dynamical  Electricity. 


[802- 


by  placing  in  contact  with  it  a  more  electropositive  metal,  and  thus  forming 
a  simple  voltaic  circuit.  This  principle  is  the  basis  of  Davy's  proposal  to 
protect  the  copper  sheathings  of  ships,  which  are  rapidly  acted  upon  by  sea- 
water.  If  zinc  or  iron  be  connected  with  the  copper,  these  metals  are  dis- 
solved and  the  copper  protected.  Davy  found  that  a  piece  of  zinc  the  size 
of  a  nail  was  sufficient  to  protect  a  surface  of  forty  or  fifty  square  inches  ; 
unfortunately  the  proposal  has  not  been  of  practical  value,  for  the  copper 
must  be  attacked  to  a  certain  extent  to  prevent  the  adherence  of  marine 
jrian4#.and  shellfish. 

I  803.  Poles  and  electrodes. — If  the  wire  connecting  the  two  terminal 
plates  of  a  voltaic  couple  be  cut,  it  is  clear,  from  what  has  been  said  about 
the  origin  and  direction  of  the  current,  that  positive  electricity  will  tend  to 
accumulate  at  the  end  of  the  wire  attached  to  the  copper  or  negative  plate, 
and  negative  electricity  on  the  wire  attached  to  the  zinc  or  positive  plate. 
These  terminals  have  been  called  the  poles  of  the 
battery.  For  experimental  purposes,  more  especi- 
ally in  the  decomposition  of  salts,  plates  of  platinum 
are  attached  to  the  ends  of  the  wires.  Instead  of  the 
term  poles,  the  word  electrode  (rj\€KTpov  and  686s  a 
way)  is  now  commonly  used ;  for  these  are  the  ways 
through  which  the  respective  electricities  emerge.  It 
is  important  not  to  confound  the  positive  plate  with 
the  positive  pole  or  electrode.  The  positive  electrode 
is  that  connected  with  the  negative  plate,  while  the 
negative  electrode  is  connected  with  the  positive  plate. 
\/~^04.  Voltaic  pile.  Voltaic  battery. —When  a 
series  of  voltaic  elements  or  pairs  are  arranged  so 
that  the  zinc  of  one  element  is  connected  with  the 
copper  of  another,  the  zinc  of  this  with  the  copper 
of  another,  and  so  on,  the  arrangement  is  called  a 
voltaic  battery  ;  and  by  its  means  the  effects  pro- 
duced by  a  single  element  are  capable  of  being  very 
greatly  increased. 

The  earliest  of  these  arrangements  was  devised  by 
Volta  himself.  It  consists  (fig.  706)  of  a  series  of  discs 
piled  one  over  the  other  in  the  following  order  : — At 
the  bottom,  on  a  frame  of  wood,  is  a  disc  of  copper, 
then  a  disc  of  cloth  moistened  by  acidulated  water,  or 
by  brine,  then  a  disc  of  zinc  ;  on  this  a  disc  of  copper, 
and  another  disc  of  moistened  cloth,  to  which  again 
follow  as  many  sets  of  zinc-cloth-copper,  always  in  the 
same  order,  as  may  be  convenient,  the  highest  disc 
being  of  zinc.  The  discs  are  kept  in  a  vertical  position  by  glass  rods. 

It  will  be  readily  seen  that  we  have  here  a  series  of  simple  voltaic  couples, 
Fhe  moisture  in  the  cloth  acting  as  the  liquid  in  the  cases  already  mentioned, 
and  that  the  terminal  zinc  is  the  negative  and  the  terminal  copper  the 
positive  pole.  From  the  mode  of  its  arrangement,  and  from  its  discoverer, 
the  apparatus  is  known  as  the  voltaic  pile,  a  term  applied  to  all  apparatus  of 
this  kind  for  accumulating  the  effects  of  dynamical  electricity. 


Fig.  706. 


-805] 


Wollaston's  Battery. 


747 


The  distribution  of  electricity  in  the  pile  varies  according  as  it  is  in  con- 
nection with  the  earth  by  one  of  its  extremities,  or  as  it  is  insulated  by  being 
placed  on  a  non-conducting  cake  of  resin  or  glass. 

In  the  former  case,  the  end  in  contact  with  the  ground  is  neutral,  and  the 
rest  of  the  apparatus  contains  only  one  kind  of  electricity  ;  this  is  negative 
if  the  copper  disc,  and  positive  if  the  zinc  disc  is  in  contact  with  the  ground. 

In  the  insulated  pile  the  electricity  is  not  uniformly  distributed.  By 
means  of  a  proof  plane  and  electroscope  it  may  be  demonstrated  that  the 
middle  part  is  in  a  neutral  state,  and  that  one-half  is  charged  with  positive 
and  the  other  with  negative  electricity,  the  potential  increasing  from  the 
middle  to  the  ends.  The  half  terminated  by  a  zinc  disc  is  charged  with  nega- 
tive electricity,  and  that  by  a  copper  with  positive  electricity.  The  pile  is 
thus  similar  to  a  charged  Leyden  jar  ;  with  this  difference,  however,  that 
when  the  jar  has  been  discharged  by  connecting  its  two  coatings,  the  elec- 
trical effects  cease  ;  while  in  the  case  of  the  pile,  the  cause  which  originally 
brought  about  the  distribution  of  electricity  restores  this  state  of  charge  after 
the  discharge  ;  and  the  continuous  succession  of  charges  and  discharges  forms 
the  current.  The  effects  of  the  pile  will  be  discussed  in  other  places. 

805.  Woliaston  s  battery. — The  original  form  of  the  voltaic  pile  has  a 
great  many  inconveniences,  and  possesses  now  only  an  historical  interest. 
It  has  received  a  great  many  improvements,  the  principal  object  of  which 
has  been  to  facilitate  manipulation,  and  to  produce  greater  electromotive 
force. 


One  of  the  earliest  of  these  modifications  was  the  crown  of  cups,  or 
couronne  des  lasses,  invented  by  Volta  himself.  An  improved  form  of  this  is 
known  as  Wollastorts  battery  (fig.  707)  ;  it  is  arranged  so  that  when  the 
current  is  not  wanted,  the  action  of  the  battery  can  be  stopped. 

The  plates  Z  are  of  thick  rolled  zinc,  and  usually  about  eight  inches  in 
length  by  six  in  breadth.  The  copper  plates,  C,  are' of  thin  sheet,  and  bent 


748  Dynamical  Electricity.  [805- 

so  as  to  surround  the  zincs  without  touching  them,  contact  being  prevented 
by  small  pieces  of  cork.  To  each  copper  plate  a  narrow  strip  of  copper,  a, 
is  soldered,  which  is  bent  twice  at  right  angles  and  is  soldered  to  the  zinc 
plate ;  and  the  first  zinc,  Z,  is  surrounded  by  the  first  copper  C  ;  these  two 
constitute  a  couple,  and  each  couple  is  immersed  in  a  glass  vessel,  containing 
acidulated  water.  The  copper,  C,  is  soldered  to  the  second  zinc  by  the  strip 
0,  and  this  zinc  is  in  turn  surrounded  by  a  second  copper,  and  so  on. 

Fig.  707  represents  a  pile  of  sixteen  couples  united  in  two  parallel  series 
of  eight  each.  All  these  couples  are  fixed  to  a  cross  frame  of  wood,  by  which 
they  can  be  raised  or  lowered  at  pleasure.  When  the  battery  is  not  wanted, 
the  couples  are  lifted  out  of  the  liquid.  The  water  in  these  vessels  is  usually 
acidulated  with  T\-  sulphuric  and  ~  of  nitric  acid. 

Hare's  deftagrator. — This  is  a  simple  voltaic  arrangement,  consisting  of 
two  large  sheets  of  copper  and  zinc  rolled  together  in  a  spiral,  but  preserved 
from  direct  contact  by  bands  of  leather  or  horsehair.  The  whole  is  immersed 
in  a  vessel  containing  acidulated  water,  and  the  two  plates  are  connected 
outside  the  liquid  by  a  conducting  wire. 

Y8o6.  Enfeeblement  of  the  current  in  batteries.  Secondary  currents. 
The  various  batteries  already  described — Volta's,  Wollaston's,  and  Hare's, 
which  consist  essentially  of  two  metals  and  one  liquid — labour  under  the 
objection  that  the  currents  produced  rapidly  diminish  in  strength. 

This  is  principally  due  to  three  causes  :  the  first  is  the  decrease  in  the 
chemical  action  owing  to  the  neutralisation  of  the  sulphuric  acid  by  its  com- 
bination with  the  zinc.  This  is  a  necessary  action,  for  upon  it  depends  the 
current ;  it  therefore  occurs  in  all  batteries,  and  is  without  remedy  except  by 
replacement  of  acid  and  zinc.  The  second  is  due  to  what  is  called  local 
action ;  that  is,  the  production  of  small  closed  circuits  in  the  active  metal, 
owing  to  the  impurities  it  contains.  These  local  currents  rapidly  wear  away 
the  active  plate,  without  contributing  anything  to  the  continuance  of  the 
general  current.  They  are  remedied  by  amalgamating  the  zinc  with  mercury, 
by  which  chemical  action  is  prevented  until  the  circuit  is  closed,  as  will  be 
more  fully  explained  (816).  The  third  arises  from  the  production  of  an 
inverse  electromotive  force,  which  tends  to  produce  a  current  in  a  contrary 
direction  to  the  principal  current,  and  therefore  to  destroy  it  either  totally 
or  partially.  In  the  fundamental  experiment  (fig.  704),  when  the  circuit  is 
closed,  zinc  sulphate  is  formed,  which  dissolves  in  the  liquid,  and  at  the 
same  time  a  layer  of  hydrogen  gas  is  gradually  formed  on  the  surface  of  the 
copper  plate.  This  diminishes  the  activity  of  the  combination  in  more  than 
one  way.  In  the  first  place,  it  interferes  with  the  contact  between  the  metal 
and  the  liquid ;  in  the  second  place,  in  proportion  as  the  copper  becomes 
coated  with  hydrogen,  we  have  virtually  a  plate  of  hydrogen  instead  of  a 
plate  of  copper  opposed  to  the  zinc,  and  in  addition,  the  hydrogen,  by  react- 
ing on  the  zinc  sulphate,  which  accumulates  in  the  liquid,  gradually  causes  a 
deposition  of  zinc  on  the  surface  of  the  copper ;  hence,  instead  of  having 
two  different  metals  unequally  attacked,  the  two  metals  become  gradually 
less  different  and,  consequently,  the  total  effect  and  the  current  become 
weaker  and  weaker. 

The  polarisation  of  the  plate  (as  this  phenomenon  is  termed)  may  be 
destroyed  by  breaking  the  circuit  and  exposing  the  copper  plate  to  the  air  ; 


-808]  Darnell's  Battery.  749 

the  deposited  hydrogen  is  thus  more  or  less  "completely  got  rid  of,  and  on 
again  closing  the  circuit  the  current  has  nearly  its  original  strength.  The 
same  result  is  obtained  when  the  current  of  another  battery  is  transmitted 
through  the  battery  in  a  direction  opposite  to  that  of  the  first. 

When  platinum  electrodes  are  used 
to  decompose  water,  a  similar  pheno- 
menon is  produced,  called#0/artsafi0n 
of  the  electrodes,  which  may  be  illus- 
trated by  an  arrangement  represented 
in  fig.  708,  in  which  B  is  a  constant 
element,  V  a  voltameter  (845),  G  a 
galvanometer  (821),  and  H  a  mercury 
cup.  The  wire  L  being  disconnected 
from  H,  a  current  is  produced  in  the 
voltameter,  the  direction  of  which  is 
from  P  to  P'  j  if  now  the  wire  F  be 
detached  from  H,  and  L  be  connected  therewith,  a  current  is  produced  in 
the  voltameter,  the  direction  of  which  is  from  P  to  P' ;  if  now  the  wire  F 
be  detached  from  H,  and  L  be  connected  therewith,  a  current  is  produced 
through  the  galvanometer  the  direction  of  which  is  from  P'  to  P  :  that  is,  the 
opposite  of  that  which  the  element  had  previously  produced.  Becquerel  and 
Faraday  have  shown  that  this  polarisation  of  the  metals  results  from  the 
deposits  caused  by  the  passage  of  the  current,  and  an  important  application 
of  this  phenomenon  will  be  found  described  farther  on  (849). 

CONSTANT   CURRENTS. 

/^8o7.  Constant  currents. — With  few  exceptions,  batteries  composed  of 
elements  with  a  single  liquid  have  almost  gone  out  of  use,  in  consequence 
of  the  rapid  enfeeblement  of  the  current  produced.  They  have  been  replaced 
by  batteries  with  two  liquids,  which  are  called  constant  batteries  because 
their  action  continues  without  material  alteration  for  a  considerable  period 
of  time.  The  essential  point  to  be  attended  to  in  securing  a  constant  current 
is  to  prevent  the  polarisation  of  the  inactive  metal ;  in  other  words,  to  hinder 
any  permanent  deposition  of  hydrogen  on  its  surface.  This  is  effected  by 
placing  the  inactive  metal  in  a  liquid  upon  which  the  deposited  hydrogen 
can  act  chemically. 

^808.  Daniell  s  battery. — This  was  the  first  form  of  the  constant  battery, 
and  was  invented  by  Daniell  in  the  year  1836.  As  regards  the  constancy 
of  its  action,  it  is  perhaps  still  the  best  of  all  constant  batteries.  Fig.  709 
represents  a  single  element.  A  glass  or  porcelain  vessel,  V,  contains  a 
saturated  solution  of  copper  sulphate,  in  which  is  immersed  a  copper 
cylinder,  G,  open  at  both  ends,  and  perforated  by  holes.  At  the  upper  part 
of  this  cylinder  there  is  an  annular  shelf,  G,  also  perforated  by  small  holes, 
and  below  the  level  of  the  solution  ;  this  is  intended  to  support  crystals  of 
copper  sulphate  to  replace  that  decomposed  as  the  electrical  action  pro- 
ceeds. Inside  the  cylinder  is  a  thin  porous  vessel,  P,  of  unglazed  earthen- 
ware. This  contains  either  water  or  solution  of  common  salt  or  dilute 
sulphuric  acid,  in  which  is  placed  the  cylinder  of  amalgamated  zinc,  Z.  Two 


750 


Dynamical  Electricity. 


[808- 


thin  strips  of  copper,  p  and  ;z,  fixed  by  binding  screws  to  the  copper  and  to 
the  zinc,  serve  for  connecting  the  elements  in  series. 

When  a  Daniell's  element  is  closed,  the  hydrogen   resulting  from  the 
action  of  the  dilute  acid  on  the  zinc  is  liberated  on  the  surface  of  the  copper 
plate,  but  meets  there  the  copper  sulphate,  which  is  reduced,  forming  sul- 
phuric acid  and  metallic  copper,  which  is  deposited  on  the  surface  of  the 
copper  plate.     In  this  way  copper  sulphate  in 
solution  is  taken  up ;  and  if  it  were   all  con- 
sumed,  hydrogen  would  be  deposited   on  the 
copper,   and  the    current  would    lose  its  con- 
stancy.    This  is   prevented  by  the  crystals  of 
copper  sulphate  which  keep  the  solution  satu- 
rated.     The  sulphuric   acid   produced   by   the 
decomposition   of  the  sulphate    permeates  the 
porous  cylinder,  and  tends  to  replace  the  acid 
used  up  by  its  action  on  the  zinc  ;  and  as  the 
quantity  of  sulphuric  acid  formed  in  the   solu- 
tion of  copper  sulphate  is  regular,  and  propor- 
•  tional  to  the  acid  used  in  dissolving  the  zinc,  the 
action  of  this  acid  on  the  zinc  is  regular  also,  and 
thus  a  constant  current  is  produced. 
Flg'  7°9'  In   order  to  join  together   several  of  these 

elements  to  form  a  battery,  the  zinc  of  one  is  connected  either  by  a  copper 
wire  or  strip  with  the  copper  of  the  next,  and  so  on,  from  one  element  to 
another,  as  shown  in  fig.  713,  for  another  kind  of  battery. 

Instead  of  a  porous  earthenware  vessel  a  bag  of  sailcloth  may  be  used 
for  the  diaphragm  separating  the  two  liquids.  The  effect  is  at  first  more 
powerful,  but  the  two  solutions  mix  more  rapidly,  which  weakens  the  current. 
The  object  of  the  diaphragm  is  to  allow  the  current  to  pass,  but  to  prevent 
as  much  as  possible  the  mixture  of  the  two  liquids. 

The  current  produced  by  a  Daniell's  battery  is  constant  for  some  hours  ; 

its  action  is  stronger  when  it  is 
placed  in  hot  water.  Its  electro- 
motive force  is  about  ri2  volt. 

v"8o~9.  Grove's  battery. — In  this 
battery  the  copper  sulphate  solution 
is  replaced  by  nitric  acid,  and  the 
copper  by  platinum,  by  which 
greater  electromotive  force  is  ob- 
tained. Fig.  710  represents  one 
of  the  forms  of  a  couple  of  this 
battery.  It  consists  of  a  glass 
vessel,  A,  partially  filled  with  dilute 
sulphuric  acid  (i  :  8) ;  of  a  cylinder 
of  zinc,  Z,  open  at  both  ends  ;  of  a 
vessel,  V,  made  of  porous  earthen- 
ware, and  containing  ordinary  nitric 


Fig.  710. 


Fig.  711. 


acid  ;  of  a  plate  of  platinum,  P  (fig.  711),  bent  in  the  form  of  an  S>  and  fixed 
to  a  cover,  ^,  which  rests  on  the  porous  vessel.      The  platinum  is  con- 


-810] 


Buns  en 's  Battery. 


751 


nected  with  a  binding  screw,  £,  and  there  is  a  similar  binding  screw  on  the 
zinc.  In  this  battery  the  hydrogen,  which  would  be  disengaged  on  the 
platinum  meeting  the  nitric  acid,  decomposes  it,  forming  hyponitrous  acid, 
which  dissolves,  or  is  disengaged,  as  nitrous  fumes.  Grove's  battery  is  the 
most  convenient,  and  one  of  the  most  powerful  of  the  two  fluid  batteries. 
It  is,  however,  expensive,  owing  to  the  high  price  of  platinum  ;  besides 
which  the  platinum  is  liable,  after  some  time,  to  become  brittle  and  break 
very  easily.  But  as  the  platinum  is  not  consumed,  it  retains  most  of  its 
value,  and  when  the  plates  which,  have  been  used  in  a  battery  are  heated  to 
redness,  they  regain  their  elasticity. 

8 10.  Bunsen's  battery. — Bunsen's,  also  known  as  the  zinc  carbon 
battery,  was  invented  in  1843  ;  it  is  in  effect  a  Grove's  battery,  where 
the  plate  of  platinum  is  replaced  by  a  cylinder  of  carbon.  This  is  made 
either  of  the  graphitoidal  carbon  deposited  in  gas  retorts,  or  by  calcin- 
ing in  an  iron  mould  an  intimate  mixture  of  coke  and  bituminous  coal,  finely 
powdered  and  strongly  compressed.  Both  those  modifications  of  carbon  are 
good  conductors.  Each  element  consists  of  the  following  parts  :  i.  a  vessel, 


Fig.  712. 

F  (fig.  7 1 2),  either  of  stoneware  or  of  glass,  containing  dilute  sulphuric  acid  ; 
2.  a  hollow  cylinder,  Z,  of  amalgamed  zinc  ;  3.  a  porous  vessel,  V,  in  which 
is  ordinary  nitric  acid  ;  4.  a  rod  of  carbon,C,  prepared  in  the  above  manner. 
In  the  vessel  F  the  zinc  is  first  placed,  and  in  it  the  carbon  C  in  the  porous 
vessel  V  as  seen  in  P.  To  the  carbon  is  fixed  a  binding  screw,  m,  to  which 
a  copper  wire  is  attached,  forming  the  positive  pole.  The  zinc  is  provided 
with  a  similar  binding  screw,  72,  and  wire,  which  is  thus  a  negative  pole. 

A  single  cell  of  the  ordinary  dimensions,  20  cm.  in  height  and  9  in  dia- 
meter, gives  a  current  of  12  to  13  amperes  when  on  short  circuit,  that  is  when 
it  is  closed  without  measurable  resistance. 

The  elements  are  arranged  to  form  a  battery  (fig.  713)  by  connecting  each 
carbon  to  the  zinc  of  the  following  one  by  means  of  the  clamps  mn,  and  a 
strip  of  copper,  c,  represented  in  the  top  of  the  figure.  The  copper  is  pressed 
at  one  end  between  the  carbon  and  the  clamp,  and  at  the  other  it  is  soldered 
to  the  clamp  n,  which  is  fitted  on  the  zinc  of  the  following  element,  and  so  forth. 
The  clamp  of  the  first  carbon  and  that  of  the  last  zinc  are  alone  provided 
with  binding  screws,  to  which  are  attached  the  wires. 


752  Dynamical  Electricity.  [810- 

The  chemical  action  of  Bunsen's  battery  is  the  same  as  that  of  Grove's, 
and  being  equally  powerful,  while  less  costly,  is  very  generally  used  on  the 
Continent.  But  though  its  first  cost  is  less  than  that  of  Grove's  battery, 
it  is  more  expensive  to  work,  and  is  not  so  convenient  to  manipulate. 


Fig.  713. 

Callaris  battery  is  a  modified  form  of  Grove's.  Instead  of  zinc  and  plati- 
num, zinc  and  platinised  lead  are  used,  and  instead  of  pure  nitric  acid  Callan 
used  a  mixture  of  sulphuric  acid,  nitric  acid,  and  saturated  solution  of  nitre. 
The  battery  is  said  to  be  equal  in  its  action  to  Grove's,  and  is  much  cheaper. 

Callan  has  also  constructed  a  battery  in  which  zinc  in  dilute  sulphuric 
acid  forms  the  positive  plate,  and  cast  iron  in  strong  nitric  acid  the  negative. 
Under  these  circumstances  the  iron  becomes  passive  :  it  is  strongly  electro- 
negative, and  does  not  dissolve.  If,  however,  the  nitric  acid  becomes  too 
weak,  the  iron  is  dissolved  with  simultaneous  disengagement  of  nitrous  fumes. 

After  being  in  use  some  time,  all  the  batteries  in  which  the  polarisation  is 
prevented  by  nitric  acid  disengage  nitrous  fumes  in  large  quantities,  and  this 
is  a  serious  objection  to  their  use,  especially  in  closed  rooms.  To  prevent 
this,  nitric  acid  is  frequently  replaced  by  chromic  acid,  or,  better,  by  a  mixture 
of  4  parts  potassium  bichromate,  4  parts  sulphuric  acid,  and  18  water.  The 
liberated  hydrogen  reduces  the  chromic  acid  to  the  state  of  oxide  of  chromium, 
which  remains  dissolved  in  sulphuric  acid.  With  the  same  view,  sesqui- 
chloride  of  iron  is  sometimes  substituted  for  nitric  acid  ;  it  becomes  reduced 
to  protochloride.  But  the  action  of  the  elements  thus  modified  is  consider- 
ably less  than  when  nitric  acid  is  used,  owing  to  the  increased  resistance. 

811.  Smees  battery. — In  this  battery  the  polarisation  of  the  negative 
plate  is  prevented  by  mechanical  means.  Each  element  consists  of  a  sheet  of 
platinum  placed  between  two  vertical  plates  of  zinc,  as  in  Grove's  battery  ; 
but  as  there  is  only  a  single  liquid,  dilute  sulphuric  acid,  the  elements  have 
much  the  form  of  those  in  Wollaston's  battery.  The  adherence  of  hydrogen 
to  the  negative  plate  is  prevented  by  covering  the  platinum  with  a  deposit  of 
finely  divided  platinum.  In  this  manner  the  surface  is  roughened,  which 
facilitates  the  disengagement  of  hydrogen  to  a  remarkable  extent,  and  con- 


-812] 


Recent  Batteries. 


753 


sequently  diminishes  the  resistance  of  a  couple.  Instead  of  platinum,  silver 
covered  with  a  deposit  of  finely  divided  platinum  is  frequently  substituted,  as 
being  cheaper. 

Walkers  battery. — This  resembles  Smee's  battery,  but  the  electronegative 
plate  is  either  gas  graphite  or  platinised  graphite  \  it  is  excited  by  dilute 
sulphuric  acid.  This  battery  is  used  in  all  the  stations  of  the  South-Eastern 
Railway  ;  it  has  considerable  electromotive  force,  is  convenient  and  economi- 
cal in  manipulation,  and  large-sized  elements  can  be  constructed  at  a  cheap  rate. 

812.  Recent  batteries. — The  mercury  sulphate  battery  (fig,  714)  de- 
vised by  Marie  Davy,  is  essentially  a  zinc-carbon  element,  but  of  smaller 
dimensions  than  those  elements  usually  are.  In  the  outer  vessel,  V,  ordi- 
nary water  or  brine  is  placed,  and  in  the  porous  vessel  mercury  sulphate  This 
salt  is  agitated  with  about  three  times  its  volume  of  water,  in  which  it  is 
difficultly  soluble,  and  the  liquid  poured  off  from  the  pasty  mass.  The  carbon 
being  placed  in  the  porous  vessel,  the  spaces  are  filled  with  the  residue,  and 
then  the  decanted  liquid  poured  into  it. 

Chemical  action  takes  place  only  when  the  cell  is  closed.  The  zinc  then 
decomposes  the  water,  liberating  hydrogen,  which,  traversing  the  porous 
vessel,  reduces  the  mercury  sulphate,  forming  metallic  mercury,  which  collects 
at  the  bottom  of  the  vessel,  while  the  sulphuric  acid  formed  at  the  same  time 
traverses  the  diaphragm  to  act  on  the  zinc  and  thus  increases  the  action. 

The  mercury  which  is  deposited  may  be  used  to  prepare  a  quantity  of 
sulphate  equal  to  that  which  has  been  consumed.  A  small  quantity  of  the 
solution  of  mercury  sulphate  may  also  pass  through  the  diaphragm  ;  but  this 
is  rather  advantageous,  as  its  effect  is  to  amalgamate  the  zinc. 

The  electromotive  force  of  this  element  is  about  a  quarter  greater  than  that 
of  Daniell's  element,  but  it  has  greater  resistance  ;  it  is  rapidly  exhausted 
when  continuously  worked,  though  it  appears  well  suited  for  discontinuous 
work,  as  with  the  telegraph,  and  with  alarums. 


Fig.  71 


Fig.  715- 


Fig.  716. 

Gravity  batteries. — The  use  of  porous  vessels  is  open  to  many  objections, 
more  especially  in  the  case  of  Daniell's  battery,  in  which  they  gradually 
become  encrusted  with  copper,  which  destroys  them.  A  kind  of  battery  has 
been  devised  in  which  the  porous  vessel  is  entirely  dispensed  with,  and  the 
separation  of  the  liquids  is  effected  by  the  difference  of  density.  Such 
batteries  are  called  gravity  batteries.  Fig.  715  represents  a  form  devised 

3C 


754  Dynamical  Electricity.  [812- 

by  Callaud.  V  is  a  glass  or  earthenware  vessel  in  which  is  a  copper  plate 
soldered  to  a  wire  insulated  by  gutta-percha.  On  the  plate  is  a  layer  of 
crystals  of  copper  sulphate.  C  ;  the  whole  is  then  filled  with  water,  and  the 
zinc  cylinder  Z,  is  immersed  in  it.  The  lower  part  of  the  liquid  becomes 
saturated  with  copper  sulphate  ;  the  action  of  the  battery  is  that  of  a  Daniell, 
and  the  zinc  sulphate  which  gradually  forms,  floats  on  the  solution  of  copper 
sulphate  owing  to  its  lower  density.  This  battery  is  easily  manipulated,  the 
consumption  of  copper  sulphate  is  economical,  and  when  not  agitated  it 
works  constantly  for  some  time,  provided  care  be  taken  to  replace  the  water 
lost  by  evaporation. 

Meidingers  element,  which  is  much  used  in  Germany,  is  essentially  a 
gravity  battery  of  special  construction,  with  zinc  in  solution  of  magnesium 
sulphate,  and  copper  in  solution  of  copper  sulphate. 

Minotttfs  battery. — This  may  be  described  as  a  Daniell's  element,  in 
which  the  porous  vessel  is  replaced  by  a  layer  of  sawdust  or  of  sand.  At 
the  bottom  of  an  earthenware  vessel  (fig.  716)  is  placed  a  layer  of  coarsely- 
powdered  copper  sulphate  #,  and  on  this  a  copper  plate  provided  with  an 
insulated  copper  wire  i.  On  this  there  is  a  layer  of  sand  or  of  sawdust  be, 
and  then  the  whole  is  filled  with  water,  in  which  rests  a  zinc  cylinder  Z. 
The  action  is  just  that  of  a  Daniell ;  the  sawdust  prevents  the  mixture  of  the 
liquids,  but  it  also  offers  great  resistance,  which  increases  with  its  thickness. 
From  its  simplicity  and  economy,  and  the  facility  with  which  it  is  constructed, 
this  battery  merits  increased  attention. 

De  la  Rue  and  Mutter's  element  consists  of  a  glass  tube  about  6  inches 
long  by  075  inch  in  diameter,  closed  by  a  vulcanised  india-rubber  stopper 
through  which  passes  a  zinc  rod  criS  inch  in  diameter  and  5  inches  long. 
A  flattened  silver  wire  also  passes  through  the  stopper  to  the  bottom  of  the 
tube,  in  which  is  placed  about  half  an  ounce  of  silver  chloride,  the  greater 
part  of  the  cell  being  filled  with  solution  of  sal-ammoniac.  The  hydrogen 
evolved  at  the  negative  plate  reduces  the  chloride  to  metallic  silver,  which 
is  thereby  recovered.  Since  there  is  only  one  liquid,  and  the  solid  electro- 
lyte is  not  acted  upon  when  the  circuit  is  open,  the  element  is  easily  worked 
and  requires  little  attention.  It  is  very  compact,  1,000  elements  occupying 
a  space  of  less  than  a  cubic  yard  ;  De  la  Rue  and  Miiller  have  used  as  many 
as  14,400  such  cells  in  investigations  on  the  stratification  of  the  electric  light. 
A  battery  of  8,040  of  these  cells  gave  a  spark  |  of  an  inch  in  length  in  air 
under  the  ordinary  atmospheric  pressure  ;  while  under  a  pressure  of  a  quarter 
of  an  atmosphere  the  striking  distance  was  \\  inch. 

The  electromotive  force  of  a  silver  chloride  cell  is  1-03  of  a  volt,  and  that 
of  one  made  with  silver  bromide  is  0*908  ;  hence  a  series  of  4  cells,  three  of 
the  silver  chloride  cells  with  one  of  bromide,  give  an  average  electromotive 
force  of  i  volt  (814). 

Latimer  ClarKs  element  consists  of  pure  mercury  as  a  negative  plate 
covered  with  a  paste  obtained  by  boiling  sulphate  of  mercury  in  a  saturated 
solution  of  zinc  sulphate.  The  positive  metal  is  a  plate  of  zinc  resting  on 
this  paste  of  sulphate.  Insulated  wires,  leading  to  the  mercury  and  the  zinc 
respectively,  form  the  connections.  This  battery  is  not  well  adapted  for 
continuous  work,  but^'it  furnishes  a  standard  of  electromotive  force,  which  is 
constant  and  can  be?relied  upon.  Its  electromotive  force  is  1-46  volts. 


-813] 


Ledanchf  s  Element. 


755 


Fig.  7*7- 


A  convenient  form  of  element  for  many  purposes  is  the  potassium  bichro- 
mate, or,  as  it  is  frequently  termed,  the  bichromate  of  potass  element  (fig.  7 1 7). 
It  consists  of  a  zinc  plate,  Z,  attached  to  a  brass 
rod,  which  slides  up  and  down  in  a  brass  tube  in  an 
ebonite  or  porcelain  cover,  so  that  it  can  be  wholly 
or  partially  immersed  in  the  liquid.  Two  graphite 
plates,  C  C,  are  similarly  fitted  in  the  cover,  and  by 
means  of  strips  of  brass  the  carbon  and  the  zinc 
plates  are  respectively  in  connection  with  the  binding 
screws,  -which  thus  form  the  poles.  The  exciting 
liquid  is  a  mixture  of  i  part  of  potassium  bichromate, 
2  of  sulphuric  acid,  and  i  oof  water. 

The  electromotive  force  is  about  1*8  or  1*9  that 
of  a  Daniell  ;  when  the  element  is  closed  by  a  wire 
of  small  resistance  its  E.  M.  F.  increases  slightly  at 
first,  then  remains  constant  for  some  time,  after  which 
it  rapidly  sinks  to  half  its  original  amount. 

In  Niaudefs  element  a  zinc  cylinder  dips  in  a 
solution  of  common  salt  and  surrounds  a  porous  cell, 
in  which  is  a  carbon  plate  surrounded  by  pieces  of 

carbon  and  filled  with  chloride  of  lime,  which  does  not  act  on  the  zinc  even 
when  the  circuit  is  closed.     The  electromotive  force  is  r6  that  of  a  Daniell. 

813.  Leclancht-'s  element.  —  This 
consists  (fig.  718)  of  a  rod  of  carbon, 
C,  placed  in  a  porous  pot,  which  is  then 
very  tightly  packed  with  a  mixture  of 
pyrolusite  (peroxide  of  manganese)  and 
gas  graphite  M.  This  is  covered  over 
with  a  layer  of  pitch.  At  the  top  of  the 
carbon  is  soldered  a  mass  of  lead,  L,  to 
which  is  affixed  a  binding  screw.  The 
positive  plate  is  a  rod  of  zinc  Z,  in  which 
is  fixed  a  copper  wire.  The  exciting 
liquid  consists  of  a  strong  solution  of  sal- 
ammoniac,  contained  in  a  glass  vessel  G, 
which  is  not  more  than  one-third  full. 
The  electromotive  force  of  the  element 
is  said  to  be  about  one-third  greater 
than  that  of  a  Daniell's  element  ;  its  in- 
ternal resistance  varies  of  course  with  the 
size,  but  is  stated  to  be  from  two  to 
three  times  that  of  an  ohm.  The  battery 
is  not  adapted  for  continuous  work,  as  in 
heavy  telegraphic  circuits,  or  in  electro- 
plating, since  it  soon  becomes  polarised  ; 
it  has,  however,  the  valuable  property  of  quickly  regaining  its  original 
strength  when  left  at  rest,  and  is  extremely  well  adapted  for  discontinuous 
work,  such  as  that  of  electrical  bells. 

A  rod  of  carbon  4*  x  i|  x  /0-  inches  should  have  a  maximum  resistance  of 

3C2 


Fig.  718. 


756  Dynamical  Electricity.  [813- 

i  ohm  ;  but  good  plates  made  from  the  carbon  of  gas  retorts  do  not  average 
more  than  0-5,  and  in  some  cases  cri  ohm.  If  the  resistance  equals  an  ohm, 
the  conducting  power  of  carbon  is  about  0*003  that  of  mercury. 

A  drawback  to  the  use  of  carbon  is  that,  from  its  porosity,  the  exciting 
liquid  rises,  and  forms,  at  the  junction  with  the  binding  screw,  local  cur- 
rents which  injure  or  destroy  contact.  This  may  be  remedied  to  a  very 
great  extent  by  soaking  the  plates  before  use  in  hot  melted  paraffine,  which 
penetrates  into  the  pores,  expelling  the  air.  On  cooling  it  solidifies  and 
prevents  the  capillary  action  mentioned  above.  By  carefully  scraping  the 
paraffine  from  the  outside,  a  surface  is  exposed  which  is  as  good  a  conductor 
as  if  the  pores  were  filled  with  air.  Measurements  have  shown  that  the 
resistance  of  a  rod  thus  prepared  is  not  altered. 

In  a  recent  modification  of  his  element  Leclanche  dispensed  with  the 
porous  cell,  and  placed  the  carbon  plate  C  between  two  similar  flat  prisms 
made  by  compressing  a  mixture  of  55  parts  of  graphite,  40  parts  of  pyrolusite, 
and  5  parts  of  shellac  in  steel  moulds  at  a  temperature  of  100°  under  a  pressure 
of  300  atmospheres. 

814.  Electromotive  force  of  different  elements.  —  The  following  num- 
bers represent  the  electromotive  force  of  some  of  the  elements  most  frequently 
used,  compared  with  that  of  an  ordinary  DanielFs  cell  charged  as  above 
described  ;  they  are  the  means  of  many  careful  determinations  :  — 


Daniell's  element  set  up  with  water         .         .        i  >rfp/i       . 
„  „  „     pure  zinc  and  pure  water,  with  pure 

copper  and  pure  saturated  solution 
of  copper  sulphate       •  '.*  '-••'••V-i          1*02 

Leclanche's    „  „     zinc    in   saturated   solution   of   am- 

monium chloride     .        -j  '      *•'       ,     1*32 

Marie  Davy's  ......         ,*;r   v        ;     1*41 

Bunsen's         „  „     carbon  in  nitric  acid         .-*•  •    .         .     177 

„  „  „     carbon  in  chromic  acid     .'   ;  •-  <>     v    r8/ 

Grove's          „  „     platinum  in  nitric  acid      t*W  ***<     i     1*82 

The  greatest  electromotive  force  as  yet  observed  is  by  Beetz  in  a  couple 
consisting  of  potassium  amalgam  in  caustic  potash,  combined  with  pyrolusite 
in  a  solution  of  potassium  permanganate.  It  is  three  times  as  much  as  that 
of  a  Daniell's  element. 

The  standard  of  electromotive  force  on  the  C.  G.  S.  system  is  the  Volt. 
This  is  equal  to  1,000,000,000  or  io9  absolute  electromagnetic  units  (709). 
The  volt  is  rather  less  than  the  electromotive  force  of  a  Daniell's  cell,  the 
mean  value  of  which  may  be  taken  at  1*12  volt.  The  unit  of  current,  which 
is  called  an  Ampere,  is  the  current  due  to  an  electromotive  force  of  one  volt 
wopkmg  through  a  resistance  of  one  ohm. 

X  815.  Comparison  of  the  voltaic  "battery  with  a  frictional  electrical 
machine.  —  Except  in  the  case  of  batteries  consisting  of  a  very  large  number 
of  couples,  the  difference  of  potentials  between  the  terminals  is  far  weaker 
than  in  frictional  electrical  machines,  and  is  insufficient  to  give  any  visible 
spark.  With  De  la  Rue  and  Miiller's  great  battery  the  striking  distance 
between  two  terminals  was  found  to  increase  with  the  potential,  but  for  high 


—816]  Amalgamated  Zinc.     Local  Currents.  757 

potentials  rather  more  rapidly  than  in  direct  ratio.  Thus  while  the  striking 
distance  was  0-012  in.  with  the  potential  due  to  1,200  of  their  cells,  it  was 
0-049  in-  with  4,800  cells,  and  0^133  in.  with  11,000  cells. 

In  the  case  of  a  small  battery  or  of  a  single  cell,  very  delicate  tests  are 
required  to  detect  any  signs  of  free  electrification.  But  by  means  of  a  deli- 
cate condensing  electroscope,  and  by  extremely  careful  insulation,  it  can  be 
shown  that  one  pole  possesses  a  positive  and  the  other  a  negative  charge. 
For  this  purpose  one  of  the  plates  of  the  electroscope  is  connected  with 
one  pole,  and  the  other  with  the  other  pole  or  with  the  ground.  The  electro- 
scope thus  becomes  charged,  and  on  breaking  the  connection  electroscopic 
indications  are  observed. 

On  the  other  hand  the  strength  of  current  which  a  voltaic  element  can 
produce  in  a  good  conductor  is  much  greater  than  that  which  can  be  pro- 
duced by  a  machine.  Faraday  immersed  two  wires — one  of  zinc,  and  the 
other  of  platinum,  each  T\  of  an  inch  in  diameter— in  acidulated  water  for  ~ 
of  a  second.  The  effect  thus  produced  on  a  magnetic  needle  in  this  short 
time  was  greater  than  that  produced  by  23  turns  of  the  large  electrical 
machine  of  the  Royal  Institution. 

Nystrom  has  ascertained  by  quantitative  measurements  that  the  potential 
of  the  charge  of  the  cover  of  an  ordinary  electrophorus  is  not  less  than  50,000 
times  as  great  as  the  potential  of  a  Meidinger's  cell  (812) ;  that  is,  that  not 
less  than  50,000  of  those  elements  would  be  required  to  produce  the  same 
potential  as  the  electrophorus.  In  practice,  a  far  greater  number  would  be 
needed,  owing  to  the  difficulty  of  getting  good  insulation. 

8 1 6.  Amalgamated  zinc.  Local  currents. — Perfectly  pure  distilled 
zinc  is  not  attacked  by  dilute  sulphuric  acid,  but  becomes  so  when  immersed 
in  that  liquid  in  contact  with  a  plate  of  copper  or  of  platinum.  Ordinary 
commercial  zinc,  on  the  contrary,  is  rapidly  dissolved  by  dilute  acid.  This, 
doubtless,  arises  from  the  impurity  of  the  zinc,  which  always  contains  traces 
either  of  iron  or  lead.  Being  electronegative  towards  zinc,  they  tend  to  pro- 
duce local  electrical  currents,  which  accelerate  the  chemical  action  without 
increasing  the  quantity  of  electricity  in  the  connecting  wire. 

Zinc,  when  amalgamated,  acquires  the  properties  of  perfectly  pure  zinc, 
and  is  unaltered  by  dilute  acid,  so  long  as  it  is  not  in  contact  with  a  copper 
or  platinum  plate  immersed  in  the  same  liquid.  To  amalgamate  a  zinc  plate, 
it  is  first  immersed  in  dilute  sulphuric  or  hydrochloric  acid  so  as  to  obtain  a 
clean  surface,  and  then  a  drop  of  mercury  is  placed  on  the  plate  and  spread 
over  it  with  a  brush.  The  amalgamation  takes  place  immediately,  and  the 
plate  has  the  brilliant  aspect  of  mercury.  Zinc  as  well  as  other  metals  are 
readily  amalgamated  by  dipping  them  in  an  amalgam  of  one  part  sodium 
and  200  parts  of  mercury.  Zinc  plates  may  also  be  amalgamated  by  dipping 
them  in  a  solution  of  mercury  prepared  by  dissolving  one  pound  of  mercury 
in  five  pounds  of  aqua  regia  (one  part  of  nitric  to  three  of  hydrochloric  acid), 
and  then  adding  five  parts  more  of  hydrochloric  acid. 

The  amalgamation  of  the  zinc  removes  from  its  surface  all  the  impurities, 
especially  the  iron.  The  mercury  effects  a  solution  of  pure  zinc,  which  covers 
the  surface  of  the  plate,  as  with  a  liquid  layer.  The  process  was  first  applied 
to  electrical  batteries  by  Kemp.  Amalgamated  zinc  is  not  attacked  so  long 
.as  the  circuit  is  not  closed — that  is,  when  there  is  no  current ;  when  closed 


758  Dynamical  Electricity.  [816- 

the  current  is  more  regular,  and  at  the  same  time  stronger,  for  the  same 
quantity  of  metal  dissolved. 

817.  Dry  piles. — In  dry  piles the  liquid  is  replaced  by  a  solid  hygrometric 
substance,  such  as  paper  or  leather.  They  are  of  various  kinds  ;  in  Zamboni's, 
which  is  most  extensively  used,  the  electromotors  are  tin  or  silver,  and  bin- 
oxide  of  manganese.     To  construct  one  of  these  a  piece  of  paper  silvered  or 
tinned  on  one  side  is  taken  ;  the  other  side  of  the  paper  is  coated  with  finely- 
powdered  binoxide  of  manganese  by  slightly  moistening  it,  and  rubbing  the 
powder  on  with  a  cork.     Having  placed  together  seven  or  eight  of  these 
sheets,  they  are  cut  by  means  of  a  punch  into  discs  an  inch  in  diameter. 
These  discs  are  then  arranged  in  the  same  order,  so  that  the  tin  or  silver  of 
each  disc  is  in  contact  with  the  manganese  of  the  next.    Having  piled  up  1,200 
or  i, 800  couples,  they  are  placed  in  a  glass  tube,  which  is  provided  with  a 
brass  cap  at  each  end.     In  each  cap  there  is  a  rod  and  knob,  by  which  the 
leaves  can  be  pressed  together,  so  as  to  produce  better  contact.     The  knob 
in  contact  with  the  manganese  corresponds  to  the  positive  pole,  while  that 
at  the  other  end,  which  is  in  contact  with  the  silver  or  tin,  is  the  negative 
pole. 

Dry  piles  are  remarkable  for  the  permanence  of  their  action,  which  may 
continue  for  several  years.  Their  action  depends  greatly  on  the  temperature 
and  on  the  hygrometric  state  of  the  air.  It  is  stronger  in  summer  than  in 
winter,  and  the  action  of  a  strong  heat  revives  it  when  it  appears  extinct.  A 
Zamboni's  pile  of  2,000  couples  gives  neither  shock  nor  spark,  but  can  charge 
a  Leyden  jar  and  other  condensers.  A  certain  time  is,  however,  necessary, 
for  electricity  only  moves  slowly  in  the  interior. 

8 1 8.  Bohnenberger's  electroscope.— Bohnenberger  constructed  a  dry- 
pile  electroscope  of  great  delicacy.    It  is  a  condensing  electroscope  (fig.  679), 
from  the  rod  of  which  is  suspended  a  single  gold  leaf.     This  is  at  an  equal 
distance  from  the  opposite  poles  of  two  dry  piles  placed  vertically,  inside  the 
bell  jar,  on  the  plate  of  the  apparatus.     As  soon  as  the  gold  leaf  possesses 
any  free  electricity  it  is  attracted  by  one  of  the  poles  and  repelled  by  the 
other,  and  its  electricity  is  obviously  contrary  to  that  of  the  pole  towards 
which  it  moves. 


-820] 


Oersted's  Experiment. 


759 


CHAPTER   II. 

DETECTION   AND   MEASUREMENT   OF  VOLTAIC   CURRENTS. 

i  819.  Detection  and  measurement  of  voltaic  currents. — The  remark- 
able phenomena  of  the  voltaic  battery  may  be  classed  under  the  heads  phy- 
siological, chemical,  mechanical,  and  physical  effects  ;  and  these  latter  may 
be  again  subdivided  into  the  thermal,  luminous,  and  magnetic  effects.  For 
ascertaining  the  existence  and  measuring  the  strength  of  voltaic  currents, 
the  magnetic  effects  are  more  suitable  than  any  of  the  others,  and,  accord- 
ingly, the  fundamental  magnetic  phenomena  will  be  described  here,  and  the 
description  of  the  rest  postponed  to  a  special  chapter  on  electro-magnetism. 
-  \^S20.  Oersted's  experiment. — Oersted  published  in  1819  a  discovery 
which  connected  magnetism  and  electricity  in  a  most  intimate  manner,  and 
became,  in  the  hands  of  Ampere  and  of  Faraday,  the  source  of  a  new  branch 
of  physics.  The  fact  discovered  by  Oersted  is  the  directive  action  which  a 
fixed  current  exerts  at  a  distance  on  a  magnetic  needle. 

To  make  this  experiment  a  copper  wire  is  suspended  horizontally  in  the 
direction  of  the  magnetic  meridian  over 
a  movable  magnetic  needle,  as  repre- 
sented in  fig.  719.  So  long  as  the  wire 
is  not  traversed  by  a  current,  the  needle 
remains  parallel  to  it ;  but  as  soon  as 
the  ends  of  the  wire  are  respectively 
connected  with  the  poles  of  a  battery 
or  of  a  single  element,  the  needle  is  de- 
flected, and  tends  to  take  a  position 
•which  is  the  more  nearly  at  right  angles 
to  the  magnetic  meridian  in  proportion 
as  the  current  is  stronger.  * ig>  ?I9> 

In  reference  to  the  direction  in  which  the  poles  are  deflected,  there  are 
several  cases  which  may,  however,  be  referred  to  a  single  principle.  Re- 
membering our  assumption  as  to  the  direction  of  the  current  in  the  con- 
necting wire  (803)  the  preceding  experiment  presents  the  following  four 
cases : — 

i.  If  the  current  passes  above  the  needle,  and  goes  from  south  to  north, 
the  north  pole  of  the  magnet  is  deflected  towards  the  west ;  this  arrangement 
is  represented  in  the  above  figure. 

ii.  If  the  current  passes  below  the  needle,  also  from  south  to  north,  the 
north  pole  is  deflected  towards  the  east. 

iii.  When  the  current  passes  above  the  needle,  but  from  north  to  south, 
the  north  pole  is  deflected  towards  the  east. 


- 


76o 


Dynamical  Electricity. 


[820- 


iv.  Lastly,  the  deflection  is  towards  the  west  when  the  current  goes  from 
north  to  south  below  the  needle. 

Ampere  has  given  the  following  memoria  technica  by  which  all  the  various 
directions  of  the  needle  under  the  influence  of  a  current  may  be  remembered. 
If  we  imagine  an  observer  placed  in  the  connecting  wire  in  such  a  manner 
that  the  current  entering  by  his  feet  issues  by  his  head,  and  that  his  face  is 
always  turned  towards  the  needle,  we  shall  see  that  in  the  above  four  posi- 
tions the  north  pole  is  always  deflected  towards  the  left  of  the  observer.  By 
thus  personifying  the  current,  the  different  cases  may  be  comprised  in  this 
general  principle  :  In  the  directive  action  of  currents  on  magnets •,  the  north 
polei^always  deflected  towards  the  left  of  the  current. 

Y^2L  Galvanometer  or  multiplier. — The  name  galvanometer,  or  some- 
times multiplier  or  rheometer,  is  given  to  a  very  delicate  apparatus  by  which 
the  existence,  direction,  and  intensity  of  currents  may  be  determined.  It 
was  invented  by  Schweigger  a  short  time  after  Oersted's  discovery. 

In  order  to  understand  its  principle,  let  us  suppose  a  magnetic  needle 
suspended  by  a  filament  of  silk  (fig.  720),  and  surrounded  in  the  plane  of  the 


Fig.  720. 

magnetic  meridian  by  a  copper  wire,  mnopq,  forming  a  complete  circuit 
round  the  needle  in  the  direction  of  its  length.  When  this  wire  is  traversed 
by  a  current,  it  follows,  from  what  has  been  said  in  the  previous  paragraph, 
that  in  every  part  of  the  circuit  an  observer  lying  in  the  wire  in  the  direction 
of  the  arrows,  and  looking  at  the  needle  ah,  would  have  his  left  always  turned 
towards  the  same  point  of  the  horizon,  and  consequently,  that  the  action  of 
the  current  in  every  part  would  tend  to  turn  the  north  pole  in  the  same 
direction  ;  that  is  to  say,  that  the  actions  of  the  four  branches  of  the  circuit 
concur  to  give  the  north  pole  the  same  direction.  By  coiling  the  copper 
wire  in  the  direction  of  the  needle,  as  represented  in  the  figure,  the  action 
of  the  current  has  been  multiplied.  If,  instead  of  a  single  one,  there  are 
several  circuits,  provided  they  are  insulated,  the  action  becomes  still  more 
multiplied,  and  the  deflection  of  the  needle  increases.  Nevertheless,  the 
action  of  the  current  cannot  be  multiplied  indefinitely  by  increasing  the 
number  of  windings,  for,  as  we  shall  presently  see,  the  strength  of  a  current 
diminishes  as  the  length  of  the  circuit  is  increased. 

As  the  directive  action  of  the  earth  continually  tends  to  keep  the  needle 
in  the  magnetic  meridian,  and  thus  opposes  the  action  of  the  current,  the 
effect  of  the  latter  is  increased  by  using  an  astatic  system  of  two  needles, 


-821] 


Galvanometer  or  Multiplier. 


76 1 


.as  shown  in  fig.  721.  The  action  of  the  earth  on  the  needle  is  then  very 
feeble,  and,  further,  the  actions  of  the  current  on  the  two  needles  become 
accumulated.  In  fact,  the  action  of  the  circuit,  from  the  direction  of  the 
current  indicated  by  the  arrows,  tends  to  deflect  the  north  pole  of  the  lower 
needle  towards  the  west.  The  upper  needle  a'b',  is  subjected  to  the  action 
of  two  contrary  currents,  no  and  qp^  but  as  the  first  is  nearer,  its  action  pre- 
ponderates. Now  this  current  passing  below  the  needle,  evidently  tends  to 
turn  the  pole  a'  towards  the  east,  and,  consequently,  the  pole  b'  towards  the 
west ;  that  is  to  say,  in  the  same  direction  as  the  pole  a  of  the  other  needle. 

From  these  principles  it  will  be  easy  to  understand  the  action  of  the 
multiplier.  The  apparatus  represented  in  fig.  722  consists  of  a  thick  brass 
plate,  D,  resting  on  levelling 
screws  ;  on  this  is  a  rotating 
plate,  P,  of  the  same  metal, 
to  which  is  fixed  a  copper 
frame,  the  breadth  of  which 
is  almost  equal  to  the  length 
of  the  needles.  On  this  is 
coiled  a  great  number  of 
turns  of  wire  covered  with 
silk.  The  two  ends  terminate 
in  binding  screws,  i  and  o. 
Above  the  frame  is  a  gradu- 
ated circle,  C,  with  a  central 
slit  parallel  to  the  direction 
in  which  the  wire  is  coiled. 
The  zero  corresponds  to  the 
position  of  this  slit,  and  there 
are  two  graduations  on  the 
scale,  the  one  on  the  right 
and  the  other  on  the  left  of 
zero,  but  they  only  extend  to 
90°.  By  means  of  a  very  fine 
filament  of  silk,  an  astatic 
system  is  suspended ;  it  con- 
sists of  two  needles  ab  and 
a'b',  one  above  the  scale, 
and  the  other  within  the  cir- 
cuit itself.  These  needles, 
which  are  joined  together  by  a  copper  wire,  like  those  in  fig.  608  and  fig. 
721,  and  cannot  move  separately,  must  not  have  exactly  the  same  magnetic 
intensity  ;  for  if  they  are  exactly  equal,  every  current,  strong  or  weak,  would 
always  put  them  at  right  angles  with  itself. 

In  using  this  instrument  the  diameter,  to  which  corresponds  the  zero  of 
the  graduation,  is  brought  into  the  magnetic  meridian  by  turning  the  plate 
P  until  the  end  of  the  needle  ab  corresponds  to  zero.  The  instrument  is 
fixed  in  this  position  by  means  of  the  screw-clamp  T. 

The  length  and  diameter  of  the  wire  vary  with  the  purpose  for  which  the 
galvanometer  is  intended.  For  one  which  is  to  be  used  in  observing  the 


7  62  Dynamical  Electricity.  [821- 

currents  due  to  chemical  actions,  a  wire  about  %  millimetre  in  diameter,  and 
making  about  800  turns,  is  well  adapted.  Those  for  thermo-electric  currents, 
which  have  low  intensity,  require  a  thicker  and  shorter  wire  ;  for  example, 
thirty  turns  of  a  wire  §  millimetre  in  diameter.  For  very  delicate  experi- 
ments, as  in  physiological  investigations,  galvanometers  with  as  many  as 
30,000  turns  have  been  used. 

By  means  of  a  delicate  galvanometer  consisting  of  2,000  or  3,000  turns 
of  fine  wire,  the  coils  of  which  are  carefully  insulated  by  means  of  silk  and 
shellac,  currents  of  high  potential,  as  those  of  the  electrical  machine  (791) 
may  be  shown.  One  end  of  the  galvanometer  is  connected  with  the  con- 
ductor, and  the  other  with  the  ground,  and  on  working  the  machine  the 
needle  is  deflected,  affording  thus  an  illustration  of  the  identity  of  statical 
with  dynamical  electricity. 

The  deflection  of  the  needle  increases  with  the  strength  of  the  current ; 
the  relation  between  the  two  is,  however,  so  complex,  that  it  cannot  well 
be  deduced  from  theoretical  considerations,  but  requires  to  be  determined 
experimentally  for  each  instrument.  And  in  the  majority  of  cases  the  in- 
strument is  used  as  a  galvanoscope  or  rheoscope — that  is,  to  ascertain  rather 
the  presence  and  direction  of  currents — than  as  a  galvanotneter  or  rheometcr 
in  the  strict  sense  ;  that  is,  as  a  measurer  of  their  intensity.  The  term 
galvanometer  is,  however,  commonly  used. 

The  differential  galvanometer  consists  of  a  needle,  as  in  an  ordinary 
galvanometer,  but  round  the  frame  of  which  are  coiled  two  wires  of  the  same 
kind  and  dimensions,  carefully  insulated  from  each  other,  and  provided  with 
suitable  binding  screws,  so  that  separate  currents  can  be  passed  through 
each  of  them.  If  the  currents  are  of  the  same  strength  but  in  different  direc- 
tions, no  deflection  is  produced  ;  where  the  needle  is  deflected  one  of  the 
currents  differs  from  the  other.  Hence  the  apparatus  is  used  to  ascertain  a 
difference  in  strength  of  two  currents,  and  to  this  it  owes  its  name. 

When  a  current  is  passed  through  a  galvanometer,  the  needle  does  not 
usually  at  once  attain  its  final  position  of  equilibrium,  but  oscillates  about  this 
position,  which  in  observations  causes  much  loss  of  time.  These  oscillations 
are  damped  partly  by  surrounding  the  needle  by  thick  masses  of  copper,  the 
effect  of  which  will  be  afterwards  explained  (905),  and  partly  by  increasing  the 
magnetisation  of  the  needle.  Galvanometers  in  which  the  needle  acquires  at 
once  this  final  deflection  are  known  as  aperiodic,  or  dead-beat  galvanometers. 

When  a  current  of  very  small  duration  is  passed  through  a  galvanometer, 
a  momentary  deflection  or  swing  of  the  needle  will  be  produced.  The 
product  of  a  constant  into  the  sine  of  half  the  angle  of  the  first  swing  is  then 
a  measure  of  the  strength  of  the  current,  so  that  if  momentary  currents  of 
different  strengths  are  passed  through  one  and  the  same  galvanometer  they 
will  be  measured  by  the  sines  of  the  corresponding  angles  of  deflection  or 
swings,  or  by  the  angles  themselves  where  these  are  small.  This  is  known 
as  the  ballistic  method of  measuring  currents,  and  the  galvanometers  adapted 
for  the  purpose  are  known  as  ballistic  galvanometers. 

822.  Sir  IV.  Thomson's  marine  galvanometer. — In  laying  submarine 
cables  the  want  was  felt  of  a  galvanometer  sufficiently  sensitive  to  test  insula- 
tion, which  at  the  same  time  was  not  affected  by  the  pitching  and  rolling  of  the 
ship.  For  this  purpose,  Sir  W.  Thomson  invented  his  marine  galvanometer. 


-822] 


Sir  IT.  Thomsons  Marine  Galvanometer. 


76: 


B  (fig.  723)  represents  a  coil  of  many  thousand  turns  of  the  finest  copper  wire, 
carefully  insulated  throughout,  terminating  in  the  binding  screws,  EE.  In 
the  centre  of  this  coil  is  a  slide,  which  carries  the  magnet,  the  arrangement  of 
which  is  represented  on  a  larger  scale  in  D.  The  magnet  itself  is  made  of  a 
piece  of  fine  watch-spring  about  f  of  an  inch  in  length,  and  does  not  weigh 
more  than  a  grain ;  it  is  attached  to  a  small  and  very  slightly  concave  mirror 
of  very  thin  silvered  glass.  A  single  fibre  of  silk  is  stretched  across  the  slide, 
and  the  mirror  and  magnet  are  attached  to  it  in  such  a  manner  that  the 
fibre  passes  exactly  through  the  centre  of  gravity  in  every  position.  As  the 
mirror  and  magnet  weigh  only  a  few  grains,  they  retain  their  position  rela- 
tively to  the  instrument,  however  the  ship  may  pitch  and  roll.  The  slide  fits  in 
a  groove  in  the  coil,  and  the  whole  is  enclosed  within  a  wrought-iron  case 
with  an  aperture  in  front  and  a  wrought-iron  lid  on  the  top.  The  object  of 


Fig.  723. 

this  is  to  counteract  the  influence  of  terrestrial  magnetism  when  the  ship 
changes  its  course. 

Underneath  the  coil  is  a  large  curved  steel  magnet  N,  which  compensates 
the  earth's  directive  action  upon  the  magnet  D  (700) ;  and  in  the  side  of  the 
case,  and  on  a  level  with  D,  a  pair  of  magnets,  C,  are  placed  with  opposite 
poles  together.  By  a  screw,  suitably  adjusted,  the  poles  of  the  magnets  may 
be  brought  together ;  in  which  case  they  quite  neutralise  each  other,  and  thus 
exert  no  action  on  the  suspended  magnet,  or  they  may  be  slid  apart  from 
each  other  in  such  a  manner  that  the  action  of  either  pole  on  D  prepon- 
derates to  any  desired  extent.  This  small  magnet  is  thus  capable  of  very 
delicate  adjustment.  The  large  magnet  N,  and  the  pair  of  magnets,  C,  are 
analogous  to  the  coarse  and  fine  adjustment  of  a  microscope. 

At  a  distance  of  about  three  feet,  there  is  a  scale  with  the  zero  in  the 
centre  and  the  graduation  extending  on  each  side.  Underneath  this  zero 
point  is  a  narrow  slit,  through  which  passes  the  light  of  a  paraffine  lamp,  and 
which,  traversing  the  window,  is  reflected  from  the  curved  mirror  against  the 
graduated  scale.  By  means  of  the  adjusting  magnets  the  image  of  the  slit 
is  made  to  fall  on  the  centre  of  the  graduation. 


764 


Dynamical  Electricity. 


[822- 


This  being  the  case,  if  any  arrangement  for  producing  a  current,  however 
weak,  be  connected  with  the  terminal,  the  spot  of  light  is  deflected  either  to 
one  side  or  the  other,  according  to  the  direction  of  the  current ;  the  stronger 
the  current  the  greater  the  deflection  of  the  spot ;  and  if  the  current  remains 
of  constant  strength  for  any  length  of  time,  the  spot  is  stationary  in  a  cor- 
responding position. 

The  movement,  on  a  screen,  of  a  spot  of  light  reflected  from  a  body,  is  the 
most  delicate  and  convenient  means  of  observing  motions  which  of  them- 
selves are  too  small  for  direct  measurement  or  observation.  Hence  this 
principle  is  frequently  applied  in  experimental  investigations  and  in  lecture 
illustrations  (522).  It  is  used  in  observing  the  motion  of  oscillating  bodies, 
in  measuring  the  variations  of  magnetism,  in  determining  the  expansion  of 
solids,  &c. 

It  will  be  seen  from  the  article  on  the  Electric  Telegraph,  how  alter- 
nate deflections  of  the  spot  of  light  may  be  utilised  in  forming  a  code  of 
signal^ 

Y523.  Tangent  compass,  or  tangent  galvanometer. — When  a  magnetic 
needle  is  suspended  in  the  centre  of  a  voltaic  current  in  the  plane  of  the 
magnetic  meridian,  it  can  be  proved  that  the  strength  of  a  current  is  directly 

proportional  to  the  tangent  of  the 
angle  of  deflection,  provided  the 
dimensions  of  the  needle  are  suffi- 
ciently small  as  compared  with  the 
diameter  of  the  circuit.  An  instru- 
ment based  on  this  principle  is 
called  the  tangent  galvanometer  or 
tangent  compass.  It  consists  of  a 
copper  ring,  12  inches  in  diameter 
(fig.  724),  and  about  an  inch  in 
breadth,  mounted  vertically  on  a 
stand  ;  the  lower  half  of  the  ring  is 
generally  fitted  in  a  semicircular 
frame  of  wood  to  keep  it  steady.  In 
the  centre  of  the  ring  is  suspended 
a  delicate  magnetic  needle,  whose 
length  must  not  exceed  ~  or  ^  of 
the  diameter  of  the  circle.  Under- 
Flg>  ?24>  neath  the  needle  there  is  a  graduated 

•circle.  The  ends  of  the  ring  are  prolonged  in  copper  wires,  fitted  with 
mercury  cups,  ab,  by  which  it  can  be  connected  with  a  battery  or  element. 
The  circle  is  placed  in  the  plane  of  the  magnetic  meridian,  and  the  deflection 
of  the  needle  is  directly  read  off  on  the  circle,  and  its  corresponding  value 
obtained  from  a  table  of  tangents. 

On  account  of  its  small  resistance,  the  tangent  galvanometer  is  well 
adapted  for  currents  of  low  potential,  but  in  which  a  considerable  quantity 
of  electricity  is  set  in  motion. 

To  prove  that  the  intensities  of  various  currents  are  proportional  to  the 
tangents  of  the  corresponding  angles  of  deflection,  let  NS,  fig.  725,  represent 
the  wire  of  the  galvanometer  and  ns  the  needle,  and  let  0  be  the  angle  of 


-824]  Tangent  Galvanometer'.  765. 

deflection  produced  when  a  current  C  is  passed.  Two  forces  now  act  upon 
the  needle — the  force  of  the  earth's  magnetism,  which  we  will  .denote  by  Hr 
which  tends  to  place  the  needle  in  the  magnetic  meridian,  and  the  strength 
of  the  current  C,  which  strives  to  place  it  at  right  angles  to  the  magnetic 
meridian.  Let  the  magnitudes  of  these  forces  be  represented  by  the  corre- 
sponding lines  an  and  bn.  Now  the  whole  intensities  of  these  forces  do  not 
act  so  as  to  turn  the  point  of  the  needle  round,  but  only  those  components 
which  are  at  right  angles  to  the  needle.  Resolving  them,  we  have  ng  and  nf 
as  the  forces  acting  in  opposite  directions  on  the  needle  ;  and  since  the 
needle  is  at  rest  these  forces  must  be  equal. 

The  angle  nag  is  equal  to  the  angle  </>,  and  therefore  ng=  an  sin  <£  ;  and 
in  like  manner  the  angle  bnf'is  equal  to  <£  and  nf=bn  cos  <p  ;  and  therefore 

since  nf=ng,  bn  cos  <b  =  an  sin  cf>,  or  bn  =  an  S  ^-Qmatt  tan  <f> ;  that  is, 

cos  <p 

C  =  H  tan  <£. 

If  any  other  current  be  passed  through  the  galvanometer  we  shall  have 
similarly  C'  =-  H  tan  </>' ;  and  since  the  earth's  magnetism  does  not  appreciably 
alter  in  one  and  the  same  place  C  :  C/  =  tan  <f>  :  tan  $'. 

In  this  reasoning  it  has  been  assumed  that  the  action  of  the  current  on 
the  needle  is  the  same  whatever  be  the  angle  by  which  it  is  deflected.  This 
is  only  the  case  when  the  dimensions  of  the  needle  are 
small  compared  with  the  diameter  of  the  ring  :  it  should 
not  be  more  than  £  or  T\  the  diameter.  In  order  to  measure 
with  accuracy  the  deflection  a  light  index  is  placed  at 
right  angles  to  the  needle. 

Wiedemanris  tangent  galvanometer  consists  of  a  short 
thick  copper  tube,  in  which  is  suspended,  instead  of  a 
needle,  a  thin  piece  of  soft  iron,  silvered  on  one  side  so  as 
to  act  as  a  mirror,  the  position  of  which  can  be  observed 
by  a  microscope  and  scale  (522).  On  each  side  of  the 
copper  tube,  and  sliding  in  grooves,  are  coils  of  wire  which 
can  be  pushed  over  the  tube.  By  this  lateral  arrangement 
of  the  current  in  reference  to  the  magnetic  needle,  the 
error  of  the  tangent  galvanometer  is  diminished;  for  s 

when  the  needle  is  deflected,  though  one  end  moves  away  Fig.  725. 

from  the  current,  the  other  approaches  it. 

In  the  tangent  galvanometer  of  Helmholtz  and  of  Gaugain  the  wires  are 
coiled  on  the  surface  of  a  cone  the  angle  of  which  is  120°,  and  the  point  on 
which  the  needle  works  is  placed  in  the  position  of  the  corresponding  apex 
of  the  cone  :  the  law  of  the  tangent  holds  then  even  with  longer  needles,  and 
especially  if  the  wire  is  divided  between  two  such  cones,  one  on  opposite 
sides  of  the  needle. 

If  the  ring  of  the  tangent  galvanometer  is  so  constructed  that  it  can  turn 
about  its  axis,  which  is  in  the  magnetic  meridian,  the  action  of  the  current 
on  the  needle  is  inversely  proportional  to  the  cosine  of  the  angle  6,  through 
which  the  ring  is  turned.  Hence  by  increasing  0,  the  action  of  any  current 
onjJi&  needle  may  be  made  as  small  as  we  please. 

I    824.  Sine  galvanometer. — This  is    another  form    of  galvanometer  for 
measuring  powerful  currents.     Round  the  circular  frame  M  (fig.  726),  several 


766 


Dynamical  Electricity. 


[824- 


\\ 


turns  of  stout  insulated  copper  wire  are  coiled,  the  two  ends  of  which,  z, 
terminate  on^the  binding  screws  at  E.     On  a  table  in  the  centre  of  the  ring 

there  is  a  magnetic  needle,  m  ; 
a  second  light  needle,  ;z,  fixed  to 
the  first,  serves  as  pointer  along 
the  graduated  circle  N.  Two 
copper  wires,  a,  b,  from  the 
sources  of  electricity  to  be  mea- 
sured, are  connected  with  E. 
The  circles  M  and  N  are 
supported  on  a  foot  O,  which 
can  move  about  a  vertical  axis 
passing  through  the  centre  of  a 
fixed  horizontal  circle  H. 

The  circle  M  being  then 
placed  in  the  magnetic  meridian, 
and  therefore  in  the  same  plane 
as  the  needle,  the  current  is 
allowed  to  pass.  The  needle 
being  deflected,  the  circuit  M  is 
turned  until  it  coincides  with  the 
vertical  plane  passing  through 
the  magnetic  needle  ;//.  The 
directive  action  of  the  current  is 
now  exerted  perpendicularly  to 
the  direction  of  the  magnetic 
needle,  and  it  may  be  shown 
that  the  strength  ot  the  current  is  proportional  to  the  sine  of  the  angle  of 
deflection  :  this  angle  is  measured  on  the  circle  H  by  means  of  a  vernier  on 
the  piece  C.  This  piece  C,  fixed  to  the  foot  O,  turns  it  by  means  of  a  knob 
A.  This  angle  of  deflection,  and  hence  its  sine,  being  known,  the  intensity 
of  the  current  may  be  thus  deduced  :  let  mm'  be 
the  direction  of  the  magnetic  meridian,  d  the  angle 
of  deflection,  C  the  strength  of  the  current,  and  H 
the  directive  action  of  the  earth.  If  the  direction 
and  intensity  of  this  latter  force  be  represented  by 
ak,  it  may  be  replaced  by  two  components,  ah  and 
ac  (fig.  727).  Now,  as  the  first  has  no  directive 
action  on  the  needle,  the  component  ac  must  alone 
counterpoise  the  force  C  ;  that  is,  C  =  ac.  But  in 
the  triangle  ack,  ac  =  ak  cos  cak,  from  which  ac-H 
sin  d,  for  the  angle  cak  is  the  complement  of  the 
angle  */,  and  ak  is  equal  to  H  ;  hence,  lastly,  C  =  H 
sin  d,  which  was  to  be  proved.  In  like  manner  for 
any  other  current  C',  which  produces  a  deflection 
H  sin  d",  whence  C  :  C'  =  sin  d :  sin  d'. 


Fig.  727. 

we  shall  have 


5     ' 

•  825.  Ohm's  law. — For  a  knowledge  of  the  conditions  which  regulate 
the  action  of  the  voltaic  current,  science  is  indebted  to  the  late  G.  S.  Ohm. 
His  results  were  at  first  deduced  from  theoretical  considerations  ;  but  by 


-825]  Ohms  Law.  767 

his  own  researches  as  well  as  by  those  of  Fechner,  Pouillet,  Daniell,  De  la 
Rive,  Wheatstone,  and  others,  they  have  received  the  fullest  confirmation, 
and  their  great  theoretical  and  practical  importance  has  been  fully  estab- 
lished. 

i.  The  force  or  cause  by  which  electricity  is  set  in  motion  in  the  voltaic 
circuit  is  called  the  electromotive  force.  The  quantity  of  electricity  which  in 
any  unit  of  time  flows  through  a  section  of  the  circuit  is  called  the  intensity, 
or,  perhaps  better,  the  strength  of  the  current.  Ohm  found  that  this  strength 
is  the  same  in  all  parts  of  one  and  the  same  circuit,  however  heterogeneous 
they  were  ;  one  and  the  same  magnetic  needle  is  deflected  to  the  same 
extent  over  whatever  part  of  the  circuit  it  is  suspended  ;  and  the  same 
voltameter,  wherever  interposed  in  the  circuit,  indicates  the  same  disengage- 
ment of  gas  ;  he  also  found  that  the  strength  is  proportional  to  the  electro- 
motive force. 

It  has  further  been  found  that  when  the  current  from  the  same  couple 
is  passed  respectively  through  a  short  and  through  a  long  wire  of  the  same 
material,  its  action  on  the  magnetic  needle  is  less  in  the  latter  case  than  in 
the  former.  Ohm  accordingly  supposed  that  in  the  latter  case  there  was  a 
greater  resistance  to  the  passage  of  the  current  than  in  the  former  ;  and  he 
proved  that  '  the  resistance  is  inversely  proportional  to  the  strength  of  the 
current} 

On  these  principles  Ohm  founded  the  celebrated  law  which  bears  his 
name,  that  the  strength  of  the  curre?it  is  equal  to  the  electromotive  force 
divided  by  the  resistance. 

This  is  expressed  by  the  simple  formula 

C-E 
-R' 

where  C  is  the  strength  of  the  current,  E  the  electromotive  force,  and  R  the 
resistance. 

ii.  The  resistance  of  a  conductor  depends  on  three  elements  :  its  conduc- 
tivity, which  is  a  constant,  determined  for  each  conductor  ;  its  section  •  and 
its  length.  The  resistance  is  obviously  inversely  proportional  to  the  conduc- 
tivity ;  that  is,  the  less  the  conducting  power  the  greater  the  resistance.  It 
has  been  proved  that  the  resistance  is  inversely  as  the  section  and  directly 
as  the  length  of  a  conductor.  If  then  *  is  the  conductivity,  co  the  section,  and  A 
the  length  of  a  conductor,  we  have 

R-  *andC  =  .?  =  ^; 


that  is,  the  strength  of  a  current  is  inversely  proportional  to  the  length  of  the 
.conductor  and  directly  proportional  to  its  section  and  conductivity. 

iii.  In  a  voltaic  battery  composed  of  different  elements,  the  strength  of 
the  current  is  equal  to  the  sum  of  the  electromotive  forces  of  all  the  elements 
divided  by  the  sum  of  the  resistances.  Usually,  however,  a  battery  is  com- 
posed of  elements  of  the  same  kind,  each  having,  in  intention  at  least,  the 
same  electromotive  force  and  the  same  resistance. 

In  an  ordinary  element  there  are  essentially  two  resistances  to  be  con- 
sidered :  i.  That  offered  by  the  liquid  conductor  between  the  two  plates, 


768  Dynamical  Electricity.  [825- 

which  is  frequently  called  the  internal  or  essential  resistance  ;  and  2.  That- 
offered  by  the  interpolar  conductor  which  connects  the  two  plates  outside  the 
liquid  ;  this  conductor  may  consist  either  wholly  of  metal,  or  may  be  partly  of 
metal  and  partly  of  liquids  to  be  decomposed:  it  is  the  external  o\  non-essential 
resistance.  Calling  the  former  R  and  the  latter  r,  Ohm's  formula  becomes 

C-      E 
'  RTr 

iv.  If  any  number,  n,  of  similar  elements  are  joined  together,  there  is  n 
times  the  electromotive  force,  but  at  the  same  time  ;/  times  the    internal 

resistance,  and  the  formula  becomes  —?  —  .     If  the  resistance  in  the  inter- 

nR  +  r 

polar,  r,  is  very  small  —  which  is  the  case,  for  instance,  when  it  is  a  short,. 
thick  copper  wire  —  it  may  be  neglected  in  comparison  with  the  internal 
resistance,  and  then  we  have 

7?EE 


that  is,  a  battery  consisting  of  several  elements  produces  in  this  case  no 
greater  effect  than  a  single  element. 

v.  If,  however,  the  external  resistance  is  very  great,  as  when  the  current 
has  to  produce  the  electric  light,  or  to  work  a  long  telegraphic  circuit,  advan- 
tage is  gained  by  using  a  large  number  of  elements,  for  then  we  have  the 
formula 

r  _ 
~ 

If  r  is  very  great  as  compared  with  ;*R,  the  latter  may  be  neglected,  and  the 
expression  becomes 


that  is,  that  the  strength,  within  certain  limits,  is  proportional  to  the  number 
of  elements. 

In  a  thermo-electric  pile,  which  consists  of  very  short  metallic  conductors, 
the  internal  resistance  R  is  so  small  that  it  may  be  neglected,  and  the 
strength  is  inversely  as  the  length  of  the  connecting  wire. 

vi.  If  the  plates  of  an  element  be  made  m  times  as  large,  there  is  no- 
increase  in  the  electromotive  force,  for  this  depends  on  the  nature  of  the 
metals  and  of  the  liquid  (802)  ;  but  the  resistance  is  m  times  as  small,  for  the 
section  is  m  times  larger  :  the  expression  becomes  then 

c=    E  wE 

~R      "  R  +  mr' 
m 

Hence,  an  increase  in  the  size  of  the  plate  —  or,  what  is  the  same  thing,  a 
decrease  in  the  internal  resistance—  does  not  increase  the  strength  to  an  in- 
definite extent  ;  for  ultimately  the  resistance  of  the  element  R  vanishes  in 
comparison  with  the  resistance  r,  and  the  strength  continually  approximates 
•p» 

to  the  value  C=*-. 
r 


-825] 


Ohm's  Law. 


769 


vii.  Ohm's  law  enables  us  to  arrange  a  battery  so  as  to  obtain  the  greatest 
effect  in  any  given  case.  For  instance,  with  a  battery  of  six  elements  there 
are  the  following  four  ways  of  arranging  them  : — I.  In  a  single  series  (fig. 
728),  in  which  the  zinc  Z  of  one  element  is  united  with  the  copper  C  of  the 
second,  the  zinc  of  this  with  the  copper  of  the  third,  and  so  on.  2.  Arranged 
in  a  system  of  three  double  elements,  each  element  being  formed  by  joining 
two  of  the  former  (fig.  729).  3.  In  a  system  of  two  elements,  each  of  which 
consists  of  three  of  the  original  elements  joined,  so  as  to  form  one  of  triple 


Fig.    72t 


IHc 


Fig.  731- 

the  surface  (fig.  730).  Lastly,  of  one  large  element,  all  the  zincs  and  all  the 
coppers  being  joined,  so  as  to  form  a  pair  of  six  times  the  surface  (fig.  731). 

With  a  series  of  twelve  elements  there  may  be  six  different  combinations, 
and  so  on  for  a  larger  number. 

Now  let  us  suppose  that  in  the  particular  case  of  a  battery  of  six  elements 
the  internal  resistance  R  of  each  element  is  3,  and  the  external  resistance 
r=i2.  Then  in  the  first  case,  where  there  are  six  elements  arranged  in 
series,  we  have  the  value 


6E 


6E 


6x3  +  12 


6E 
30 


If  they  were  united  so  as  to  form  three  elements,  each  of  double  the 


7/O  Dynamical  Electricity.  [825- 

surface,  as  in  the  second  case  (fig.  729),  the  electromotive  force  would  then 
be  the  electromotive  force  in  each  element  :  there  would  also  be  a  resistance 
R  in  each  element,  but  this  would  only  be  half  as  great,  for  the  section  of 
the  plate  is  now  double  ;  hence  the  strength  in  this  case  would  be 

"is^y*  ?r^r=33;        '•:^-:  & 

2  2 

accordingly  this  change  would  lessen  the  strength. 

If,  with  the  same  elements,  the  resistance  in  the  connecting  wire  were 
only  r  =  2,  we  should  have  the  values  in  the  two  cases  respectively — 

C__6_*E    =6E 
6x3  +  2     20' 

and  C'  = 3 = =  —  . 

3R  +  r        9  +  4      J3 

2 

The  result  in  the  latter  case  is,  therefore,  more  favourable.  If  the  re- 
sistance r  were  9,  the  strength  would  be  the  same  in  both  cases.  Hence, 
then,  by  altering  the  size  of  the  plates  or  their  arrangement,  favourable 
or  unfavourable  results  are  obtained  according  to  the  relation  between  R 
and  r. 

\T"820.  Arrangement  of  multiple  battery  for  maximum  current. — It  can 
be  shown  that  in  any  given  combination  the  maximum  effect  is  obtained  when 
the  total  resistance  in  the  elements  is  equal  to  the  resistance  of  the  interpolar. 
For  let  N  be  the  total  number  of  cells  available  for  a  given  combination,  and 
let  n  be  the  number  of  cells  arranged  tandem,  or  in  series— that  is,  when 
the  zinc  of  one  is  connected  with  the  copper  of  the  next,  and  so  on  ;  then 

there  will  be  —elements  arranged  abreast.     If  e  be  the  electromotive  force, 
n 

and  r  the  resistance  of  one  cell,  while  /  is  the  external  resistance,  then  the 
strength  of  the  current  will  be 

ne          ne  e 


C- 


nr    i     n'r  +  1     nr      / 

N  N  N      n 


Therefore   C  is  a  maximum  when  —  .  +  ~  is  a  minimum.      But    ^T  x  . 

N       n  N     n 

=  r   is  a  constant,  therefore  the  sum  nr  +  -  is  a  minimum  when  n?  =      • 
N  R      n  N       n  ' 


that  is,  when        =  /,  or  when  the  total  internal  resistance  is  equal  to  the 

external  resistance. 

A2 
For  if  x  and       are  any  two  quantities  whose  product  is  A2,  then 

A2_.r2  +  A2-2A.r  +  2A;r_(.r-A)'       A 

»£  T   -  —•  ~r  ^^~V. 


-826]       Arrangement  of  Battery  for  Maximum  Current.         771 

This  is  greater  than  2  A  unless  ;r-A  =  o,  in  which  case  it  is  equal  to  2  A,  and 
is  a  minimum.     In  that  case  ;r  =  A,  and  therefore 


It  follows  thus  from  the  above  formula  that  the  best  effect  is  obtained 

/N/ 
when  ;/  =  A  /  — 

If  in  a  given  case  we  have  8  elements,  each  offering  a  resistance  15,  and 
an  interpolar  with  the  resistance  40,  we  get  72  =  4-3.  But  this  is  an  im- 
possible arrangement,  for  it  is  not  a  whole  number,  and  the  nearest  whole 
number  must  be  taken.  This  is  4  ;  and  it  will  be  found,  on  making  a  calcu- 
lation analogous  to  that  above,  that  when  arranged  so  as  to  form  4  elements, 

each  of  double  surface,  the  greatest  effect  is  obtained. 

•p 

The  formula  for  the  strength  of  current  from  several  elements,  C  =  -~  , 

K. 

may  also  be  applied  to  the  currents  produced  by  a  magneto-electrical  ma- 
chine (920).  In  that  case  n  stands  for  the  number  of  coils  which  in  a  given 
time  pass  through  a  magnetic  field. 

The  principle  that  the  best  effect  is  obtained  when  the  total  internal  is 
equal  to  the  total  external  resistance,  holds  also  for  the  currents  produced  by 
these  machines. 


302 


772  Dynamical  Electricity.  [827- 


CHAPTER   III. 

EFFECTS   OF   THE  CURRENT. 

827.  Physiological  actions. — Under  this  name  are  included  the  effects 
produced  by  a  battery  current  on  living  organisms  or  tissues. 

When  the  electrodes  of  a  strong  battery  are  held  in  the  two  hands  a  violent 
shock  is  felt,  especially  if  the  hands  are  moistened  with  acidulated  water, 
which  increases  the  conductivity.  The  violence  of  the  shock  increases  with 
the  number  of  elements  used,  and  with  a  large  number — as  200  Bunsen's 
cells — is  even  dangerous. 

The  power  of  contracting  upon  the  application  of  a  voltaic  current  seems 
to  be  a  very  general  property  of  protoplasm — the  physical  basis  of  both 
animal  and  vegetable  life  :  if,  for  example,  a  current  of  moderate  strength  be 
passed  through  such  a  simple  form  of  protoplasm  as  an  amoeba,  it  imme- 
diately withdraws  its  processes,  ceases  its  changes  of  form,  and  contracts  into 
a  rounded  ball — soon,  however,  resuming  its  activity  upon  the  cessation  of 
the  current.  Essentially  similar  effects  of  the  current  have  been  observed  in 
the  protoplasm  of  young  vegetable  cells. 

If  a  frog's  fresh  muscle  (which  will  retain  its  vitality  for  a  considerable 
time  after  removal  from  the  body  of  the  animal)  be  introduced  into  a  galvanic 
circuit,  no  apparent  effect  will  be  observed  during  the  steady  passage  of  the 
current,  but  every  opening  or  closure  of  the  circuit  will  cause  a  muscular 
contraction,  as  will  also  any  sudden  and  considerable  alteration  in  its  in- 
tensity. By  very  rapidly  interrupting  the  current,  the  muscle  can  be  thrown 
into  a  state  of  uninterrupted  contraction,  or  physiological  tetanus,  each  new 
contraction  occurring  before  the  previous  one  has  passed  off.  Other  things 
being  equal,  the  amount  of  shortening  exhibited  by  the  muscles  increases, 
up  to  a  certain  limit,  with  the  intensity  of  the  current.  These  phenomena 
entirely  disappear  with  the  life  of  the  muscle  ;  hence  the  experiments  are 
somewhat  more  difficult  with  warm-blooded  animals,  the  vitality  of  whose 
muscles,  after  exposure  or  removal  from  the  body,  is  maintained  with  more 
difficulty ;  but  the  results  of  careful  experiment  are  exactly  the  same  here  as 
in  the  case  of  the  frog. 

The  influence  of  an  electric  current  upon  living  nerves  is  very  remark- 
able ;  as  a  general  rule,  it  may  be  stated  that  its  effect  is  to  throw  the  nerve 
into  a  state  of  activity,  whatever  its  special  function  may  be  :  thus,  if  the 
nerve  be  one  going  to  a  muscle,  the  latter  will  be  caused  to  contract ;  if  it 
be  one  of  common  sensation,  pain  will  be  produced  :  if  one  of  special  sense, 
the  sensation  of  a  flash  of  light,  or  of  a  taste,  £c.,  will  be  produced,  accord- 
ing to  the  nerve  irritated.  These  effects  do  not  manifest  themselves  during 
the  even  passage  of  the  current,  but  only  when  the  circuit  is  either  opened  or 


-828]  Electro  tonus.  773 

closed,  or  both.  Of  course  the  continuity  of  the  nerve  with  the  organ  where 
its  activity  manifests  itself  must  be  maintained  intact.  The  changes  set  up 
by  the  current  in  the  different  nerve-trunks  are  probably  similar,  the  various 
sensations,  &c.,  produced  depending  on  the  different  terminal  organs  with 
which  the  nerves  are  connected. 

Professor  Burdon  Sanderson  has  ascertained  that  the  movement  which 
causes  the  Dioncea  muscipula  (Venus's  fly-trap),  one  of  what  are  called  car- 
nivorous plants,  to  close  its  hairy  leaves  and  thereby  entrap  insects  which 
alight  upon  it,  is  accompanied  by  an  electrical  current  in  a  manner  analogous 
to  that  manifested  in  muscular  contraction.  The  manner  in  which  the  irrita- 
tion is  caused  seems  immaterial. 

828.  Electrotonus. — In  a  living  nerve,  as  will  be  stated  more  fully  in 
Chapter  X.,  certain  parts,  of  the  surface  are  electropositive  to  certain  other 
parts,  so  that  if  a  pair  of  electrodes  connected  with  a  galvanometer  be  applied 
to  these  two  points,  a  current  will  be  indicated  ;  if  now  another  part  of  the 
nerve  be  interposed  in  a  galvanic  circuit,  it  will  be  found  that,  if  this  extra- 
neous current  be  passing  in  the  same  direction  as  the  proper  nerve-current, 
the  latter  is  increased,  and  vice  versa  ;  and  this  although  it  has  previously 
been  demonstrated  experimentally  that  none  of  the  battery  current  escapes 
down  the  nerve,  so  as  to  exert  any  influence  of  its  own  on  the  galvanometer. 
This  alteration  of  its  natural  electromotive  condition,  produced  through  the 
whole  of  a  nerve  by  the  passage  of  a  constant  current  through  part  of  it,  is 
known  as  the  electrotonic  state  ;  it  is  most  intense  near  the  extraneous,  or,  as 
it  is  called,  the  exciting  current.  It  continues  as  long  as  the  latter  is  pass- 
ing, and  is  attended  with  important  changes  in  the  excitability  of  the  nerve, 
or,  in  other  words,  the  readiness  with  which  the  nerve  is  thrown  into  a  state 
of  functional  activity  by  any  stimulus  applied  to  it.  Pfliiger,  who  has  inves- 
tigated these  changes,  has  named  the  part  of  the  nerve  through  which  the 
exciting  current  is  passing  the  intrapolar  region  :  the  condition  of  the  nerve 
close  to  the  positive  pole  is  called  anelectrotonus  ;  that  near  the  negative  pole, 
kathelectrotonus.  The  excitability  of  the  nerve  is  diminished  in  the  anelec- 
trotonic  region,  so  that  with  a  motor  nerve,  for  example,  a  stronger  stimulus 
than  before  would  need  to  be  applied  at  this  part  in  order  to  obtain  a  mus- 
cular contraction  ;  in  the  kathelectrotonic  region,  on  the  contrary,  the  ex- 
citability of  the  nerve  is  heightened.  Moreover,  with  an  exciting  current  of 
moderate  strength  the  power  of  the  nerve  to  conduct  a  stimulus  is  lowered 
in  the  anelectrotonic  region,  and  increased  in  the  kathelectrotonic  ;  with 
strong  currents  it  is  said  to  be  diminished  in  both. 

These  facts  have  to  be  taken  into  account  in  the  scientific  application  of 
galvanism  to  medical  purposes.  If,  for  instance,  it  is  wished  to  diminish  the 
excitability  of  the  sensory  nerves  of  any  part  of  the  body,  the  current  should 
be  passed  in  such  a  direction  as  to  throw  the  nerves  of  that  part  into  a  state 
of  anelectrotonus — and  similarly  in  other  cases. 

If  a  powerful  electric  current  be  passed  through  the  body  of  a  recently 
killed  animal,  violent  movements  are  produced,  as  the  muscles  ordinarily 
retain  their  vitality  for  a  considerable  time  after  general  systematic  death  : 
by  this  means,  also,  life  has  been  re-established  in  animals  which  were  appa- 
rently dead — a  properly  applied  current  stimulating  the  respiratory  muscles 
to  contract. 


774 


Dynamical  Electricity. 


[829- 


-^•829.  Heating  effects. — When  a  voltaic  current  is  passed  through  a  metal 
wire  the  same  effects  are  produced  as  by  the  discharge  of  an  electric  battery 
(790) ;  the  wire  becomes  heated,  and  even  incandescent  if  it  is  very  short  and 
thin.  With  a  powerful  battery  all  metals  are  melted,  even  iridium  and  plati- 
num, the  least  fusible  of  metals.  Carbon  is  the  only  element  which  has  not 
hitherto  been  fused  by  it.  Despretz,  however,  with  a  battery  composed  of 
600  Bunsen's  elements  joined  in  six  series  (825),  raised  rods  of  very  pure 
carbon  to  such  a  temperature  that  they  were  softened  and  could  be  welded 
together,  yielding  an  incipient  fusion. 

A  battery  of  30  to  40  Bunsen's  elements  is  sufficient  to  melt  and  volatilise 
fine  wires  of  lead,  tin,  zinc,  copper,  gold,  silver,  iron,  and  even  platinum,  with 
differently  coloured  sparks.  Iron  and  platinum  burn  with  a  brilliant  white 
light ;  lead  with  a  purple  light ;  the  light  of  tin  and  of  gold  is  bluish-white  ; 

the  light  of  zinc 
is  a  mixture  of 
white  and  gold  ; 
finally,  copper 
and  silver  give 
a  green  light. 

The  thermal 
effects  of  the 
voltaic  current 
are  used  for 
firing  mines  for 
military  pur- 
poses and  for 
blasting  opera- 
tions. The  fol- 
lowing arrange- 
ment was  de- 
vised by  Colonel 
Schaw  :  —  Fig. 
Two  moderately 
gutta-percha,  are 


Fig.  732. 


732  represents  a  small  wooden  box  provided  with  a  lid. 
stout  copper  wires,  bb\  insulated  by  being  covered  with 
deprived  of  this  coating  at  the  ends,  which  are  then  passed  through  and  through 
the  box  in  the  manner  represented  in  the  figure.  The  distance  between  them 
is  f  of  an  inch,  and  a  very  fine  platinum  wire  (one  weighing  i  '92  grain  to  the 
yard  is  the  regulation  size)  is  soldered  across.  The  object  of  arranging  the 
wires  in  this  manner  is  that  they  shall  not  be  in  contact,  and  that  the  strain 
which  they  exert  may  be  spent  on  the  box,  and  not  on  the  platinum  wire 
joining  them,  which,  being  extremely  thin,  would  be  broken  by  even  a  very 
slight  pull.  The  box  is  then  filled  with  fine  grained  powder,  and  the  lid  tied 
down.  The  wires  of  the  fuse  are  then  carefully  joined  to  the  long  conducting 
wires  which  lead  to  the  battery  :  these  should  be  of  copper,  and  as  thick  as 
is  convenient,  so  as  to  offer  very  little  resistance  :  No.  16  gauge  copper  wire 
is  a  suitable  size.  The  fuse  is  then  introduced  into  the  charge  to  be  fired  : 
if  it  is  for  a  submarine  explosion  the  powder  is  contained  in  a  canister,  the 
neck  of  which,  after  the  introduction  of  the  fuse,  is  carefully  fastened  by 
means  of  cement.  When  contact  is  made  with  the  battery,  which  is  effected 


-830]       Laws  of  Heating  Effects.     Galv  another  mometer.        775 

through  the  intervention  of  mercury  cups,  the  current  traversing  the  plati- 
num wire  renders  it  incandescent,  which  fires  the  fuse  ;  and  thus  the  ignition 
is  communicated  to  the  charge  in  which  it  is  placed. 

The  heating  effect  depends  more  on  the  size  than  on  the  number  of  the 
plates  of  a  battery,  for  the  resistance  in  the  connecting  wires  is  small  (825). 
An  iron  wire  may  be  melted  by  a  single  Wollaston's  element,  the  zinc  of 
which  is  8  inches  by  6.  Hare's  battery  (805)  received  its  name  deflagrator 
on  account  of  its  greater  heating  effect,  produced  by  the  great  surface  of  its 
plates. 

When  any  circuit  is  closed,  a  definite  amount  of  heat,  H,  is  produced 
throughout  the  entire  circuit ;  and  the  amount  of  heat,  /*,  produced  in  any 
particular  part  of  the  circuit  bears  to  the  total  heat,  H,  the  same  ratio  which 
the  resistance,  r,  of  this  part  bears  to  R,  that  of  the  entire  circuit.  Hence, 
in  firing  mines,  the  wire  to  be  heated  should  be  of  as  small  section  and  of  as 
small  conductivity  as  practicable.  These  conditions  are  well  satisfied  by 
platinum,  which  has  over  iron  the  advantage  of  being  less  brittle  and  of  not 
being  liable  to  rust.  Platinum  too  has  a  slow  specific  heat,  and  is  thus  raised 
to  a  higher  temperature,  by  the  same  amount  of  heat,  than  a  wire  of  greater 
specific  heat.  On  the  other  hand,  the  conducting  wires  should  present  as 
small  a  resistance  as  possible,  a  condition  satisfied  by  a  stout  copper  wire ; 
and  again,  as  the  heating  effect  of  any  circuit  is  proportional  to  the  square 
of  the  electromotive  force,  and  inversely  as  the  resistance,  a  battery  with  a 
high  electromotive  force  and  small  resistance,  such  as  Grove's  or  Bunsen's, 
should  be  selected. 

Another  application  of  the  heating  eftect  is  to  what  are  called  safety  catches. 
These  are  lengths  of  lead  wire  or  strips  interposed  in  the  circuit  of  the 
powerful  currents  used  for  electrical  lighting  and  the  like.  Their  dimensions 
are  so  calculated  that  when  the  current  attains  a  certain  strength,  the  heat 
generated  is  sufficient  to  melt  them  and  thus  break  the  continuity  of  the 
circuit.  As  this  can  be  arranged  with  great  accuracy,  it  is  possible  so  to 
regulate  the  circuit  that  it  shall  not  exceed  a  certain  limit. 

By  means  of  a  heated  platinum  wire,  parts  of  the  body  may  be  safely 
cauterised  which  could  not  be  got  at  by  a  red-hot  iron  ;  the  removal  of 
tumours  may  be  effected  by  drawing  a  loop  of  platinum  round  their  base, 
which  is  then  gradually  pulled  together.  It  has  been  observed  that  when 
the  temperature  of  the  wire  is  about  600°  C.,  the  combustion  of  the  tissues 
is  so  complete  that  there  is  no  haemorrhage  ;  while  at  1 500°  the  action  of 
the  wire  is  like  that  of  a  sharp  knife. 

^\  83o7  Laws  of  heating  effects.  Galvanothermometer. — Although  the 
thermal  effects  are  most  obvious  in  the  case  of  thin  wires,  they  are  by  no 
means  limited  to  them.  The  laws  of  the  heating  effect  were  investigated  by 
Lenz,  by  means  of  an  apparatus  called  the  Galv  another  mometer  (fig.  733). 
A  wide-mouthed  stoppered  bottle  was  fixed  upside  down,  with  its  stopper,  £, 
in  a  wooden  box  ;  the  stopper  was  perforated  so  as  to  give  passage  to  two 
thick  platinum  wires,  connected  at  one  end  with  binding  screws,  ss,  while 
their  free  ends  were  provided  with  platinum  cones  by  which  the  wires  under 
investigation  could  be  affixed  ;  the  vessel  contained  alcohol,  the  tempera- 
ture of  which  was  indicated  by  a  thermometer  fitted  in  a  cork  inserted  in 
.a  hole  made  in  the  bottom  of  the  vessel.  The  current  is  passed  through 


77^  Dynamical  Electricity.  [830- 

the  platinum  wires,  and  its  strength  measured  by  means  of  a  tangent 
compass  interposed  in  the  circuit.  By  observing  the  increase  of  tempera- 
ture in  the  thermometer  in  a  given  time,  and 
knowing  the  weight  of  the  alcohol,  the  mass 
of  the  wire,  the  specific  heat,  and  the  calori- 
metric  values  (453)  of  the  vessel,  and  of  the 
thermometer,  compared  with  alcohol,  the  heat- 
ing effect  which  is  produced  by  the  current  in 
a  given  time  can  be  calculated. 

By  apparatus  of  this  kind  the  truth  of  the 
following  law  may  be  established. 

The  heat  disengaged  in  a  given  time,  /,  is 
directly  proportional    to    the    square   of  the 
strength  of  the  current,  and  to  the  resistance. 
This   is   known  as  Joule's  law  (831),  and 

is  expressed  in  the  formula  H  =  C2R/  =  -^ 

R 

Fi  =  EC/.  If  the  values  E,  C,  R  are  expressed  in 

ergs,  we  get  the  value  H  in  water-gramme  de- 
grees if  we  divide  by  the  mechanical  equivalent  of  a  water-gramme  degree, 
that  is  by  4-16  x  io7.  If  the  values  are  expressed  in  practical  units — volt, 
ohm,  ampere  (964) — we  get  the  value  in  the  same  unit  in  dividing  by  io7. 

If  the  current  passes  through  a  chain  of  platinum  and  silver  wire  of  equal 
sizes,  the  platinum  becomes  more  heated  than  the  silver  from  its  greater 
resistance  ;  and  with  a  suitable  current  the  platinum  may  become  incan- 
descent while  the  silver  remains  dark.  This  experiment  was  devised  by 
Children. 

If  a  long  thin  platinum  wire  be  raised  to  dull  redness  by  passing  a  voltaic 
current  through  it,  and  if  part  of  it  be  cooled  down  by  ice,  the  resistance  of 
the  cooled  part  is  diminished,  the  strength  of  the  current  increases,  and  the 
rest  of  the  wire  becomes  brighter  than  before.  If,  on  the  contrary,  a  part 
of  the  feeble  incandescent  wire  be  heated  by  a  spirit-lamp,  the  resistance  of 
the  heated  part  increases,  for  the  effect  is  the  same  as  that  of  introducing 
fresh  resistance,  the  strength  of  the  current  diminishes,  and  the  wire  ceases 
to  be  incandescent  in  the  non-heated  part. 

The  cooling  by  the  surrounding  medium  exercises  an  important  influence 
on  the  phenomenon  of  ignition.  A  round  wire  is  more  heated  by  the  same 
current  than  the  same  wire  which  has  been  beaten  out  flat  :  for  the  latter 
with  the  same  section  offers  a  greater  surface  to  the  cooling  medium  than  the 
others.  For  the  same  reason,  when  a  wire  is  stretched  in  a  glass  tube  on 
which  two  brass  caps  are  fitted  airtight,  and  the  wire  is  raised  to  dull  in- 
candescence by  the  passage  of  a  current,  the  incandescence  is  more  vivid 
when  the  air  has  been  pumped  out  of  the  tube,  because  it  now  simply  loses 
heat  by  radiation,  and  not  by  communication  to  the  surrounding  medium. 

Similarly,  a  current  which  will  melt  a  wire  in  air  will  only  raise  it  to  dull 
redness  in  ether,  and  in  oil  or  in  water  will  not  heat  it  to  redness  at  all,  for 
the  liquids  conduct  heat  away  more  readily  than  air  does. 

From  the  above  laws  it  follows  that  the  heating  effect  is  the  same  in  a  wire 
whatever  be  its  length,  provided  the  current  is  constant ;  but  it  must  be  remem- 


-832]       Relation  of  Heating  Effect  to  Work  of  a  Battery.        777 

bered  that  by  increasing  the  length  of  the  wire  we  increase  the  resistance, 

and  consequently  diminish   the  current ;  further,  in  a  long  wire  there  is  a 

greater  surface,  and  hence  more  heat  is  lost  by  radiation  and  by  conduction. 

831.   Graphical  representation  of  the  heating  effects  in  a  circuit. — 

The  law  representing  the  production  of  heat  in  a  circuit  in  the  unit  of  time 
is  very  well  seen  by  the  following  geometrical  construction,  due  to  Professor 
Foster. 

The  heat  H  produced  in  a  circuit  in  the  unit  of  time  is  proportional  to 
the  square  of  the  strength  of  the  current  C,  and  to  the  resistance  R  (830) 

F  E2 

that  is  H  =  C2R  ;  but  since  C  =  ~  (825),  we  have  H  =  _. 

R  R 

Draw  a  straight  line  DAB  (fig.  734),  and  from  any  point  A  in  it  draw  a 
line  AC,  at  right  angles  to  DAB,  and  of  a  length  proportional  to  the  electro- 


Fig.  734- 

motive  force  of  the  cell.  Lay  off  a  length  AB  proportional  to  the  resistance 
of  the  circuit.  Join  CB,  and  at  C  draw  a  line  at  right  angles  to  BC,  and  let 
D  be  the  point  where  this  line  cuts  the  line  DAB.  Then  the  length  AD  is 
proportional  to  the  heat  produced  in  the  whole  circuit  in  unit  time.  For  the 
triangles  ADC  and  ACB  are  similar,  and  therefore  AD  :  AC  =AC  :  AB  ;  that 

is,  AD  =  -      ;  that  is,  H  =  — 

By  drawing  figures  similar  to  the  above  it  will  be  found  that  for  a  given 
electromotive  force  the  heat  is  inversely  proportional  to  the  resistance,  and  for 
a  given  resistance  directly  proportional  to  the  square  of  the  electromotive 
force.  That  is,  if  the  resistance  is  doubled,  the  heat  is  reduced  to  one-half ;  if 
theejectromotive  force  is  doubled  the  heat  is  quadrupled. 
xin$32.  Relation  of  heating:  effect  to  work  of  a  battery. — In  every 
closed  circuit  chemical  action  is  continuously  going  on  ;  in  ordinary 
circuits,  the  most  common  action  is  the  solution  of  zinc  in  sulphuric  acid, 
which  may  be  regarded  as  an  oxidation  of  the  zinc  to  form  oxide  of  zinc,  and 
a  combination  of  this  oxide  of  zinc  with  sulphuric  acid  to  form  water  and 
zinc  sulphate.  It  is  a  true  combustion  of  zinc,  and  this  combustion  serves  to 
maintain  all  the  actions  which  the  circuit  can  produce,  just  as  all  the  work 
which  a  steam-engine  can  effect  has  its  origin  in  the  combustion  of  fuel  (473). 

By  independent  experiments  it  has  been  found  that,  when  a  given  weight 
of  zinc  is  dissolved  in  sulphuric  acid,  a  certain  definite  measurable  quantity 
of  heat  is  produced,  which,  as  in  all  cases  of  chemical  action,  is  the  same, 


77 8  Dynamical  Electricity.  [832- 

whatever  be  the  rapidity  with  which  this  solution  is  effected.  If  this  solution 
takes  place  while  the  zinc  is  associated  with  another  metal  so  as  to  form  a 
voltaic  couple,  the  rapidity  of  the  solution  will  be  altered  and  the  whole  cir- 
cuit will  become  heated— the  liquid,  the  plates,  the  containing  vessel  as  well 
as  the  connecting  wire.  But  although  the  distribution  of  the  heat  is  thus 
altered,  its  quantity  is  not.  If  the  values  of  all  the  several  heating  effects  in 
the  various  parts  of  the  circuit  be  determined,  it  will  still  be  found  that, 
however  the  resistance  of  the  connecting  wire  be  varied,  this  sum  is  exactly 
equivalent  to  that  produced  by  the  solution  of  a  certain  weight  of  zinc. 

If  the  couple  be  made  to  do  external  mechanical  work  the  case  is  dif- 
ferent. Joule  made  the  following  remarkable  experiment : — A  small  zinc 
and  copper  couple  were  arranged  in  a  calorimeter,  and  the  amount  of  heat 
determined  while  the  couple  was  closed  for  a  certain  length  of  time  by  a 
short  thick  wire.  The  couple  still  contained  in  the  calorimeter  was  next 
connected  with  a  small  electromagnetic  engine  (899),  by  which  a  weight  was 
raised.  It  was  thus  found  that  the  heat  produced  in  the  calorimeter  in  a 
given  time — while,  therefore,  a  certain  amount  of  zinc  was  dissolved — was 
less  while  the  couple  was  doing  work  than  when  it  was  not ;  and  the 
amount  of  this  diminution  was  the  exact  thermal  equivalent  of  the  work 
performed  in  raising  the  weight  (497). 

That  the  whole  of  the  chemical  work  and  disengagement  of  heat  in  the 
circuit  of  an  ordinary  cell  has  its  origin  in  the  solution  of  zinc  in  acid  is  con- 
firmed by  the  following  experiment,  due  to  Favre  : — 

In  the  muffle  of  his  calorimeter  (456),  five  small  zinc  platinum  elements 
were  introduced  ;  the  other  muffle  contained  a  voltameter.  Now  when  the 
element  was  closed  until  one  equivalent  of  zinc  was  dissolved  in  the  whole  of 
the  cells,  \  of  an  equivalent  of  water  should  be  decomposed  in  the  voltameter 
(846),  which  was  found  to  be  the  case.  In  one  case  the  current  of  the 
battery  was  closed  without  inserting  the  voltameter,  and  the  heat  disengaged 
during  the  solution  of  one  equivalent  of  zinc  was  found  to  be  18,796  thermal 
units  ;  when,  however,  the  voltameter  was  introduced,  the  quantity  disengaged 
was  only  11,769  thermal  units.  Now  the  difference,  7,027,  is  represented  by 
the  chemical  work  of  decomposing  \  of  an  equivalent  of  water  ;  this  agrees 

very  well  with  the  number,  6,892  =  ^^ — ,  which  represents  the  heat  disen- 
gaged during  the  formation  of  \  of  an  equivalent  of  water. 

However  complicated  may  be  a  voltaic  combination  the  total  heat  pro- 
duced in  it  is  the  sum  of  the  quantities  of  heat  which  are  produced  and  absorbed 
in  the  various  chemical  processes  which  take  place  in  it. 

We  may  illustrate  this  important  principle  by  reference  to  the  element 
of  De  la  Rue  and  Miiller  (812),  the  chemical  actions  in  which  are  perhaps 
the  simplest  of  all  constant  elements.  The  normal  action  is  that,  when  the 
element  is  closed,  zinc  decomposes  ammonium  chloride  with  the  formation 
of  zinc  chloride,  while  the  liberated  ammonium  unites  with  the  chlorine  of 
the  silver  chloride,  re-forming  ammonium  chloride  and  depositing  silver. 
The  heat  of  decomposition  and  of  re-formation  of  the  ammonium  chloride 
compensate  one  another,  and  the  net  result  is  the  formation  of  zinc  chloride, 
and  the  decomposition  of  silver  chloride.  Now  the  heat  produced  in  the 
formation  of  a  molecule  of  zinc  chloride  (ZnCl.2)  is  112,840  gramme  units, 


-833] 


Luminous  Effects. 


779 


and  that  of  the  equivalent  silver  chloride  (2Ag2Cl2)  is  58,760.  The  difference 
is  54,800,  which  is  less  than  58,360,  the  heat  required  to  decompose  a  mole- 
cule of  water.  Hence  it  is  that  one  such  element  will  not  effect  a  continuous 
decomposition  of  water,  but  at  least  two  are  required  for  the  purpose. 

In  like  manner  the  heat  disposable  in  one  DanielPscell  is  represented  by 
47,300,  and  accordingly  at  least  two  are  also  required. 

In  some  cases,  however,  the  current  of  a  single  cell  does  produce  a  feeble 
but  continuous  decomposition.  This  arises  from  the  fact  that  the  water  of  the 
voltameter  contains  air  in  solution,  and  the  hydrogen  as  it  is  liberated  unites 
with  the  dissolved  oxygen.  This  process  is  known  as  electrolytic  convection. 
S*n£y$k  luminous  effects. — In  closing  a  voltaic  battery  a  spark  is  obtained 
at  the  point  of  contact,  which  is  frequently  of  great  brilliancy.  A  similar 
spark  is  also  perceived  on  breaking  contact.  These  luminous  effects  are 
obtained,  when  the  battery  is  sufficiently  powerful,  by  bringing  the  two  elec- 
trodes very  nearly  in  contact  ;  a  succession  of  bright  sparks  springs  some- 
times across  the  interval,  which  follow  each  other  with  such  rapidity  as  to 
produce  continuous  light.  With  eight  or  ten  of  Groves's  elements  brilliant 
luminous  sparks  are  obtained  by  connecting  one  terminal  of  the  battery  with 
a  file,  and  moving  its  point  along  the  teeth  of  another  file  connected  with  the 
other  terminal. 

The  most  beautiful  effect  of  the  electric  light  is  obtained  when  two  pencils 
of  charcoal  are  connected  with  the  terminals  of  the  battery  in  the  manner 
represented  in  fig.  735. 
The  charcoal  b  is  fixed, 
while  the  charcoal  a  can 
be  raised  and  lowered  by 
means  of  a  rack  and  pinion 
motion,  c.  The  two  char- 
coals being  placed  in  con- 
tact, the  current  passes, 
and  their  ends  soon  be- 
come incandescent.  If 
they  are  then  removed  to 
a  distance  of  about  the 
tenth  of  an  inch,  according 
to  the  strength  of  the 
current,  a  luminous  arc 
extends  between  the  two 
points,  which  has  an  ex- 
ceedingly brilliant  lustre, 
and  is  called  the  voltaic 
arc. 

The  length  of  this  arc 
varies  with  the  force  of 
the  current.  In  air  it  may  exceed  2  inches  with  a  battery  of  500  elements, 
arranged  in  six  series  of  100  each,  provided  the  positive  pole  is  uppermost, 
as  represented  in  the  figure ;  if  it  is  undermost,  the  arc  is  about  one-third 
shorter.  In  a  partial  vacuum  the  distance  of  the  charcoals  may  be  greater 
than  in  air  ;  in  fact,  as  the  electricity  meets  with  no  resistance,  it  springs 


-  735- 


780  Dynamical  Electricity.  [833- 

between  the  two  charcoals,  even  before  they  are  in  contact.  The  voltaic  arc 
can  also  be  produced  in  liquids,  but  it  is  then  much  shorter,  and  its  brilliancy 
is  greatly  diminished. 

The  voltaic  arc  has  the  property  that  it  is  attracted  when  a  magnet  is  pre- 
sented to  it — a  consequence  of  the  action  of  magnets  on  currents  (865). 

Some  physicists  have  considered  the  voltaic  arc  as  formed  of  a  very  rapid 
succession  of  bright  sparks.  Its  colour  and  shape  depend  on  the  nature  of 
the  conductors  between  which  it  is  formed,  and  it  is  probably  due  to  the 
incandescent  particles  of  the  conductor,  which  are  volatilised  and  transported 
in  the  direction  of  the  current ;  that  is,  from  the  positive  to  the  negative  pole. 
The  more  easily  the  electrodes  are  disintegrated  by  the  current,  the  greater 
is  the  distance  at  which  the  electrodes  can  be  placed.  Charcoal,  which  is  a 
very  friable  substance,  is  one  of  the  bodies  which  gives  the  largest  luminous 
arc.  Edlund  has  shown  that  this  disintegration  of  the  terminals  by  the 
voltaic  arc  gives  rise  to  an  electromotive  force  opposed  in  direction  to  that 
of  the  main  current. 

Davy  first  made  the  experiment  of  the  electric  light,  in  1801,  by  means  of 
a  battery  of  2,000  plates,  each  4  inches  square.  He  used  charcoal  points 
made  of  light  wood  charcoal  which  had  been  heated  to  redness,  and  im- 
mersed in  a  mercury  bath ;  the  mercury,  penetrating  into  the  pores  of  the 
charcoal,  increased  its  conductivity.  When  any  substance  was  introduced 
into  the  voltaic  arc  produced  by  this  battery,  it  became  incandescent ;  pla- 
tinum melted  like  wax  in  the  flame  of  a  candle ;  sapphire,  magnesia,  lime, 
and  most  refractory  substances  were  fused.  Fragments  of  diamond,  of 
charcoal,  and  of  graphite  rapidly  disappeared  without  undergoing  any 
previous  fusion. 

As  charcoal  rapidly  burns  in  air,  it  was  necessary  to  operate  in  vacuo, 
and  hence  the  experiment  was  for  a  long  time  made  by  fitting  the  two  points 
in  an  electric  egg,  like  that  represented  in  fig.  684.  At  present  the  electrodes 
are  made  of  gas  graphite,  a  modification  of  charcoal  deposited  in  gas  retorts ; 
this  is  hard  and  compact,  and  only  burns  slowly  in  air ;  hence  it  is  unneces- 
sary to  operate  in  vacuo.  When  the  experiment  is  made  in  vacuo  there  is 
no  combustion,  but  the  charcoal  wears  away  at  the  positive  pole,  while  it  is 
somewhat  increased  on  the  negative  pole,  indicating  that  there  is  a  transport 
of  solid  matter  from  the  positive  to  the  negative  pole. 

834.  Foucault's  experiment. — This  consists  in  projecting  on  a  screen 
the  image  of  the  charcoal  points  produced  in  the  camera  obscura  at  the 
moment  at  which  the  electric  light  is  formed  (fig.  736).     By  means  of  this 
experiment,  which  is  made  by  the  photo-electric  microscope  already  de- 
scribed (fig.  542),  the  two  charcoals  can  be  readily  distinguished,  and  the 
positive  charcoal  is  seen  to  become  somewhat  hollow  and  diminished,  while 
the  other  increases.     The  globules  represented  on  the  two  charcoals  arise 
from  the  fusion  of  a  small  quantity  of  silica  contained  in  the  charcoal.   When 
the  current  begins  to  pass,  the  negative  charcoal  first  becomes  luminous, 
but  the  light  of  the  positive  charcoal  is  the  brightest ;  as  it  also  wears  away 
about  twice  as  rapidly  as  the  negative  electrode  it  ought  to  be  rather  the  larger. 

835.  Regulator  of  the  electric  light. — When  the  electric  light  is  to  be 
used  for  illumination,  it  must  be  as  continuous  as  other  modes  of  lighting. 
For  this  purpose,  not  only  must  the  current  be  constant,  but  the  distance  of 


-835] 


Regulator  of  the  Electric  Light. 


the  charcoals  must  not  alter,  which  necessitates  the  use  of  some  arrange- 
ment for  bringing  them  nearer  together  in  proportion  as  they  wear  away. 


Fig.  736. 

One  of  the  best  modes  of  effecting  this  is  by  an  apparatus  invented  by 
Duboscq. 

In  this  regulator  the  two  charcoals  are  movable,  but  with  unequal  veloci- 
ties, which  are  virtually  proportional  to  their  waste.  The  motion  is  trans- 
mitted by  a  drum  placed  on  the  axis  xy  (fig.  737).  This  turns,  in  the  direc- 
tion of  the  arrows,  two  wheels,  a  and  b,  the  diameters  of  which  are  as  I  :  2, 
and  which  respectively  transmit  their  motion  to  two  rackworks,  C'  and  C. 
C  lowers  the  positive  charcoal,  p,  by  means  of  a  rod  sliding  in  the  tube 
H,  while  the  other  C'  raises  the  negative  charcoal,  «,  half  as  rapidly.  By 
means  of  the  milled  head  y  the  drum  can  be  wound  up,  and  at  the  same 
time  the  positive  charcoal  moved  by  the  hand ;  the  milled  head  x  moves  the 
negative  charcoal  also  by  the  hand,  and  independently  of  the  first.  For  this 
purpose  the  axis,  xy,  consists  of  two  parts  pressing  against  each  other  with 
some  force,  so  that,  holding  the  milled  head  x  between  the  fingers,  the  other, 
v,  may  be  moved,  and  by  holding  the  latter  the  former  can  be  moved.  But 
the  friction  is  sufficient  when  the  drum  works  to  move  the  two  wheels  a  and 
b  and  the  two  rackworks. 

The  two  charcoals  being  placed  in  contact,  the  current  of  a  powerful 
battery  of  40  to  50  elements  reaches  the  apparatus  by  means  of  the  wires  E 
and  E'.  The  current  rising  in  H  descends  by  the  positive  charcoal,  then  by 
the  negative  charcoal,  and  reaches  the  apparatus,  but  without  passing  into 
the  rackwork  C,  or  into  the  part  on  the  right  of  the  plate  N  ;  these  pieces 
being  insulated  by  ivory  discs  placed  at  their  lower  part.  The  current  ulti- 
mately reaches  the  bobbin  B,  which  forms  the  foot  of  the  regulator,  and 
passes  into  the  wire  E'.  Inside  the  bobbin  is  a  bar  of  soft  iron,  which  is 
magnetised  as  long  as  the  current  passes  in  the  bobbin,  and  demagnetised 
when  it  does  not  pass,  and  this  temporary  magnet  is  the  regulator.  For  this 
purpose  it  acts  attractively  on  an  armature  of  soft  iron,  A,  open  in  the  centre 


782 


Dynamical  Electricity. 


[835- 


so  as  to  allow  the  rackwork  C'  to  pass,  and  fixed  at  the  end  of  a  lever,  which 
works  on  two  points,  mm,  and  transmits  a  slight  oscillation  to  a  rod,  d,  which, 
by  means  of  a  catch,  z,  seizes  the  wheel  2,  as  is  seen  on  a  larger  scale 

in  fig.  738.  By  an  endless 
screw,  and  a  series  of  toothed 
wheels,  the  stop  is  transmitted 
to  the  drum,  and  the  rack- 
work  being  fixed,  the  same 
is  the  case  with  the  carbons. 
This  is  what  takes  place  so 
long  as  the  magnetisation  in 
the  bobbin  is  strong  enough 
to  keep  down  the  armature 
A  ;  but  in  proportion  as  the 
carbons  wear  away,  the  cur- 
rent becomes  feebler,  though 
the  voltaic  arc  continues,  so 
that  ultimately  the  attraction 
of  the  magnet  no  longer 
counterbalances  a  spring  r, 
which  continually  tends  to 
raise  the  armature.  It  then 
ascends,  the  piece  d  dis- 
engages the  stop  z,  the  drum 
works,  and  the  carbons  come 
nearer  ;  they  do  not,  however, 
touch,  because  the  strength 
of  the  current  gains  the  upper 
hand,  the  armature  A  is 
attracted,  and  the  carbons 
remain  fixed.  As  their  dis- 
tance only  varies  within  very 
narrow  limits,  a  regular  and 
continuous  light  is  obtained 
with  this  apparatus  until  the 
carbons  are  quite  used. 

By  means  of  a  regulator, 
Duboscq  illuminates  the  pho- 
togenic apparatus  represented  in  fig.  542,  by  which  all  the  optical  experi- 
ments may  be  performed  for  which  sunlight  was  formerly  necessary. 

836.  Browning's  regulator. — A  much  simpler  apparatus,  represented  in 
fig.  738,  has  been  devised  by  Browning,  which  is  less  costly  than  the  other 
lamps,  and  also  requires  a  smaller  number  of  elements  to  work  it.  The 
current  enters  the  lamp  by  a  wire  attached  to  a  binding  screw  on  the  base  of 
the  instrument,  passing  up  the  pillar  by  the  small  electro-magnet  to  the 
centre  pillar  along  the  top  of  the  horizontal  bar,  down  the  left-hand  bar 
through  the  two  carbons,  and  away  by  a  wire  attached  to  a  binding  screw  on 
the  left  hand.  A  tube  holding  the  upper  carbon  slides  freely  up  and  down 
a  tube  at  the  end  of  the  cross-piece,  and  would  by  its  own  weight  rest  on  the 


Fig.  737- 


-837]          Properties  and  Intensity  of  the  Electric  Light.  783 

lower  carbon,  but  the  electromagnet  is  provided  with  a  keeper,  to  which  is 
attached  a  rest  that  encircles  the  carbon  tube  and  grasps  it.  When  the  electro- 
magnet works  and  attracts  the  keeper, 
the  rest  tightens,  and  thereby  prevents 
the  descent  of  the  carbon.     When  the 
keeper  is  not  attracted  the  rest  loosens, 
and  the  carbon-holder  descends. 

When  the  two  carbons  are  at  rest, 
on  making  contact  with  a  battery  the 
current  traverses  both  carbons  and  no 
light  is  produced.  But  if  the  upper 
carbon  be  raised  ever  so  little,  a 
brilliant  light  is  emitted.  When  the 
lamp  is  thus  once  set  to  work,  the  rod 
attached  to  the  upper  carbon  may  be 
let  go,  and  the  magnet  will  afterwards 
keep  the  lamp  at  work.  For  when 
some  of  the  carbon  is  consumed,  and 
the  interval  between  the  two  is  too 
great  for  the  current  to  pass,  the  magnet 
loses  some  of  its  power,  the  keeper 
loosens  its  hold  on  the  carbon,  and  this 
descends  by  its  own  weight.  When 
they  are  sufficiently  near,  but  before 
they  are  in  contact,  the  current  is  re- 
established ;  the  magnet  again  draws  on 
the  keeper,  and  the  keeper  again  checks 
the  descent  of  the  carbon,  and  so  forth. 
Thus  the  points  are  retained  at  the 
right  distances  apart,  and  the  light  is  continuous  and  brilliant. 

Stohrer  has  devised  a  regulator  for  the  electrical  light  which 
is  very  simple  in  principle,  and  which  also  only  requires  a  few 
elements.  Its  essential  features  are  represented  in  fig.  740,  in 
which  b  is  a  cylinder  containing  glycerine  and  surrounded  by  the 
wire  of  the  circuit^/!  In  this  is  a  hollow  cylindrical  floater  #, 
nearly  as  wide  as  the  vessel  ;  at  its  top  is  a  copper  tube  c, 
in  which  the  carbon  point  d  can  be  fixed.  A  stout  copper  wire 
fixed  to  the  bottom  of  the  float  dips  in  an  iron  tube  filled  with 
mercury,  with  which  is  connected  one  pole  of  the  battery  ;  the 
other  pole  is  connected  with  the  carbon  d',  which  is  supported 
in  a  suitable  manner.  The  size  of  the  float  is  such  that  it  moves 
slowly  upwards,  so  that  the  carbon  d  presses  with  but  very  slight 
force  against  d'.  This  can  be  regulated  by  placing  small  weights 
in  the  collar  on  c.  An  insulated  wire  forming  part  of  the  circuit 
is  coiled  in  a  spiral  k  round  the  cylinder,  and  aids  the  regula- 
tion. 

837.    Properties   and  intensity   of  the  electric  light. —        Fig  ?40 
The   electric   light   has  similar    chemical    properties   to   solar 
light ;  it  effects  the  combination  of  chlorine  and  hydrogen,  acts  chemically 


Fig.  739- 


784  Dynamical  Electricity.  [837- 

on  chloride  of  silver,  and  can  be  applied  in  photography,  though  not  for 
taking  portraits,  as  it  fatigues  the  sight  too  greatly. 

Passed  through  a  prism,  the  electric  light,  like  that  of  the  sun,  is  decom- 
posed and  gives  a  spectrum.  Wollaston,  and  more  especially  Fraunhofer, 
found  that  the  spectrum  of  the  electric  light  differs  from  that  of  other  lights, 
and  of  sunlight,  by  the  presence  of  several  very  bright  lines,  as  has  been 
already  stated  (578).  Wheatstone  was  the  first  to  observe  that  by  using 
electrodes  of  different  metals,  the  spectrum  and  the  lines  are  modified. 

Masson,  who  experimented  upon  the  light  of  the  electric  machine,  that  of 
the  voltaic  arc,  and  that  of  Ruhmkorff's  coil,  found  the  same  colours  in  the 
electric  spectrum  as  in  the  solar  spectrum,  but  traversed  by  very  brilliant 
luminous  bands  of  the  same  shades  as  that  of  the  colour  in  which  they  occur. 
The  number  and  position  of  these  bands  do  not  depend  on  the  intensity  of 
the  light,  but,  as  we  have  seen  (833),  upon  the  substances  between  which 
the  voltaic  arc  is  formed. 

With  carbon  the  lines  are  remarkable  for  their  number  and  brilliancy  ; 
with  zinc  the  spectrum  is  characterised  by  a  very  marked  apple-green  tint ; 
silver  produces  a  very  intense  green  ;  with  lead  a  violet  tint  predominates, 
.  and  so  on  with  other  metals. 

Bunsen,  in  experimenting  with  48  couples,  and  removing  the  charcoals  to 
a  distance  of  a  quarter  of  an  inch,  found  that  the  intensity  of  the  electric 
light  is  equal  to  that  of  572  candles. 

Fizeau  and  Foucault  compared  the  chemical  effects  of  the  solar  and  the 
electric  lights  by  investigating  their  action  on  iodised  silver  plates.  Re- 
presenting the  intensity  of  the  sun's  light  at  midday  at  1000,  these  physicists 
found  that  the  light  from  a  battery  of  46  Bunsen's  elements  was  235,  while 
that  from  one  of  80  elements  was  only  238.  It  follows  that  the  intensity  does 
not  increase  to  any  material  extent  with  the  number  of  the  couples  ;  but  ex- 
periment shows  that  it  increases  considerably  with  their  surface.  For  with 
a  battery  of  46  elements,  each  consisting  of  three  elements,  with  their  zinc 
and  copper  respectively  united  so  as  to  form  one  element  of  triple  surface 
(825),  the  intensity  was  385,  the  battery  working  for  an  hour  ;  that  is  to  say, 
more  than  a  third  of  the  intensity  of  the  solar  light. 

Too  great  precautions  cannot  be  taken  against  the  effects  of  the  electric 
light  when  they  attain  a  certain  intensity.  The  light  of  loo  couples  may 
produce  very  painful  affections  of  the  eyes.  With  600,  a  single  moment's 
exposure  to  the  light  is  sufficient  to  produce  very  violent  headaches  and 
pains  in  the  eye,  and  the  whole  frame  is  affected  as  by  a  powerful  sunstroke. 
Y83§.  Electric  lighting:. — Great  progress  has  of  late  been  made  in  the 
application  of  the  electric  light  to  purposes  of  ordinary  illumination.  This 
progress  has  been  mainly  due  to  the  improvements  which  have  been  made 
in  the  means  of  generating  electricity,  for  which  some  form  of  magnetic  or 
dynamo-electrical  machine  (916),  driven  by  steam  or  water  power  or  by  gas 
engines  (476),  is  used.  So  long  as  the  electricity  from  the  voltaic  battery 
was  alone  available  for  the  production  of  the  electric  light,  no  great  exten- 
sion was  possible,  for  the  cost  and  inconvenience  were  far  too  great  to 
permit  it  to  be  used  for  anything  more  than  lecture  purposes  and  occasional 
scenic  illumination. 

Very  considerable  improvements  have  also  been  made  in  the  lamps,  which 


-838] 


Electric  Lighting. 


7«5 


are  ordinarily  divided  into  arc  lamps,  in  which  the  light  is  produced  between 
carbon  points  automatically  kept  at  a  constant  distance  by  the  action  of  the 
current  itself,  and  incandescent  lamps,  in  which  the  light  is  produced  by  the 
incandescence  of  a  thin  continuous  solid  conductor.  To  this  may  be  added 
the  electrical  candles,  of  which  the  best  known  is  the  Jablochkoff  candle.  It 
consists  (fig.  741)  of  two  rods  of  gas  carbon,  a  and  b,  from  2  to  4  mm.  in 
diameter,  separated  by  a  layer  of  kaolin  or  Chinese  clay  about  2mm.  thick, 
fixed  respectively  in  the  supports,  to  which  the  positive  and  negative 
electrodes  A  B  are  respectively  attached.  The  rods  are  insulated  from  each 
other  by  the  whole  being  bound  by  some  insulating  material. 


Fig.  741- 


Fig.  742. 


The  current  is  started  by  a  small  piece  of  carbon,  n,  placed  across  the 
top.  As  the  arc  passes,  the  kaolin  melts  away,  and  the  arrangement  may 
therefore  fitly  be  called  a  candle.  The  positive  electrode  wears  away  twice 
as  fast  as  the  negative,  which  would  soon  destroy  the  arc,  but  by  using  alter- 
nating currents  the  unequal  waste  of  the  carbons  is  prevented. 

Fig.  736,  which  represents  one  of  the  forms  of  an  arc  lamp,  may  be  taken 
as  an  example  of  the  manner  in  which  the  regulation  of  the  arc  is  effected. 

Regnier^s  electric  lamp,  fig.  742,  consists  of  a  rectangular  copper  rod,  B, 
moving  in  a  copper  tube  A,  guided  by  four  pulleys,  n,  of  which  only  two  are 
shown ;  to  B  a  cross-piece  holding  a  thin  carbon  pencil,  a,  is  fixed,  the  lower 

3E 


786  Dynamical  Electricity.  [838- 

part  of  which  passes  through  a  silver  guide,  and  its  end  presses,  but  not 
quite  over  the  centre,  against  a  carbon  disc,  m,  which  moves  about  a  hori- 
zontal axis.  The  piece  supporting  this  is  insulated  from  A,  but  is  connected 
with  the  negative  pole  by  a  wire,  b.  The  positive  current,  entering  by  A, 
passes  by  C  to  a  small  block  of  carbon,  o,  which  presses  against  the  pencil. 
Thus  the  current  only  passes  through  a  very  small  portion  of  this  pencil, 
and  it  is  this  small  portion  which  becomes  incandescent  and  forms  the  arc. 
The  rod,  as  it  burns  away  and  sinks  by  its  own  weight,  rotates  the  disc  m 
slowly,  and  prevents  its  being  irregularly  worn  away. 

When  either  of  the  carbon  electrodes  which  produce  the  electric  light  is 
increased  in  size  its  increase  of  temperature  is  lessened,  while  that  of  the 
other  is  greater.  When  the  negative  electrode  is  large  the  light  of  the 
positive  electrode  is  very  bright.  This  is  seen  in  Werdermann 's  electric 
lamp,  which  consists  essentially  of  a  carbon  disc  about  2  inches  in  diameter 
and  an  inch  in  thickness,  which  is  connected  with  the  negative  pole  of  the 
battery ;  the  positive  pole  is  a  rod  of  carbon  about  3  cm.  in  diameter,  of  any 
suitable  length ;  it  slides  vertically  in  a  copper  tube,  which  serves  both  as  a 
guide  and  as  a  contact  for  it ;  this  is  pressed  upwards  against  the  centre  by 
a  weight  passing  over  a  pulley.  The  current  can  be  passed  abreast  through 
as  many  as  ten  of  such  lamps,  though  it  seems  that  the  total  illuminating 
power  of  this  arrangement  is  not  so  great  as  when  only  two  parallel  lights 
are  employed. 

Schwendler  has  devised  a  new  unit  of  luminous  intensity,  which  he 
calls  the  platinum  light  standard,  specially  for  use  with  the  electric  light. 
It  is  the  incandescence  produced  by  a  current  of  known  strength  passing 
through  a  U-shaped  strip  of  platinum-foil  36-28  mm.  in  length,  2  mm.  in 
breadth,  and  0*017  mm.  in  thickness.  The  circuit  contains  a  rheostat  and  a 
galvanometer  by  which  the  constancy  of  the  current  can  be  ensured  and 
observed.  When  the  strength  of  the  current  is  constant  the  intensity  of  the 
light,  radiated  by  the  platinum,  is  constant  also,  and  fulfils  all  the  conditions 
of  a  standard  measure  of  light,  as  it  can  always  be  reproduced  in  exactly  the 
same  form  from  pure  platinum. 

The  standard  of  light  adopted  by  the  International  Congress  of  Electri- 
cians in  1884  is  the  light  emitted  by  a  square  centimetre  of  melted  platinum 
when  on  the  point  of  solidifying. 

According  to  Rosetti  the  temperature  of  the  positive  carbon  is  between 
2400°  and  3900°  C. ;  it  is  higher  the  smaller  is  the  radiating  surface.  The 
temperature  of  the  negative  electrode  lies  between  2138°  and  2530°. 

The  resistance  of  the  heated  air  in  the  voltaic  arc  is  from  I  to  12  ohms. 

Incandescent  lamps,  though  not  so  economical  as  arc  lights,  lend  them- 
selves best  to  the  distribution  of  the  electric  light.  We  have  seen  that  when 
a  strong  current  of  electricity  is  passed  through  a  wire  of  small  conductivity, 
its  temperature  is  raised  to  incandescence  ;  if  the  strength  of  the  current  is 
increased,  the  brightness  of  the  light  increases,  but  in  a  greater  ratio  than 
the  strength  of  the  current.  Unfortunately,  at  such  high  temperatures, 
wires  even  of  the  most  difficultly  fusible  metals  fuse  or  are  disintegrated  ; 
and  the  only  material  which  does  not  fuse  at  the  highest  temperature  is 
carbon.  The  first  lamps  in  which  this  was  applied  were  constructed  inde- 
pendently by  Edison  in  America  and  Swan  in  this  country.  Fig.  743  is  a 


-839] 


Mechanical  Effects  of  the  Battery. 


787 


Fig-  743- 


Fig.  744. 


representation  of  Swan's  lamp.  Inside  the  globular  glass  vessel  with  a  neck, 
and  fused  to  it,  is  a  glass  rod,  through  which  pass  two  platinum  wires,  bent 
outside  in  loops.  These  loops 
can  be  easily  fitted  in  the  two 
bent  wires  in  the  holder  (fig. 
744),  which  are  in  contact  with 
the  binding  screws,  and  thus 
allow  a  current  to  be  transmitted. 
The  spring  wire  exerts  an  up- 
ward pressure,  so  as  to  always 
ensure  good  contact.  To  the 
other  ends  of  the  platinum  are 
fixed  the  characteristic  part,  the 
carbon  filament;  this  is  about 
0*25  mm.  in  diameter,  and  is 
bent  in  the  form  of  a  double  loop. 
It  is  prepared  by  immersing 
crochet  cotton  in  sulphuric  acid 
of  a  certain  strength,  by  which 
it  is  converted  into  what  is 
known  as  vegetable  parchment.  This  is  then  carbonised  by  heating  it  to  a 
high  temperature  in  closed  vessels.  Before  sealing  the  bulb  it  is  exhausted 
of  air  by  means  of  a  Sprengel  pump,  and  the  vacuum  is  so  perfect  that  elec- 
tricity does  not  pass  in  it.  The  carbon  of  such  a  lamp,  which  is  a  thread 
about  i2-7  cm.  in  length,  and  0*013  cm-  m  diameter,  has  a  resistance  when 
hot  of  143  ohms  in  its  normal  incandescence.  The  efficiency  of  a  lamp  is 
generally  expressed  as  the  number  of  candles  per  horse-power  of  the  engine 
used  in  producing  the  light ;  the  average  efficiency  of  such  a  lamp  may  be 
taken  at  200,  that  of  an  arc  light  may  be  taken  at  10  times  as  much. 

In  Edison's  lamp  the  carbon  filament  is  made  of  a  special  kind  of 
bamboo  carbonised  at  high  temperatures  in  closed  nickel  moulds.  In 
the  Maxim  lamp,  and  in  that  of  Lane  Fox,  the  carbon  filaments,  after 
being  carbonised  and  mounted,  are  heated  by  the  current  itself  in  an  atmo- 
sphere of  coal  gas  or  the  vapour  of  a  hydrocarbon  ;  in  this  way  carbon 
is  deposited  on  the  filament,  by  which  it  is  rendered  more  uniform  and 
durable. 

839.  Mechanical  effects  of  the  battery. — Under  this  head  may  be  in- 
cluded the  motion  of  solids  and  liquids  effected  by  the  current.  An  example 
of  the  former  is  found  in  the  voltaic  arc,  in  which  there  is  a  passage  of  the 
molecules  of  carbon  from  the  positive  to  the  negative  pole  (834). 

The  mechanical  action  of  the  current  may  be  shown  by  means  of  the 
following  experiment  (fig.  745).  A  glass  tube,  A  B,  bent  at  the  two  ends,  about 
50  cm.  in  length  and  i  cm.  in  diameter,  is  almost  filled  with  dilute  sulphuric 
acid,  and  a  globule  of  mercury,  ;;z,  is  introduced.  The  whole  is  fixed  in  a 
support,  and  the  level  of  the  tube  can  be  adjusted  by  the  screw  /?,  the  drop 
of  mercury  itself  serving  as  index. 

When  the  two  poles  of  a  battery  of  4  or  5  cells  are  introduced  into  the  two 
ends,  the  globule  of  mercury  elongates  and  moves  towards  the  negative  pole 
with  a  velocity  which  increases  with  the  number  of  elements.  With  24,  a 

3E2 


788  Dynamical  Electricity.  [839- 

long  column  of  mercury  can  be  moved  through  a  tube  a  metre  in  length  ; 
with  50,  the  velocity  is  greater  and  the  mercury  divides  into  globules,  all 

moving  in  the  same  direc- 
tion. If  the  direction  of  the 
current  is  reversed,  the  mer- 
cury first  remains  stationary 
and  then  moves  in  the  oppo- 
site direction. 

If  the  tube  is  gently  in- 
clined  towards  the   positive 
pole,    the    mercury    is    still 
moved  with  the  current ;  and 
a  moment  is  at  length  reached 
at  which  there  is  equilibrium 
between  the  impulsive  force 
of  the  current  and  the  weight 
of  the  mercury.     The  com- 
ponent of  this  weight  parallel  to  the  plane  may  then  be  taken  as  represent- 
ing the  mechanical  action  of  the  current  which  traverses  the  globule  of 
mercury. 

A  similar  phenomenon,  known  as  electrical  endosmose,  is  observed  in  the 
following  experiment,  due  to  Porret.  Having  divided  a  glass  vessel  into  two 
compartments  by  a  porous  diaphragm,  he  poured  water  into  the  two  com- 
partments to  the  same  height,  and  immersed  two  platinum  electrodes  in 
connection  with  a  battery  of  80  elements.  As  the  water  became  decomposed, 
part  of  the  liquid  was  carried  in  the  direction  of  the  current  through  the 
diaphragm,  from  the  positive  to  the  negative  compartment,  where  the  level 
rose  above  that  in  the  other  compartment.  A  solution  of  blue  vitriol  is  best 
for  these  experiments,  because  then  the  disturbing  influence  of  the  disengage- 
ment of  gas  at  the  negative  electrode  is  avoided. 

The  converse  of  these  phenomena  is  observed  when  a  liquid  is  forced 
through  a  diaphragm  by  mechanical  means.  Such  currents,  which  were  dis- 
covered by  Quincke,  are  called  diaphragm  currents.  A  porous  diaphragm, 
/,  is  fixed  in  a  glass  tube  (fig.  746),  in  which  are  also  fused  two  platinum 
wires  terminating  in  platinum  electrodes,  a  and  b ;  on  forcing  a  liquid 
through  the  diaphragm  the  existence  of  a  current  is  evidenced  by  a  galvano- 
meter with  which  the  wires  are  connected,  the  direction  of  which  is  that  of 
the  flow  of  the  liquid.  The  difference  of  potential  due  to  this  flow  is  pro- 
portional to  the  pressure. 

According  to  Zollner,  all  circulatory  motions  in  liquids,  especially  when 
they  take  place  in  partial  contact  with  solids,  are  accompanied  by  electrical 

currents  which  have  generally 
the  same  direction  as  that  in 
which  the  current  flows. 

^  Wertheim    found    that    the 

elasticity  of  metal  wires  is  di- 

Flg'  746'  minished   by  the   current,   and 

not  by  the  heat  alone,  but  by  the  electricity ;  he  has  also  found  that  the 
cohesion  is  diminished  by  the  passage  of  a  current. 


-840] 


Electrocapillary  Phenomena. 


789 


To  the  mechanical  effects  of  the  current  may  be  assigned  the  sounds 
produced  in  soft  iron  when  submitted  to  the  magnetising  action  of  a  discon- 
tinuous current — a  phenomenon  which  will  be  subsequently  described. 

840.  Electrocapillary  phenomena. — If  a  drop  of  mercury  be  placed  in 
dilute  sulphuric  acid  containing  a  trace  of  chromic  acid,  and  the  end  of  a 
bright  iron  wire  be  so 
fixed  that  it  dips  in  the 
acid  and  just  touches  the 
edge  of  the  mercury,  the 
latter  begins  a  series  of 
regular  vibrations  which 
may  last  for  hours.  The 
explanation  of  this  phe- 
nomenon, which  was 
first  observed  by  Kiihne, 
is  as  follows  : — When  the 
iron  first  touches  the 
mercury,  an  iron-mercury 
couple  is  formed,  in 
consequence  of  which 
the  surface  of  the  mer- 
cury is  polarised  by 
the  deposition  of  an  in- 
visible layer  of  hydro- 
gen ;  this  polarisation 
(806)  increases  the  sur- 
face-tension of  the  mer- 
cury (.138),  it  becomes  _ 
rounder,  and  contact 
with  the  iron  is  broken  ; 
the  chromic  acid  present  depolarises  the  mercury,  its  original  shape  is 
restored,  the  couple  is  again  formed,  and  the  process  repeats  itself  con- 
tinuously. 

Lippmann  has  been  led  by  the  observation  of  this  phenomenon  to  a  series 
of  interesting  experimental  results,  which  have  demonstrated  a  relation 
between  capillary  and  electrical  phenomena.  Of  these  results  the  most 
important  is  the  construction  of  a  capillary  electrometer. 

A  glass  tube,  A  (fig.  747),  is  drawn  out  to  a  fine  point,  and  is  filled 
with  mercury :  its  lower  end  dips  in  a  glass  vessel,  B,  containing  mercury 
at  the  bottom  and  dilute  sulphuric  acid  at  the  top.  Platinum  wires  are 
fused  in  the  tubes  A  and  B,  and  terminate  in  the  binding  screws  a  and  b 
respectively. 

Now  at  the  beginning  of  the  experiment,  the  position  of  the  mercury  in  the 
drawn-out  tube  is  such  that  the  capillary  action  due  to  the  surface-tension 
at  the  plane  of  separation  of  the  mercury  in  the  tube  and  the  liquid,  is  suffi- 
cient to  counterbalance  the  pressure  of  the  column  A.  This  position  is 
observed  by  means  of  a  microscope,  the  focus  of  which  is  at  the  fiducial 
mark  on  the  glass  at  which  the  mercury  stops.  If  now  a  difference  of 
potential  be  established,  by  connecting  the  poles  of  a  cell  with  the  wires  a 


Fig.  747. 


790 


Dynamical  Electricity. 


[840- 


and  £,  the  surface-tension  is  increased,  the  mercury  ascends  in  the  capillary 
tube,  and  in  order  to  bring  the  meniscus  back  to  its  former  position,  the 
pressure  on  A  must  be  increased.  This  is  most  simply  effected  by  means  of 
a  thick  caoutchouc  tube,  T,  connected  with  the  top  of  A,  and  with  a  mano- 
meter, H  ;  and  which  can  be  more  or  less  compressed  by  means  of  a  screw, 
E.  The  difference  in  level  of  the  two  legs  of  the  manometer  is  thus  a 
measure  of  the  increase  of  the  surface-tension,  and  therewith  of  the  difference 
of  potential.  Lippmann  found,  by  special  experiments,  that  this  increase  is 
almost  directly  proportional  to  the  electromotive  force,  up  to  about  0-9  of  a 
DanielPs  element.  Each  electrometer  requires  a  special  table  of  graduation, 
but  when  once  this  is  constructed  it  can  be  directly  used  for  determining 
electromotive  forces.  It  should  not  be  used  for  greater  electromotive  forces 
than  0-6  of  a  Daniell ;  but  it  can  estimate  the  one-thousandth  part  of  this 
quantity,  and,  as  its  electrical  capacity  is  very  small,  it  can  show  rapid 
changes  of  potential,  which  ordinary  electrometers  cannot  do.  For  very 

small  electromotive  forces,  the 
pressure  is  kept  constant,  and  the 
displacement  of  the  meniscus  is 
measured  by  the  microscope. 
s'~.  841.  Chemical  effects. — The 
first  decomposition  effected  by  elec- 
tricity was  that  of  water,  in  1800,  by 
Carlisle  and  Nicholson,  by  means 
of  a  voltaic  pile.  Water  is  rapidly 
decomposed  by  4  or  5  Bunsen's 
cells ;  the  apparatus  (fig.  748)  is 
convenient  for  the  purpose.  It  con- 


Fig.  748. 


sists  of  a  glass  vessel  fixed  on  a 
wooden  base.  In  the  bottom  of  the 
vessel  two  platinum  electrodes,  p  and  #,  are  fitted,  communicating  by  means 
of  copper  wires  with  the  binding  screws.  The  activity  of  these  electrodes 
is  increased  by  covering  them  with  a  deposit  of  pulverulent  platinum  by 
electrolysis.  The  vessel  is  filled  with  water  to  which  some  sulphuric  acid 
has  been  added  to  increase  its  conductivity,  for  pure  water  is  a  very  imperfect 
conductor  ;  two  glass  tubes  filled  with  water  are  inverted  over  the  electrodes, 
and  on  interposing  the  apparatus  in  the  circuit  of  a  battery,  decomposition  is 
rapidly  set  up,  and  gas  bubbles  rise  from  the  surface  of  each  pole.  The 
volume  of  gas  liberated  at  the  negative  pole  is  about  double  that  at  the 
positive,  and  on  examination  the  former  gas  is  found  to  be  hydrogen  and 
the  latter  gas  oxygen.  This  experiment  accordingly  gives  at  once  the  quali- 
tative and  quantitative  analysis  of  water.  The  oxygen  thus  obtained  has 
the  peculiar  and  penetrating  odour  observed  when  an  electrical  machine  is 
worked  (793),  and  which  is  due  to  ozone.  The  water  contains  at  the  same 
time  peroxide  of  hydrogen,  in  producing  which  some  oxygen  is  consumed. 
Moreover,  oxygen  is  somewhat  more  soluble  in  water  than  hydrogen. 
Owing  to  these  causes  the  volume  of  oxygen  is  less  than  that  required  by  the 
composition  of  water,  which  is  two  volumes  of  hydrogen  to  one  of  oxygen. 
Hence  voltametric  measurements  are  most  exact  when  the  hydrogen  alone 
is  determined,  and  when  this  is  liberated  at  the  surface  of  a  small  electrode. 


-842]  Electrolysis.  79 1 

842.  Electrolysis. — The  term  electrolyte  was  applied  to  those  sub- 
stances which,  like  water,  are  resolved  into  their  elements  by  the  voltaic 
current,  by  Faraday,  to  whom  the  principal  discoveries  in  this  subject  and 
the  nomenclature  are  due.  Electrolysis  is  the  decomposition  by  the  voltaic 
battery  ;  the  positive  electrode,  or  that  by  which  positive  electricity  enters, 
was  by  Faraday  called  the  anode,  and  the  negative  electrode  the  kathode. 
The  products  of  decomposition  are  ions  ;  kation,  that  which  appears  at  the 
kathode  ;  and  anion,  that  which  appears  at  the  anode. 

By  means  of  the  battery,  the  compound  nature  of  several  substances 
which  had  previously  been  considered  as  elements  has  been  determined.  By 
means  of  a  battery  of  250  couples,  Davy,  shortly  after  the  discovery  of  the 
decomposition  of  water,  succeeded  in  decomposing  the  alkalies  potass  and 
soda,  and  proved  that  they  were  the  oxides  of  the  hitherto  unknown  metals 
potassium  and  sodium.  The  decomposition  of  potass  may  be  demonstrated, 
with  the  aid  of  a  battery  of  4  to  6  elements,  in  the  following  manner  :  a 
small  cavity  is  made  in  a  piece  of  solid  caustic  potass,  which  is  moistened, 


Fig.  749-  Fig.  750. 

and  a  drop  of  mercury  placed  in  it  (fig.  749).  The  potass  is  placed  on  a 
piece  of  platinum  connected  with  the  positive  pole  of  the  battery.  The 
mercury  is  then  touched  with  the  negative  pole.  When  the  current  passes, 
the  potass  is  decomposed,  oxygen  is  liberated  at  the  positive  pole,  while  the 
potassium  liberated  at  the  negative  pole  amalgamates  with  the  mercury.  On 
distilling  this  amalgam  out  of  contact  with  air,  the  mercury  passes  off, 
leaving  the  potassium. 

A  very  convenient  arrangement  for  the  preparation  of  metallic  magnesium 
and  some  of  the  rarer  metals  consists  of  an  ordinary  clay  tobacco  pipe  (fig.  750) 
in  the  stem  of  which  an  iron  wire  is  inserted  just  extending  to  the  bowl,  which 
is  nearly  filled  with  a  mixture  of  the  chlorides  of  potassium  and  magnesium. 
This  is  melted  by  a  Bunsen's  burner,  and  a  piece  of  graphite  connected  by  a 
wire  with  the  positive  pole  of  a  battery  is  dipped  in  it,  the  wire  in  the  stem 
forming  the  negative  pole.  When  the  current  passes,  chlorine  gas  is  liberated 
at  the  positive  pole,  while  metallic  magnesium  collects  about  the  end  of  the 
iron  wire  in  the  bowl. 

The  decomposition  of  binary  compounds — that  is,  bodies  containing  two 
elements— is  quite  analogous  to  that  of  water  and  of  potass ;  one  of  the 
elements  goes  to  the  positive  and  the  other  to  the  negative  pole.  The  bodies 


792  Dynamical  Electricity.  [842- 

separated  at  the  positive  pole  are  called  electronegative  elements,  because  at 
the  moment  of  separation  they  are  considered  to  be  charged  with  negative 
electricity,  while  those  separated  at  the  negative  pole  are  called  electro- 
positive elements.  One  and  the  same  body  may  be 
electronegative  or  electropositive,  according  to  the 
body  with  which  it  is  associated.  For  instance, 
sulphur  is  electronegative  towards  hydrogen,  but 
is  electropositive  towards  oxygen.  The  various 
elements  may  be  arranged  in  such  a  series  that  any 
one  in  combination  is  electronegative  to  any  fol- 
lowing, but  electropositive  towards  all  preceding 
ones.  This  is  called  the  electrochemical  series, 
and  begins  with  oxygen  as  the  most  electronega- 
tive element,  terminating  with  potassium  as  the 
most  electropositive. 

The  decomposition  of  hydrochloric  acid  into  its 
constituents,  chlorine  and  hydrogen,  may  be  shown 
by  means  of  the  apparatus  represented  in  fig.  751. 

Carbon  electrodes  must,  however,  be  substituted  for  those  of  platinum, 
which  is  attacked  by  the  liberated  chlorine  ;  a  quantity  of  common  salt  also 
must  be  added  to  the  hydrochloric  acid,  in  order  to  diminish  the  solubility 
of  the  liberated  chlorine.  The  decomposition  of  potassium  iodide  may  be 
demonstrated  by  means  of  a  single  element.  For  this  purpose  a  piece  of 
bibulous  paper  is  soaked  with  a  solution  of  starch,  to  which  potassium 
iodide  has  been  added.  On  touching  this  paper  with  the  electrodes,  a  blue 
spot  is  produced  at  the  positive  pole,  due  to  the  action  of  the  liberated 
iodine  on  the  starch. 

One  of  the  best  methods  of  determining  whether  a  body  is,  or  is  not,  an 
electrolyte,  is  to  place  it  between  the  two  platinum  electrodes  of  a  battery, 
and  then,  disengaging  the  electrodes  from  the  battery,  connect  it  with  a 
galvanometer,  and  observe  whether  a  reverse  current,  due  to  polarisation  of 
the  electrodes  (806)  passes  through  the  galvanometer.  Such  a  current,  being 
due  to  the  accumulation  .of  different  substances  on  the  two  electrodes,  is  a 
proof  that  the  substance  has  been  electrolytically  decomposed  by  the  original 
current  from  the  battery.  This  method  can  often  be  applied  when  it  is  dif- 
ficult, by  direct  chemical  methods,  to  detect  the  presence  of  products  of 
decomposition  at  the  electrodes. 

843.  Decomposition  of  salts. — Ternary  salts  in  solution  are  decomposed 
by  the  battery,  and  then  present  effects  varying  with  the  chemical  affinities 
and  the  intensity  of  the  current.  In  all  cases  the  acid,  or  the  body  which  is 
chemically  equivalent  to  it,  is  electronegative  in  its  action  towards  the  other 
constituent.  The  decomposition  of  salts  may  be  readily  shown  by  means  of 
the  bent  tube  represented  in  fig.  751.  This  is  nearly  filled  with  a  saturated 
solution  of  a  salt,  say  sodium  sulphate,  coloured  with  syrup  of  violets. 
The  platinum  electrodes  of  a  battery  of  four  Bunsen's  elements  are  then, 
placed  in  the  two  legs  of  the  tube.  After  a  few  minutes  the  liquid  in  the 
positive  leg,  A,  becomes  of  a  red,  and  that  in  the  negative  leg,  B,  of  a  green 
colour,  showing  that  the  salt  has  been  resolved  into  acid  which  has  passed 
to  the  positive,  and  into  a  base  which  has  gone  to  the  negative  pole,  for  these 


-844]  Transmissions  effected  by  the  Current.  793 

are  the  effects  which  a  free  acid  and  a  free  base  respectively  produce  on 
syrup  of  violets. 

In  a  solution  of  copper  sulphate,  free  acid  and  oxygen  gas  appear  at 
the  positive  electrode,  and  metallic  copper  is  deposited  at  the  negative  elec- 
trode. In  like  manner,  with  silver  nitrate,  metallic  silver  is  deposited  on 
the  negative,  while  free  acid  and  oxygen  appear  at  the  positive  electrode. 

This  decomposition  of  salts  was  formerly  explained  by  saying  that  the 
acid  was  liberated  at  the  positive  electrode  and  the  base  at  the  negative.  Thus 
potassium  sulphate,  K2OSO3,  was  considered  to  be  resolved  into  sulphuric 
acid,  SO3,  and  potash,  K2O.  This  view  regarded  salts  composed  of  three 
elements  as  different  in  their  constitution  from  binary  or  haloid  salts.  Their 
electrolytic  deportment  has  led  to  a  mode  of  regarding  the  constitution  of 
salts  which  brings  all  classes  of  them  under  one  category.  In  potassium 
sulphate,  for  instance,  the  electropositive  element  is  potassium,  while  the 
electronegative  element  is  a  complex  of  sulphur  and  oxygen,  which  is  regarded 
as  a  single  group,  SO4,  and  to  which  the  name  oxy-sulphion  may  be  assigned. 
The  formula  of  potassium  sulphate  would  thus  be  K2SO4,  and  its  decom- 
position would  be  quite  analogous  to  that  of  potassium  chloride,  KC1, 
lead  chloride,  PbCl2,  potassium  iodide,  KI.  The  electronegative  group 
SO4  corresponds  to  a  molecule  of  chlorine  or  iodine.  In  the  decomposition 
of  potassium  sulphate,  the  potassium  liberated  at  the  negative  pole  decom- 
poses water,  forming  potash  and  liberating  hydrogen.  In  like  manner  the 
electronegative  constituent  SO4,  which  cannot  exist  in  the  free  state,  decom- 
poses into  oxygen  gas,  which  is  liberated,  and  into  anhydrous  sulphuric  acid, 
SO3,  which  immediately  combines  with  water  to  form  ordinary  sulphuric 
acid,  H2SO4.y  In  fact,  where  the  action  of  the  battery  is  strong,  these  gases 
are  liberated  at  the  corresponding  poles  ;  in  other  cases  they  combine  in 
the  liquid  itself,  reproducing  water.  The  constitution  of  copper  sulphate, 
CuSO4,  and  of  silver  nitrate,  AgNO3,  and  their  decomposition,  will  be 
re^adily  understood  from  these  examples. 

^  844.  Transmissions  effected  by  the  current. — In  chemical  decomposi- 
tions effected  by  the  battery  there  is  not  merely  a  separation  of  the  elements, 
but  a  passage  of  the  one  to  the  positive  and  of  the  other  to  the  negative 
electrode.  This  phenomenon 
was  demonstrated  by  Davy  by 
means  of  several  experiments, 
of  which  the  two  following  are 
examples  : — 

i.  He  placed  solution  of  so- 
dium sulphate  in  two  capsules 
connected  by  a  thread  of  as- 
bestos moistened  with  the  same 
solution,  and  immersed  the 

positive  electrode  in  one  of  the  capsules,  and  the  negative  electrode  in  the 
other.  The  salt  was  decomposed,  and  at  the  expiration  of  some  time  all  the 
sulphuric  acid  was  found  in  the  first  capsule,  and  the  soda  in  the  second. 

ii.  Having  taken  three  glasses,  A,  B,  and  C  (fig.  752),  he  poured  into  the 
first  solution  of  sodium  sulphate,  into  the  second  dilute  syrup  of  violets, 
and  into  the  third  pure  water,  and  connected  them  by  moistened  threads 


794  Dynamical  Electricity.  [844-- 

of  asbestos.  The  current  was  then  passed  in  the  direction  from  C  to  A. 
The  sulphate  in  the  vessel  A  was  decomposed,  and  in  the  course  of  time 
there  was  nothing  but  soda  in  this  glass,  which  formed  the  negative  end, 
while  all  the  acid  had  been  transported  to  the  glass  C,  which  was  positive. 
If,  on  the  contrary,  the  current  passed  from  A  to  C,  the  soda  was  found  in  C, 
while  all  the  acid  remained  in  A  ;  but  in  both  cases  the  remarkable  pheno- 
menon was  seen  that  the  syrup  of  violets  in  B  neither  became  red  nor 
green  by  the  passage  of  the  acid  or  base  through  its  mass,  a  phenomenon  the 
explanation  of  which  is  based  on  the  hypothesis  enunciated  in  the  following 
paragraph. 

s  845.  Grothiiss  s  hypothesis. — Grothiiss  has  given  the  following  expla- 
nation of  the  chemical  decompositions  effected  by  the  battery.  Adopting  the 
hypothesis  that  in  every  binary  compound,  or  body  which  acts  as  such,  one 
of  the  elements  is  electropositive,  and  the  other  electronegative,  he  assumes 
that,  under  the  influence  of  the  contrary  electricities  of  the  electrodes,  there 
is  effected,  in  the  liquid  in  which  they  are  immersed,  a  series  of  successive 
decompositions  and  recompositions  from  one  pole  to  the  other.  Hence  it  is 
only  the  elements  of  the  terminal  molecules  which  do  not  recombine,  but 
remaining  free  appear  at  the  electrodes.  Water,  for  instance,  is  formed  of 
one  atom  of  oxygen  and  two  atoms  of  hydrogen  ;  the  first  gas  being  electro- 
negative, the  second  electropositive.  Hence  when  the  liquid  is  traversed  by 
a  sufficiently  powerful  current,  the  molecule  a  in  contact  with  the  positive 
pole  arranges  itself  as  shown  in  fig.  753 — that  is,  the  oxygen  is  attracted  and 
the  hydrogen  repelled.  The  oxygen  of  this  molecule  is  then  given  off  at  the 
positive  electrode,  the  liberated  hydrogen  immediately  unites  with  the  oxygen 
of  the  molecule  ^,  the  hydrogen  of  this  with  the  oxygen  of  the  molecule  <:, 
and  so  on,  to  the  negative  electrode,  where  the  last  atoms  of  hydrogen 
become  free  and  appear  on  the  poles.  The  same  theory  applies  to  the 
metallic  oxides,  to  the  acids  and  salts,  and  explains  why  in  the  experiment 

mentioned  in  the  preceding  para- 
graph the  syrup  of  violets  in  the 
vessel  B  becomes  neither  red  nor 
green.  The  reason  why,  in  the 
fundamental  experiment,  the  hy- 
drogen is  given  off  at  the  negative 
pole  when  the  circuit  is  closed  will 
be  readily  understood  from  a  consideration  of  this  hypothesis. 

Clausius  objects  that,  according  to  this  theory,  a  very  great  force  must 
be  required  for  overcoming  the  affinity  for  each  other  of  the  oppositely 
electrolysed  particles  of  the  compound  ;  and  that  below  a  certain  minimum 
strength  of  current  no  decomposition  could  occur.  Now  Buff  has  shown  that 
the  action  of  even  the  feeblest  currents  continued  for  a  long  time  can  pro- 
duce decomposition.  Again,  when  the  necessary  strength  of  the  current  is 
obtained,  it  should  be  sudden  and  complete  ;  whereas  we  know  it  to  be  pro- 
portional to  the  strength  of  the  current. 

To  overcome  this  difficulty  Clausius  applies  the  theory  now  generally 
admitted  of  the  constitution  of  liquids  (292).  The  particles  of  a  compound 
liquid  have  not  the  rigid  unalterable  condition  of  a  solid  body ;  they  are  in  a 
perpetual  state  of  separation  and  reunion,  so  that  we  must  suppose  compound 


-846]  Laws  of  Electrolysis.  795 

bodies  and  their  elementary  constituents  to  coexist  with  each  other  in  a  liquid. 
Water,  for  instance,  contains  particles  of  water,  together  with  particles  of 
oxygen  and  of  hydrogen  ;  the  former  are  being  continually  decomposed  and 
the  latter  continually  reunited.  When  the  voltaic  current  passes  it  acts  on 
the  motion  of  the  molecules  in  such  a  manner  that  the  negatively  electrical 
particles  of  oxygen  pass  to  the  positive  electrode,  and  the  positively  elec- 
trical particles  of  hydrogen  to  the  negative  electrode.  Hence  the  current 
does  not  bring  about  the  decomposition,  but  utilises  it,  to  give  definite 
direction  to  the  particles  which  are  already  separated. 

In  dealing  with  molecular  magnitudes,  theoretical  investigations  make  it 
probable  that  the  electrolytic  resistance,  which  the  molecules  experience  in 
their  being  moved  by  the  current,  is  of  the  same  order  of  magnitude  as  the 
capillary  resistance  which  results  from  their  friction  in  the  liquid  (147). 
Nothing  is  opposed  to  the  idea  that  electrolysis  is  a  purely  mechanical  pro- 
cess. Decomposition  occurs  in  the  first  place  by  dissociation  ;  the  differ- 
ence of  potential  is  the  force  in  virtue  of  which  the  previously  united  mole- 
cules are  urged  in  contrary  directions.  The  moving  molecules  are  the 
carriers  of  the  motion  of  electricity  and  produce  the  current ;  the  resistance 
which  they  thereby  experience  is  the  electrical  resistance  of  the  liquid.  This, 
therefore,  is  the  cause  of  the  development  of  heat  in  the  circuit. 

These  considerations  explain  why  the  conductivity  of  a  liquid  increases 
with  the  temperature  (958)  ;  for  the  velocity  of  the  molecules  (294)  and  the 
number  of  the  partial  molecules  are  thereby  increased.  It  also  shows  that  the 
conductivity  should  increase  with  the  concentration  of  the  liquid,  seeing  that 
a  great  number  01"  decomposable  molecules  must  be  favourable  to  the  move- 
ment of  electricity.  On  the  other  hand,  an  increase  in  the  number  must 
be  owing  to  the  increased  number  of  collisions  ;  hence  it  is  that,  though 
the  conductivity  increases  with  the  concentration,  it  does  so  more  slowly 
than  in  direct  ratio,  and  it  is  not  difficult  to  understand  that  for  some  liquids 
a  maximum  concentration  corresponds  to  a  maximum  conductivity, 
ytr  846.  laws  of  electrolysis. — The  laws  of  electrolysis  were  discovered 
'by  Faraday  ;  the  most  important  of  them  are  as  follows  : — 

I.  Electrolysis  cannot  take  place  unless  the  electrolyte  is  a  conductor. 
Hence  ice  is  not  decomposed  by  the  battery,  because  it  is  a  bad  conductor. 
Other  bodies,  such  as  lead  oxide,  silver  chloride,  etc.,  are  only  electrolysed 
in  a  fused  state — that  is,  when  they  can  conduct  the  current. 

II.  The  energy  of  the  electrolytic  action  of  the  current  is  the  same  in  all 
its  parts. 

III.  The  same  quantity  of  electricity — that  is,  the  same  electric  current — 
decomposes  chemically  equivalent  quantities  of  all  the  bodies  which  it  tra- 
verses ;  from  which  it  follows,  that  the  weights  of  elements  separated  in  these 
electrolytes  are  to  each  other  as  their  chemical  equivalents. 

In  a  circuit  containing  a  voltameter,  V,  Faraday  introduced  a  tube,  AB, 
containing  tin  chloride  kept  in  a  state  of  fusion  by  the  heat  of  a  spirit 
lamp  (fig.  754).  In  the  bottom  of  this  the  negative  pole  was  fused,  while  the 
positive  electrode  consisted  of  a  rod  of  graphite  ;  when  the  current  passed 
chlorine  was  liberated  at  the  positive,  while  tin  collected  at  the  negative 
pole ;  in  like  manner  lead  oxide  was  electrolysed  and  yielded  lead  at  the 
negative  and  oxygen  at  the  positive  pole.  Comparing  the  quantities  of 


Dynamical  Electricity. 


[846 


substances  liberated,  they  are  found  to  be  in  a  certain  definite  relation. 
Thus  for  every  18  parts  of  water  decomposed  in  the  voltameter  there  will 
be  liberated  2  parts  of  hydrogen,  207  parts  of  lead,  and  117  of  tin  at  the 
respective  negative  electrodes,  and  16  parts  of  oxygen,  and  71  (or  2  x  35*5) 


Fig.  754- 

parts  of  chlorine  at  the  corresponding  positive  electrodes.     Now  these  num- 
bers are  exactly  as  the  equivalents  (not  as  the  atomic  weights)  of  the  bodies. 
It  will  further  be  found  that  in  each  of  the  cells  of  the  battery  65  parts  by 
weight  of  zinc  have  been  dissolved  for  every  two  parts  by  weight  of  hydrogen 
liberated  ;  that  is,  that  for  every  equivalent  of  a  substance  decomposed  in  the 
circuit  one  equivalent  of  zinc  is  dissolved.     This  is  the  case  whatever  be  the 
number  of  cells.     An  increase  in  the  number  only  has  the  effect  of  over- 
coming the  great  resistance  which  many 
electrolytes  offer,  and  of  accelerating  the 
decomposition.     It  does  not  increase  the 
quantity   of  electrolyte  decomposed.      If 
in  any  of  the  cells  more  than  65  parts  of 
zinc  are  dissolved  for  every  two  parts  of 
hydrogen  liberated,  this  arises  from  a  dis- 
advantageous local  action  ;  and  the  more 
perfect  the  battery,  the  more  nearly  does 
it  approach  this  ratio. 

If  the  current  be  passed  in  succession 
through  a  series  of  oxides  and  of  sesqui- 
oxides,  it  is  found  that  equivalents  of  the 
metalloids,  and  not  of  the  metals,  are 
separated. 

IV.  It  follows  from  the  above  law, 
that  the  quantity  of  a  body  decomposed  in 
a  given  time  is  proportional  to  the  strength 

of  the  current.     On  this  is  founded  the 

use  of  Faraday's  voltameter,  in  which  the 
intensity  of  a  current  is  ascertained  from 
the  quantity  of  water  which  it  decomposes  in  a  given  time. 

A  convenient  form  of  this  instrument  is  that  represented  in  fig.  755.    The 
vessel  a  is  that  in  which  the  water  is  decomposed,  and  contains  two  platinum 


846] 


Laws  of  Electrolysis. 


797 


plates,  and  is  in  connection  with  the  flask  b,  which  contains  water.  In  this 
is  a  lateral  delivery  tube,  c,  which  is  inclined  until  the  level  of  the  liquid  in 
it  is  the  same  as  in  the  funnel  tube  n.  The  air  is  then  under  the  same  pres- 
sure as  the  atmosphere.  When  the  battery  is  connected  with  the  decom- 
posing cell  a,  the  gases  disengaged  expel  a  corresponding  volume  of  water 
through  the  delivery  tube  c ;  at  the  conclusion  of  the  experiment,  this  tube 
is  inclined  until  the  liquid  is  at  the  same  level  in  the  tube  n,  and  in  the 
flask.  The  weight  of  the  liquid  expelled  is  then  a  direct  measure  of  the 
volume  of  the  disengaged  gases. 

The  use  of  this  voltameter  appears  simple  and  convenient ;  and  hence 
some  physicists  have  proposed  as  unit  of  the  strength  of  current,  that  cur- 
rent which  in  one  minute  yields  a  cubic  centimetre  of  mixed  gas  reduced 
to  the  temperature  o°  and  the  pressure  760  mm.  This  is  Jacobins  unit.  It 
is  equal  to  0-09567  ampere.  Yet,  for  reasons  mentioned  before  (841),  the 
measurements  should  be  based  on  the  volume  of  hydrogen  liberated. 

PoggendorfFs  silver  voltameter,  fig.  756,  is  an  instrument  for  measuring 
the  strength  of  the  current.  A  solution  of  silver  nitrate  of  known  strength 
is  placed  in  a  platinum  dish  which  rests 
on  a  brass  plate  that  can  be  connected 
with  the  negative  pole  of  the  battery  by 
means  of  the  binding  screw  b.  In  this 
solution  dips  the  positive  pole,  which  con- 
sists of  a  rod  of  silver  wrapped  round  with 
muslin,  and  suspended  to  an  adjustable 
support.  When  the  current  passes,  silver 
separates  at  the  negative  pole,  and  is 
washed,  dried,  and  weighed  ;  and  the 
weight  thus  produced  in  a  given  time  is 
a  very  accurate  measure  of  the  strength 
of  the  current.  Some  silver  particles 
which  are  apt  to  become  detached  from 
the  positive  pole  are  retained  in  the 
muslin. 

It  has  been  found  by  experiment  that, 
when  water  is  decomposed,  a  current  of 
i  ampere  liberates  0-00001045  gramme 
or  0-1168  cc.  of  hydrogen  in  a  second  ;  * 
this,  then,  is  the  electrochemical  equiva- 
lent of  hydrogen,  and  from  this  we  can 


Flg- 


deduce  the  weight  of  any  element  liberated  in  the  same  time  by  unit  current 
if  we  multiply  it  by  the  equivalent  (not  atomic)  weight  of  the  element  referred 
to  hydrogen.  The  equivalent  of  silver  is  usually  taken  at  108  ;  hence,  if  any 
of  its  salts  are  decomposed,  the  weight  of  silver  liberated  by  an  ampere  in 
a  second  is  0-0011286  gramme;  this  is  the  electrochemical  equivalent  of 
silver,  and  similarly  that  of  copper  is  0-0003313. 

The  current  from  the  electrical  machine,  which  is  of  very  high  potential, 
is  capable  of  traversing  any  electrolyte,  but  the  quantity  which  it  can  decom- 
pose is  extremely  small  as  compared  with  even  the  smallest  voltaic  apparatus, 
and  the  quantity  of  electricity  developed  by  the  frictional  machine  is  very 


798  Dynamical  Electricity.  [846- 

small  as  compared  with  that  developed  by  chemical  action.  It  has  been 
calculated  by  Weber,  that  if  the  quantity  of  positive  electricity  required  to 
decompose  a  grain  of  water  were  accumulated  on  a  cloud  at  a  distance  of 
3,000  feet  from  the  earth's  surface,  it  would  exert  an  attractive  force  upon 
the  earth  of  upwards  of  1,500  tons. 

846^.  Migration  of  the  Ions. — From  what  has  been  said,  it  would  seem 
that  when  a  solution  of  copper  sulphate  is  electrolysed  between  copper  elec- 
trodes, for  every  equivalent  of  copper  deposited  at  the  negative  electrode, 
an  equivalent  weight  should  be  dissolved  at  the  positive,  and  the  transfer 
taking  place  as  described,  the  concentration  of  the  solution  should  remain 
unchanged.  This,  however,  is  not  the  case  ;  when  the  operation  takes 
place  without  any  agitation  of  the  solution,  the  liquid  about  the  negative 
pole  becomes  lighter  in  colour,  indicating  that  the  solution  there  is  weaker. 

This  phenomenon,  which  was  investigated  by  Hittorf,  is  ascribed  by  him 
to  the  fact  that  in  electrolysis  the  ions  or  products  of  electrolytical  decom- 
position travel  in  the  liquid  with  unequal  velocities,  each  ion  having  a  special 
velocity  in  the  liquid,  and  this  transference  is  called  the  migration  of  the 
ions.  The  number  which  expresses  the  rate  of  travel  is  called  ;/,  and  has 
this  meaning :  let  us  conceive  a  vertical  layer  in  the  liquid  the  concentration 
of  which  remains  unchanged  ;  then,  if  after  electrolysis  we  determine  the 
quantity  of  the  constituents  on  each  side,  there  is  an  increase  of  the  positive 
on  one  side  and  of  the  negative  on  the  other.  The  number  n  expresses 
then  the  ratio  of  the  number  of  molecules  of  the  anion  which  passes  through 
this  imaginary  layer  in  a  given  time  to  that  of  the  electrolyte  decomposed. 

847.  Comparison  between  the  tangent  galvanometer  and  the  volta- 
meter.— There  are  several  objections  to  the  use  of  the  voltameter.  In  the 
first  place,  it  does  not  indicate  the  strength  at  any  given  moment,  for  in  order 
to  obtain  measurable  quantities  of  gas  the  current  must  be  continued  for  some 
time.  Again,  the  voltameter  gives  no  indications  of  the  changes  which  take 
place  in  this  time,  but  only  the  mean  intensity.  It  offers  also  great  resistance, 
and  can  thus  only  be  used  in  the  case  of  strong  currents  ;  for  such  currents 
either  do  not  decompose  water,  or  only  yield  quantities  too  small  for  accurate 
measurement.  In  addition  to  this,  the  indications  of  the  voltameter  depend 
not  only  on  the  strength  of  the  current,  but  on  the  acidity  of  the  water,  and 
on  the  distance  and  size  of  the  electrodes.  But  although  it  does  not  measure 
the  strength  of  the  current  at  any  one  time,  it  does,  apart  from  accidental 
influences,  give  a  measure  of  the  total  quantity  of  electricity  that  has  passed 
within  the  period  of  observation. 

The  magnetic  measurements  are  preferable  to  the  chemical  ones.  Not 
only  are  they  more  delicate  and  offer  less  resistance,  but  they  give  the 
strength  at  any  moment.  On  the  other  hand,  indications  furnished  by  the 
tangent  galvanometer  hold  only  for  one  special  instrument.  They  vary 
with  the  diameter  of  the  ring  and  the  number  of  turns  ;  moreover,  one 
and  the  same  instrument  will  give  different  indications  on  different  places, 
seeing  that  the  force  of  the  earth's  magnetism  varies  from  one  place  to 
another  (701). 

The  indications  of  the  two  instruments  may,  however,  be  readily  com- 
pared with  one  another.  For  this  purpose  the  voltameter  and  the  tangent 
galvanometer  are  simultaneously  inserted  in  the  circuit  of  a  battery,  and  the 


-848]  Polarisation.  799 

deflection  of  the  needle  and  the  amount  of  gas  liberated  in  a  given  time  are 
noted.     In  one  set  of  experiments  the  following  results  were  obtained  : — 


Number  of  Elements 

Deflection 

Gas  liberated  in  three  minutes 

12 

28-5° 

I25CC. 

8 

24-8 

106 

6 

22-0 

93 

3 

1375 

56 

2 

6-9 

24 

If  we  divide  the  tangents  of  the  angles  into  the  corresponding  volumes  of 
gas  liberated  in  one  minute,  we  should  obtain  a  constant  magnitude  which 
represents  how  much  gas  is  developed  in  a  minute  by  a  current  which  could 
produce  on  the  tangent  galvanometer  the  deflection  45°,  for  tang.  45°  =  i. 
Making  this  calculation  with  the  above  observations,  we  obtain  a  set  of 
closely  agreeing  numbers  the  mean  of  which  is  76-5.  The  gas  was  measured 
under  a  pressure  of  737mm.  and  at  a  temperature  of  15°,  and  therefore 
under  normal  conditions  (332)  its  volume  would  be  70  cubic  centimetres. 
That  is  to  say,  this  is  the  volume  of  gas  which  corresponds  to  a  deflection 
of  45°.  Hence  in  chemical  measure  the  strength  C  of  a  current  which  pro- 
duces in  this  particular  tangent  galvanometer  a  deflection  of  $°  is 

C  =  70  tang.  <£. 

For  instance,  supposing  a  current  produced  in  this  tangent  galvanometer 
a  deflection  of  54°,  this  current,  if  it  passed  through  a  voltameter,  would 
liberate  in  a  minute  70  x  tang.  54°  =  70  x  1-376  =  96-32  cubic  centimetres  of 
gas. 

If  once  the  reduction  factor  for  a  tangent  galvanometer  has  been  deter- 
mined, the  strength  of  any  current  may  be  readily  calculated  in  chemical 
measure  by  a  simple  reading  of  the  angle  of  deflection.  This  reduction  factor 
of  course  only  holds  for  one  special  instrument,  and  for  experiments  in  the 
same  place,  seeing  that  the  force  of  the  earth's  magnetism  varies  in  different 
places. 

The  indications  of  the  sine- compass  may  be  compared  with  those  of  the 
galvanometer  in  a  similar  manner. 

/*  848.  Polarisation. — When  the  platinum  electrodes,  which  have  been 
/  used  in  decomposing  water,  are  disconnected  from  the  battery,  and  connected 
with  a  galvanometer,  the  existence  of  a  current  is  indicated  which  has  the 
opposite  direction  to  that  which  had  previously  passed.  This  phenomenon 
is  explained  by  the  fact  that  oxygen  has  been  condensed  on  the  surface  of  the 
positive  plate,  and  hydrogen  on  the  surface  of  the  negative  plate,  analogous 
to  what  has  been  already  seen  in  the  case  of  the  nonconstant  batteries  (806). 
The  effect  of  this  is  to  produce  two  different  electromotors,  which  produce  a 
current  opposed  in  direction  to  the  original  one,  and  which,  therefore,  must 
weaken  it.  As  the  two  electrodes  thus  become  the  poles  of  a  new  current, 
they  are  said  to  be  polarised,  and  the  current  is  called  a  polarisation  current. 
The  polarisation  is  not  instantaneous,  but  may  increase  continuously  from 
zero  to  a  certain  maximum  limit  which  may  be  considerable  ;  it  increases 


8oo  Dynamical  Electricity.  [848- 

with  the  strength  of  the  current,  attaining  the  force  of  2*6  volts  with  platinum 
plates  in  dilute  sulphuric  acid.  It  constitutes  a  negative  electromotive  force 
and  must  be  allowed  for  in  Ohm's  formula. 

The  quantity  of  electricity  required  to  produce  a  given  state  of  polarisa- 
tion depends  on  the  condition  and  dimensions  of  the  plate,  and  is  often 
called  the  capacity  of  polarisation  relative  to  the  given  system. 

849.  Secondary  batteries. — Ritter  was  the  first  to  show  that  on  this 
principle  batteries  might  be  constructed  of  pieces  of  metal  of  the  same  kind 
— for  instance,  platinum — which  otherwise  give  no  current.  A  piece  of 
moistened  cloth  is  interposed  between  each  pair,  and  each  end  of  this 
system  is  connected  with  the  poles  of  a  battery.  After  some  time  the  appa- 
ratus has  received  a  charge,  and  if  separated  from  the  battery  can  itself  pro- 
duce all  the  effects  of  a  voltaic  battery.  Such  batteries  are  called  secondary 
batteries.  Their  action  depends  on  an  alteration  of  the  surface  of  the  metal 
produced  by  the  electric  current,  the  constituents  of  the  liquid  with  which 
the  cloth  is  moistened  having  become  accumulated  on  the  opposite  plates  of 
the  circuit. 

Plante  first  showed  the  practical  importance  of  these  batteries.  His  ele- 
ment (fig.  757),  is  constructed  as  follows  :  A  broad  strip  of  sheet  lead  with  a 

tongue  is  laid  upon  a  second 
similar  sheet,  contact  being 
prevented  by  narrow  strips 
of  felt  ;  and  two  similar 
strips  having  been  laid  on 
the  upper  piece,  the  sheets 
are  rolled  together  so  as  to 
form  a  compact  cylinder. 
This  is  placed  in  a  vessel 
containing  dilute  sulphuric 
acid,  and,  being  connected 
by  wires  attached  to  the 

tongues  with  a  battery  of  two  Grove's  cells,  a  current  is  passed  through  it. 
The  effect  of  this  is  that  water  is  decomposed,  oxygen  being  liberated  at 
the  anode,  or  plate,  which  serves  as  positive  pole,  and  there  unites  with 
the  lead,  forming  peroxide  of  lead,  while  hydrogen  is  accumulated  at  the 
other  plate.  If  now  the  plates  are  detached  from  the  charging  battery  and 
are  connected  with  each  other,  a  powerful  polarisation  current  is  produced 
in  the  opposite  direction  to  the  primary ;  the  oxygen  of  the  peroxide  at  the 
anode  decomposes  the  dilute  acid,  combining  with  its  hydrogen,  and  so 
travels  through  to  the  other  plate,  where  it  combines  with  the  lead.  When 
these  operations  are  repeated  several  times  the  activity  of  the  element  in- 
creases, owing  in  great  measure  to  the  alteration  in  the  surfaces  which  is 
thereby  produced.  The  element  does,  in  fact,  require  some  time  and  energy 
to  charge  it.  Faure  has  made  an  improvement  in  this  direction.  It  con- 
sists in  coating  the  lead  plates  with  a  thick  paste  of  red  lead,  Pb3O4,  so  as  to 
have  about  one  gramme  to  the  square  centimetre.  This  is  kept  in  its  place 
by  a  sheet  of  parchment  paper  and  slips  of  felt,  and  is  then  coiled  up  as 
in  Plante's  (fig.  757).  When  the  current  is  passed,  the  ultimate,  effect  is 
that  the  red  lead  at  the  one  electrode  is  oxidised  to  Pb.^O4,  and  that  at  the 


-849]  Secondary  Batteries.  80 1 

other  into  metallic  lead  in  the  form  of  a  sponge,  which  therefore  exposes  a 
greater  surface. 

The  inverse  electromotive  force  of  such  a  couple  is  about  2^  times  that  of 
a  DanielPs  cell,  so  that  three  Daniell's  or  two  Grove's 
cells  are  required  to  charge  it.  In  charging,  a  con- 
siderable number  of  elements  are  joined  together  by 
their  similar  poles,  and  connected  with  the  respective 
electrodes  of  the  charging  battery  ;  the  effect  is  the 
same  as  that  of  using  a  single  element  of  a  surface 
equal  to  the  sum  of  the  surfaces  of  all  the  elements. 
By  means  of  a  specially  contrived  commutator  they 
may  be  arranged  tandem,  and  then  discharged,  and 
in  this  way  very  high  potentials  can  be  obtained.  So 
long  as  such  batteries  could  be  charged  only  from  a 
voltaic  battery  they  could  never  be  economical ;  but 
the  fact  that  after  having  been  once  charged  they 
retain  the  charge  for  a  considerable  time,  has  led  to 
their  use  in  what  is  called  'storing  electricity'  pro- 
duced by  mechanical  power  through  the  agency  of  p. 
dynamo  and  magneto-electrical  machines.  What  they 

do  is  to  store  the  products  of  chemical  decomposition,  and  that  in  a  form 
in  which  they  are  immediately  available  for  electrical  effects. 

The  following  experiments  will  give  a  fair  idea  of  the  results  produced 
by  their  means.  A  battery  of  thirty-five  cells,  each  weighing  nearly  44  kilog., 
was  connected  with  a  Siemens  dynamo  machine  (918),  in  working  which  one 
horse-power  was  employed  during  thirty-five  hours.  When  this  was  dis- 
charged through  eleven  Maxim's  lamps,  these  were  kept  lighted  for  10  hours 
40  minutes.  The  measured  work  transmitted  to  the  dynamo  machine  in  that 
time  was  9,570,000  kilogrammetres  (61).  This  accumulated  in  the  battery  an 
amount  of  electric  energy  of  6,382,000  kgm.,  or  71  per  cent.  While  the 
battery  was  being  discharged  it  yielded  3,809,000,  or  60  per  cent,  of  the  work 
stored  in  the  form  of  electricity,  which  is  therefore  equivalent  to  40  per  cent, 
of  the  work  transmitted  to  the  dynamo  machine. 

It  thus  appears  that  each  kilogramme  weight  of  battery — that  is,  the 
weight  of  the  lead  and  coating,  together  with  the  acid,  requires  a  work  of 
6,257  kilogrammetres  to  charge  it,  and  yields  2,500  kgm.  in  the  form  of 
electricity.  Each  of  the  above  lamps  gave  a  light  equal  to  1-4  Carcel  lamps — 
a  standard  lamp  much  used  in  France  and  equal  to  7-4  standard  candles  (509). 
This,  therefore,  is  equal  to  1,214  candles  for  one  hour;  hence  this  represents 
3iI35  kgm.  per  hour  per  candle,  which  is  equal  to  0-012  of  a  horse-power,  or 
an  amount  of  energy  equal  to  one  horse-power  in  the  accumulator  would 
produce  82  candles  ;  so  that  one  horse-power  in  the  engine  is  equivalent  to 
the  production  of  33  candles  when  worked  through  a  battery  of  this  kind. 

Many  instructive  comparisons  may  be  made  between  a  secondary  bat- 
tery and  a  charged  Leyden  jar.  Thus,  for  instance,  when  the  poles  of  a 
secondary  battery  have  been  connected  until  no  current  passes,  and  are 
then  disconnected  for  a  while,  a  current  in  the  same  direction  as  the  first  is 
obtained  on  again  connecting  them  \  this  is  the  residual  discharge.  The 
capacity  of  a  secondary  battery  depends  on  the  area  of  the  electrodes,  on 

3F 


802 


Dynamical  Electricity. 


[849- 


their  nature,  and  on  that  of  the  interposed  liquid,  but  not  on  the  distance 
between  them.  The  energy  of  the  Leyden  jar  is  stored  in  that  state  of  strain 
which  is  called  polarisation  of  the  dielectric  ;  in  the  secondary  battery  the 
energy  consists  in  the  products  which  are  stored  up  on  the  surface  of  the 
electrodes  in  a  state  ranging  from  chemical  combination  to  mechanical 
adherence  or  simple  juxtaposition. 

A  dry  pile  which  has  become  inactive  may  be  used  as  a  secondary 
battery.  When  a  current  is  passed  through  it,  in  a  direction  contrary  to  that 
which  the  active  battery  yields,  it  then  regains  its  activity. 

850.  Grove's  g-as  battery. — On  the  property,  which  metals  have,  of  con- 
densing gases  on  their  surfaces,  Grove  constructed  his  gas  battery,  fig.  758. 

A  single  cell 
consists  of  two 
glass  tubes,  B 
and  A,  in  each 
of  which  is 
fused  a  plati- 
num electrode, 
provided  on 
the  outside 
with  binding 
screws.  These 
electrodes  are 
made  more 
efficient  by 
being  covered 
with  finely  di- 
vided plati- 
num. One  of  the  tubes  is  partially  filled  with  hydrogen,  and  the  other  partially 
with  oxygen,  and  they  are  inverted  over  dilute  sulphuric  acid,  so  that  half 
the  platinum  is  in  the  liquid  and  half  in  gas.  On  connecting  the  electrodes 
with  a  galvanometer,  the  existence  of  a  current  is  indicated  whose  direction 
in  the  connecting  wire  is  from  the  platinum  in  oxygen  to  that  in  hydrogen ; 
so  that  the  latter  is  negative  towards  the  former.  As  the  current  passes 
through  water  this  is  decomposed  :  oxygen  is  separated  at  the  positive  plate 
and  hydrogen  at  the  other.  These  gases  unite  with  the  gases  condensed  on 
their  surface,  so  that  the  volume  of  gas  in  the  tubes  gradually  diminishes, 
but  in  the  ratio  of  one  volume  of  oxygen  to  two  volumes  of  hydrogen.  These 
elements  can  be  formed  into  a  battery  (fig.  710)  by  joining  the  dissimilar 
plates  with  one  another  just  as  they  are  joined  in  an  ordinary  battery.  One 
element  of  such  a  battery  is  sufficient  to  decompose  potassium  iodide,  and 
four  will  decompose  water. 

851.  Passive  state  of  iron. — With  polarisation  is  probably  connected  a 
very  remarkable  chemical  phenomenon,  which  many  metals  exhibit,  but  more 
especially  iron.  When  this  is  immersed  in  concentrated  nitric  acid  it  is 
unattacked.  This  condition  of  iron  is  called  the  passive  state,  and  upon  it 
depends  the  possibility  of  the  zinc-iron  battery  (810).  It  is  probable  that  in 
the  above  experiment  a  thin  superficial  layer  of  protosesquioxide  of  iron  is 
formed,  which  is  then  negative  towards  platinum. 


-853 J        A  rbor  Saturni,  or  Lead  Tree.     A  rbor  Diana.  803 

/*  852.  Xffobiii's  rings. — When  a  drop  of  acetate  of  copper  is  placed  on  a 
"silver  plate,  and  the  silver  is  touched  in  the  middle  of  a  drop  with  a  piece 
of  zinc,  there  are  formed  around  the  point  of  contact  a  series  of  copper  rings 
alternately  dark  and  light.  These  are  Nobilfs  coloured  rings.  They  may 
be  obtained  in  beautiful  iridescent  colours  by  the  following  process  :  A  solu- 
tion of  lead  oxide  in  potash  is  obtained  by  boiling  finely  powdered  litharge 
in  a  solution  of  potash.  In  this  solution  is  immersed  a  polished  plate  of 
silver  or  of  German  silver,  which  is  connected  with  the  positive  electrode  of 
a  battery  of  eight  Bunsen's  elements.  With  the  negative  pole  is  connected 
a  fine  platinum  wire  fused  in  glass,  so  that  only  its  point  projects  ;  and  this 
is  placed  in  the  liquid  at  a  small  distance  from  the  plate.  Around  this  point 
binoxide  of  lead  is  separated  on  the  plate  in  very  thin  concentric  layers,  the 
thickness  of  which  decreases  from  the  middle.  They  show  the  same  series 
of  colours  as  Newton's  coloured  rings  in  transmitted  light.  The  binoxide  of 
lead  owes  its  origin  to  a  secondary  decomposition  ;  by  the  passage  of  the 
current  some  lead  oxide  is  decomposed  into  metallic  lead,  which  is  depo- 
sited at  the  negative  pole,  and  oxygen  which  is  liberated  at  the  positive  ;  and 
this  oxygen  combines  with  some  oxide  of  lead  to  form  bioxide,  which  is 
deposited  on  the  positive  pole  as  the  decomposition  proceeds. 

The  effects  are  also  well  seen  if  a  solution  of  copper  sulphate  is  placed 
on  a  silver  plate,  which  is  touched  with  a  zinc  rod,  the  point  of  which  is 
in  the  solution  ;  for  then  a  current  is  formed  by  these  metals  and  the  liquid. 

853.  Arbor  Saturni,  or  lead  tree.  Arbor  Dianae. — When,  in  a  solu- 
tion of  a  salt,  is  immersed  a  metal  which  is  more  oxidisable  than  the  metal 
of  the  salt,  the  latter  is  precipitated  by  the  former,  while  the  immersed  metal 
is  substituted  equivalent  for  equivalent  for  the  metal  of  the  salt.  This  pre- 
cipitation of  one  metal  by  another  is  partly  attributable  to  the  difference 
in  their  affinities,  and  partly  to  the  action  of  a  current  which  is  set  up  as 
soon  as  a  portion  of  the  less  oxidisible  metal  has  been  deposited.  The 
action  is  promoted  by  the  presence  of  a  slight  excess  of  acid  in  the  solution. 

A  remarkable  instance  of  the  precipitation  of  one  metal  by  another  is 
the  Arbor  Saturni.  This  name  is  given  to  a  series  of  brilliant  ramified 
crystallisations  obtained  by  zinc  in  solutions  of  lead  acetate.  A  glass 
flask  is  filled  with  a  clear  solution  of  this  salt,  and  the  vessel  closed  with  a 
cork,  to  which  is  fixed  a  piece  of  zinc  in  contact  with  some  copper  wire. 
The  flask,  being  closed,  is  left  to  itself.  The  copper  wire  at  once  begins  to 
be  covered  with  a  moss-like  growth  of  metallic  lead,  out  of  which  brilliant 
crystallised  laminae  of  the  same  metal  continue  to  form ;  the  whole  pheno- 
menon has  great  resemblance  to  the  growth  of  vegetation,  from  which  indeed 
the  old  alchemical  name  is  derived.  For  the  same  reason  the  name  arbor 
DiancB  has  been  given  to  the  metallic  deposit  produced  in  a  similar  manner 
by  mercury  in  a  solution  of  silver  nitrate. 


3F2 


804  Dynamical  Electricity  [854- 


ELECTROMETALLURGY. 

854.  Electrometallurgy. — The  decomposition  of  salts  by  the  battery 
nas  received  a  most  important  application  in  electrometallurgy,  or  galvano- 
plastics,  or  the  art  of  precipitating  certain  metals  from  their  solutions  by 
the  slow  action  of  a  galvanic  current,  by  which  means  the  salts  of  certain 
metals  are  decomposed,  the  metal  being  deposited  on  the  negative  pole, 
while  the  acid  is  liberated  at  the  positive.  The  art  was  discovered  inde- 
pendently by  Spencer  in  England  and  by  Jacobi  in  Petersburg. 

In  order  to  obtain  a  galvanoplastic  reproduction  of  a  medal  or  any  other 
object,  a  mould  must  first  be  made,  on  which  the  layer  of  metal  is  deposited 
by  the  electric  current. 

For  this  purpose  several  substances  are  in  use,  and  one  or  the  other 
is  preferred  according  to  circumstances.  For  medals  and  similar  objects 
which  can  be  submitted  to  pressure,  gutta-percha  may  be  used  with  advan- 
tage. The  gutta-percha  is  softened  in  hot  water,  pressed  against  the  object 
to  be  copied,  and  allowed  to  cool,  when  it  can  be  detached  without  difficulty. 
For  the  reproduction  of  engraved  woodblocks  or  type,  wax  moulds  are 
now  commonly  used.  They  are  prepared  by  pouring  into  a  narrow  flat  pan 
a  suitable  mixture  of  wax,  tallow,  and  Venice  turpentine,  which  is  allowed  to 
set,  and  is  then  carefully  brushed  over  with  very  finely  powdered  graphite. 
While  this  composition  is  still  somewhat  soft,  the  woodblock  or  type  is 
pressed  upon  it  either  by  a  screw  press,  or,  still  better,  by  hydraulic  pressure. 
If  plaster  of  Paris  moulds  are  to  be  made  use  of,  it  is  essential  that  they  be 
first  thoroughly  saturated  with  wax  or  tallow  so  as  to  become  impervious  to 
water. 

In  all  cases,  whether  the  moulds  be  of  gutta-percha  or  wax,  or  any  non- 
conducting substance,  it  is  of  the  highest  importance  that  the  surface  be 
brushed  over  very  carefully  with  graphite,  and  so  made  a  good  conductor. 
The  conducting  surface  thus  prepared  must  also  be  in  metallic  contact  with 
a  wire  or  a  strip  of  copper  by  which  it  is  connected  with  the  negative  elec- 
trode. Sometimes  the  moulds  are  made  of  a  fusible  alloy  (340),  which  may 
consist  of  5  parts  of  lead,  8  of  bismuth,  and  3  of  tin.  Some  of  the  melted 
alloy  is  poured  into  a  shallow  box,  and  just  as  it  begins  to  solidify,  the  medal 
is  placed  horizontally  on  it  in  a  fixed  position.  When  the  alloy  has  become 
cool,  a  slight  shock  is  sufficient  to  detach  the  medal.  A  copper  wire  is  then 
bound  round  the  edge  of  the  mould,  by  which  it  can  be  connected  with 
the  negative  electrode  of  the  battery,  and  then  the  edge  and  the  back  are 
covered  with  a  thin  non-conducting  layer  of  wax,  so  that  the  deposit  is  only 
formed  on  the  mould  itself. 

The  most  suitable  arrangement  for  producing  an  electro-deposit  of  copper 
consists  of  a  trough  of  glass,  slate,  or  of  wood,  lined  with  india-rubber  or 
coated  with  marine  glue  (fig.  759).  This  contains  an  acid  solution  of  copper 
sulphate,  and  across  it  are  stretched  copper  rods,  B  and  D,  connected  respec- 
tively with  the  negative  and  positive  poles  of  a  battery.  By  their  copper 
conductors  the  moulds,  m,  are  suspended  in  the  liquid  from  the  negative 
rod  B,  whilst  a  sheet  of  copper,  C,  presenting  a  surface  about  equal  to  that 


-855] 


Electrogilding. 


805 


of  the  moulds  to  be  covered,  is  suspended  from  the  positive  rod  D,  at  the 
distance  of  about  2  inches,  directly  opposite  to  them. 

The  battery  employed  for  the  electric  deposition  of  metals  ought  to  be 
one  of  great  constancy,  and  Daniell's  and  Smee's  are  mostly  in  use.  The  cur- 
rents of  electricity  furnished  by  magneto-electrical  machines  of  a  special 
construction  are 
also  used  in 
large  establish- 
ments (913). 

The  copper 
plate  suspended 
from  the  posi- 
tive pole  serves 
a  double  pur- 
pose ;  it  not  only 
closes  the  cur- 
rent, but  it  keeps 
the  solution  in 
a  state  of  con- 
centration, for  the  acid  liberated  at  the  positive  pole  dissolves  the  copper, 
and  reproduces  a  quantity  of  copper  sulphate  equal  to  that  decomposed  by 
the  current. 

Another,  and  very  simple,  process  for  producing  the  electric  deposit  of 
copper  consists  in  making  use  of  what  is  in  effect  a  Daniell's  cell.  A  porous 
pot,  or  a  glass  cylinder  covered  at  the  bottom  with  bladder  or  with  vegetable 
parchment,  is  immersed  in  a  vessel  of  larger  capacity  containing  a  concen  - 
trated  solution  of  copper  sulphate.  The  porous  vessel  contains  acidulated 
water,  and  in  it  is  suspended  a  piece  of  amalgamated  zinc  of  suitable  form, 
and  having  a  surface  about  equal  to  that  of  the  mould.  The  latter  is  attached 
to  an  insulated  wire  connected  with  the  zinc,  and  is  immersed  in  the  solution 
of  copper  sulphate  in  such  a  position  that  it  is  directly  opposite  to  the 
diaphragm.  The  action  commences  by  the  mould  becoming  covered  with 
copper,  commencing  at  the  point  of  contact  with  the  conductor,  and  gradu- 
ally increasing  in  thickness  in  proportion  to  the  action  of  the  Daniell's 
element  thus  formed.  It  is  of  course  essential  in  the  process  to  keep  the  solu- 
tion of  copper  sulphate  at  a  uniform  strength,  which  is  done  by  suspending 
it  in  muslin  bags  filled  with  crystals  of  this  salt. 

How  great  is  the  delicacy  which  such  electric  deposits  can  attain  appears 
from  the  fact  that  galvanoplastic  copies  can  be  made  of  daguerreotypes,  which 
are  of  the  greatest  accuracy. 

855.  Electrogilding-. — The  old  method  of  gilding  was  by  means  of 
mercury.  It  was  effected  by  an  amalgam  of  gold  and  mercury,  which  was 
applied  on  the  metal  to  be  gilt.  The  objects  thus  covered  were  heated  in  a 
furnace,  the  mercury  volatilised,  and  the  gold  remained  in  a  very  thin  layer 
on  the  objects.  The  same  process  was  used  for  silvering  ;  but  they  were 
expensive  and  unhealthy  methods,  and  have  now  been  entirely  replaced  by 
eiectrogilding  and  electrosilvering.  Electrogilding  only  differs  from  the 
process  described  in  the  previous  paragraph  in  that  the  layer  is  thinner  and 
adheres  more  firmly.  Brugnatelli,  a  pupil  of  Volta,  appears  to  have  been 


806  Dynamical  Electricity.  [855- 

the  first,  in  1803,  to  observe  that  a  body  could  be  gilded  by  means  of  the 
battery  and  an  alkaline  solution  of  gold  ;  but  De  la  Rive  was  the  first  who 
really  used  the  battery  in  gilding.  The  methods  both  of  gilding  and  silver- 
ing owe  their  present  high  state  of  perfection  principally  to  the  improve- 
ments of  Elkington,  Ruolz,  and  others. 

The  pieces  to  be  gilt  have  to  undergo  three  processes  before  gilding. 

The  first  consists  in  heating  them  so  as  to  remove  the  fatty  matter  which 
has  adhered  to  them  in  previous  processes. 

As  the  objects  to  be  gilt  are  usually  of  what  is  called  gilding  metal  or  red 
brass,  which  is  a  special  kind  of  brass  rich  in  copper,  and  their  surface 
during  the  operation  of  heating  becomes  covered  with  a  layer  of  cupric  or 
cuprous  oxide,  this  is  removed  by  the  second  operation.  For  this  purpose 
the  objects,  while  still  hot,  are  immersed  in  very  dilute  nitric  acid,  where 
they  remain  until  the  oxide  is  removed.  They  are  then  rubbed  with  a  hard 
brush,  washed  in  distilled  water,  and  dried  in  gently  heated  sawdust. 

To  remove  all  spots  they  must  undergo  the  third  process,  which  consists 
in  rapidly  immersing  them  in  ordinary  nitric  acid,  and  then  in  a  mixture  of 
nitric  acid,  bay  salt,  and  soot. 

When  thus  prepared  the  objects  are  attached  to  the  negative  pole  of  a 
battery,  consisting  of  three  or  four  Bunsen's  or  DanielFs  elements.  They  are 
then  immersed  in  a  bath  of  gold,  as  previously  described.  They  remain  in 
the  bath  for  a  time  which  depends  on  the  thickness  of  the  desired  deposit. 
There  is  a  great  difference  in  the  composition  of  the  baths.  That  most  in 
use  consists  of  I  part  of  gold  chloride  and  10  parts  of  potassium  cyanide, 
dissolved  in  200  parts  of  water.  In  order  to  keep  the  bath  in  a  state  of  con- 
centration, a  piece  of  gold  is  suspended  from  the  positive  electrode,  which 
dissolves  in  proportion  as  the  gold  dissolved  in  the  bath  is  deposited  on  the 
objects  attached  to  the  negative  pole. 

The  method  which  has  just  been  described  can  also  be  used  for  silver, 
bronze,  German  silver,  etc.  But  other  metals,  such  as  iron,  steel,  zinc,  tin. 
and  lead,  are  very  difficult  to  gild  well.  To  obtain  a  good  coating,  they  must 
first  be  covered  with  a  layer  of  copper,  by  means  of  the  battery  and  a  bath 
of  copper  sulphate  ;  the  copper  with  which  they  are  coated  is  then  gilded, 
as  in  the  previous  case. 

856.  Electrosiivering. — What  has  been  said  about  gilding  applies  exactly 
to  the  process  of  electrosilvering.     The  difference  is  in  the  composition  of 
the  bath,  which  consists  of  2  parts  of  silver  cyanide  and  2  parts  of  potas- 
sium cyanide,  dissolved  in  250  parts  of  water.     To  the  positive  electrode  is 
suspended  a  plate  of  silver,  which  prevents  the  bath  from  becoming  poorer  ; 
the  pieces  to  be  silvered,  which  must  be  well  cleaned,  are  attached  to  the 
negative  pole.     It  may  here  be  observed  that  these  processes  succeed  best 
with  hot  solutions. 

857.  Electric  deposition  of  iron  and  nickel. — One  of  the  most  valuable 
applications  of  the  electric  deposition  of  metals  is  to  what  is  called  the 
steeling  (aderage}  of  engraved  copper  plates.     The  bath  required  for  this 
purpose  is  obtained  by  suspending  a  large  sheet  of  iron,  connected  with  the 
positive  pole  of  a  battery,  in  a  trough  filled  with  a  saturated  solution  of  sal- 
ammoniac  ;  whilst  a  thin  strip  of  iron,  also  immersed,  is  connected  with  the 
negative  pole.     By  this  means  iron  from  the  large  plate  is  dissolved  in  the 


-857]  Electric  Deposition  of  Iron  and  Nickel.  807 

sal-ammoniac,  while  hydrogen  is  given  off  on  the  surface  of  the  small  one. 
When  the  bath  has  thus  taken  up  a  sufficient  quantity  of  iron,  an  engraved 
copper  plate  is  substituted  for  the  small  negative  strip.  A  bright  deposit  of 
iron  begins  to  form  on  it  at  once,  and  the  plate  assumes  the  colour  of  a 
polished  steel  plate.  The  deposit  thus  obtained  in  the  course  of  half  an  hour 
is  exceedingly  thin,  and  an  impression  of  the  plate  thus  covered  does  not 
seem  different  from  an  uncovered  plate  ;  it  possesses,  however,  an  extraordi- 
nary degree  of  hardness,  so  that  a  very  large  number  of  impressions  can  be 
taken  from  such  a  plate  before  the  thin  coating  of  iron  is  worn  off.  When, 
however,  this  is  the  case,  the  film  of  iron  is  dissolved  off  by  dilute  nitric  acid 
and  the  plate  is  again  covered  with  the  deposit  of  iron. 

An  indefinite  number  of  perfect  impressions  may,  by  this  means,  be 
obtained  from  one  copper  plate,  without  altering  the  original  sharp  condition 
of  the  engraving. 

The  covering  of  metals  by  a  deposit  of  nickel  has  of  late  come  into  use. 
The  process  is  essentially  the  same  as  that  just  described.  The  bath  used 
for  the  purpose  can,  however,  be  made  more  directly  by  mixing,  in  suitable 
proportions,  salts  of  nickel  with  those  of  ammonia.  The  positive  pole  con- 
sists of  a  plate  of  pure  nickel.  A"  special  difficulty  is  met  with  in  the  electric 
deposition  of  nickel,  owing  to  the  tendency  of  this  metal  to  deposit  in  an  un- 
even manner,  and  then  to  become  detached.  This  is  got  over  by  frequently 
removing  the  articles  from  the  bath,  and  submitting  them  to  a  polishing 
process. 

Objects  coated  with  nickel  show  a  highly  polished  surface  of  the  charac- 
teristic bright  colour  of  this  metal.  The  coating  is  moreover  very  hard  and 
durable,  and  is  not  affected  either  by  the  atmosphere  or  even  by  sulphuretted 
hydrogen. 


8o8 


Dynamical  Electricity. 


[858- 


CHAPTER   IV. 

ELECTRODYNAMICS.      ATTRACTION   AND   REPULSION   OF   CURRENTS   BY 

CURRENTS. 


858.  Electrodynamics. — By  the  term  electrodynamics  is  understood  the 
laws  of  electricity  in  a  state  of  motion,  or  the  action  of  electric  currents  upon 
each  other  and  upon  magnets,  while  electrostatics  deals  with  the  laws  of 
electricity  in  a  state  of  rest. 

The  action  of  one  electrical  current  upon  another  was  first  investigated 
by  Ampere,  shortly  after  the  discovery  of  Oersted's  celebrated  fundamental 


Fig.  760. 

experiment  (820).     All  the  phenomena,  even  the  most  complicated,  follow 
from  two  simple  laws,  which  are — 

I.  Two  currents  which  are  parallel,  and  in  the  same  direction,  attract  one 
another. 

II.  Two  currents  parallel,  but  in  contrary  directions,  repel  one  another. 
In  order  to  demonstrate  these  laws,  the  circuit  which  the  current  traverses 

must  consist  of  two  parts,  one  fixed  and  the  other  movable.    This  is  effected 


-859] 


Rogefs  Vibrating  Spiral. 


809 


Fig.  761. 


by  the  apparatus  (fig.  760),  which  is  a  modified  and  improved  form  of  one 
originally  devised  by  Ampere. 

It  consists  of  two  brass  columns,  A  and  D,  between  which  is  a  shorter 
one.  The  column  D  is  provided  with  a  multiplier  (821)  of  20  turns,  MN  (fig. 
762),  which  greatly  increases  the  sensitiveness  of  the  instrument.  This  can 
be  adjusted  at  any  height,  and  in  any  position,  by  means  of  a  universal  screw 
clamp  (see  figs.  762-764). 

The  short  column  is  hollow,  and  in  its  interior  slides  a  brass  tube  termi- 
nating in  a  mercury  cup,  <r,  which  can  be  raised  or  lowered.  On  the  column 
A  is  another  mercury  cup  represented  in  section  at 
fig.  761  in  its  natural  size.  In  the  bottom  is  a 
capillary  aperture  through  which  passes  the  point 
of  a  sewing  needle  fixed  to  a  small  copper  ball. 
This  point  extends  as  far  as  the  mercury,  and  turns 
freely  in  the  hole.  The  movable  part  of  the  circuit 
consists  of  a  copper  wire  proceeding  from  a  small 
ball,  and  turning  in  the  direction  of  the  arrows 
from  the  cup  a  to  the  cup  c.  The  two  lower  branches  are  fixed  to  a  thin 
strip  of  wood,  and  the  whole  system  is  balanced  by  two  copper  balls, 
suspended  to  the  ends. 

The  details  being  known,  the  current  of  a  Bunsen's  battery  of  4  or  5  cells 
ascending  by  the  column 
A  (fig.  762)  to  the  cup  <z, 
traverses  the  circuit  BC, 
reaches  the  cup  <r,  descends 
the  central  column,  and 
thence  passes  by  a  wire,  P, 
to  the  multiplier  MN,  from 
whence  it  returns  to  the  bat- 
tery by  the  wire  Q.  Now  if, 
before  the  current  passes, 
the  movable  circuit  has 
been  arranged  in  the  plane 
of  the  multiplier,  with  the 
sides  B  and  M  opposite 
each  other,  when  the  cur- 
rent passes,  the  side  B  is  re- 
pelled, which  demonstrates 
the  second  law ;  for  in  the  branches  B  and  M  the  currents,  as  indicated 
by  the  arrows,  are  proceeding  in  opposite  directions. 

To  demonstrate  the  first  law  the  experiment  is  arranged  as  in  fig.  764 
— that  is,  the  multiplier  is  reversed  ;  the  current  is  then  in  the  same  direc- 
tion both  in  the  multiplier  and  in  the  movable  part ;  and  when  the  latter  is 
removed  out  of  the  plane  of  the  multiplier,  so  long  as  the  current  passes  it 
tends  to  return  to  it,  proving  that  there  is  attraction  between  the  two  parts. 

859.  Regret's  vibrating  spiral. — The  attraction  of  parallel  currents  may 
also  be  shown  by  an  experiment  known  as  that  of  Rogefs  vibrating  spiral. 
A  copper  wire  about  0*7  mm.  in  diameter  is  coiled  in  a  spiral  of  about  30 
coils  of  25  mm.  in  diameter.  At  one  end  it  is  hung  vertically  from  a  binding 


8io 


Dynamical  Electricity. 


[859- 


screw,  while  the  other  just  dips  in  a  mercury  cup.  On  passing  the  current 
of  a  battery  of  3  to  5  Grove's  cells  through  the  spiral  by  means  of  the  mer- 
cury cup  and  the  binding  screw,  its  coils  are  traversed  by  parallel  currents  ; 
they  therefore  attract  one  another,  and  rise,  and  thus  the  contact  with  the 
mercury  is  broken.  The  current  having  thus  ceased,  the  coils  no  longer 
attract  each  other,  they  fall  by  their  own  weight,  contact  with  the  mercury 
is  re-established,  and  the  series  of  phenomena  are  indefinitely  produced. 
The  experiment  is  still  more  striking  if  a  magnetised  rod  the  thickness  of  a 
pencil  is  introduced  into  the  interior.  This  will  be  intelligible  if  we  consider 
the  action  between  the  parallel  Amperian  currents  of  the  magnet  and  of  the 
helix. 

860.  Laws  of  angular  currents. — I.  Two  rectilinear  currents,  the  direc- 
tions of  which  form  an  angle  with  each  other,  attract  one  another  when  both 
approach,  or  recede  from,  the  apex  of  the  angle. 

II.  They  repel  one  another,  if  one  approaches  and  the  other  recedes  from 
the  apex  of  the  angle. 

These  two  laws  may  be  demonstrated  by  means  of  the  apparatus  above 

described,  replac- 
ing  the  movable 
circuit  by  the  cir- 
cuit BC.  If  then 
the  multiplier  is 
placed  horizontally, 
so  that  its  current 
is  in  the  same  direc- 
tion as  in  the  mov- 
able current,  if  the 
latter  is  removed 
and  the  current 
passes  so  that  the 
direction  is  the 
same  as  in  the 
movable  part,  on 
removing  the  latter  it  quickly  approaches  the  multiplier,  which  verifies  the 
first  law. 

To  prove  the  second  law,  the  multiplier  is  turned  so  that  the  currents  are 
in  opposite  directions,  and  then  repulsion  ensues  (fig.  763). 

In  a  rectilinear  current  each  element  of  the  current  repels  the  succeeding 
one,  and  is  itself  repelled. 

This  is  an  important  consequence  of  Ampere's  law,  and  may  be  experi- 
mentally demonstrated  by  the  following  arrangement,  which  was  devised 
by  Faraday.  A  U-shaped  piece  of  copper  wire,  whose  ends  dip  in  two 
separate  deep  mercury  cups,  is  suspended  from  one  end  of  a  delicate  balance 
and  suitably  equipoised.  When  the  mercury  cups  are  connected  with  the 
two  poles  of  a  battery,  the  wire  rises  very  appreciably,  and  sinks  again 
to  its  original  position  when  the  current  ceases  to  pass.  The  current  passes 
into  the  mercury  and  into  the  wire  ;  but  from  the  construction  of  the  appa- 
ratus the  former  is  fixed,  while  the  latter  is  movable,  and  is  accordingly 
repelled. 


Fig.  763. 


-862] 


Action  of  an  Infinite  Current. 


811 


86 1.  Xiaws    of  sinuous    currents. —  The  action  of  a   sinuous  current 
is  equal  to  that  of  a   rectilinear  current  of  the  same  length  in  projection. 
This  principle  is  demon- 
strated by  arranging  the 

multiplier  vertically  and 
placing  near  it  a  movable 
circuit  of  insulated  wire 
half  sinuous  and  half 
rectilinear  (fig.  764).  It 
will  be  seen  that  there 
is  neither  attraction  nor 
repulsion,  showing  that 
the  action  of  the  sinuous 
portion  mn  is  equalled 
by  that  of  the  rectilinear 
portion. 

An  application  of  this 
principle     will    presently 

be  met  with   in   the   ap-  Fig.  764. 

paratus    called    solenoids 

(874),  which  are  formed  of  the  combination  of  a  sinuous  with  a  rectilinear 
current. 

0  •___  DIRECTION   OF   CURRENTS   BY  CURRENTS. 

862.  Action  of  an  infinite  current  on  a  current  perpendicular  to  its 
direction. — From  the  action  exerted  between  two  angular  currents  (860)  the 
action  of  a  fixed  and  infinite  rectilinear  current,  PQ  (fig.  765),  on  a  movable 
current,  KH,  perpendicular  to  its  direction  can  be  determined.     Let  OK  be 
the  perpendicular  common  to  KH  and  PQ,  which  is  null  if  the  two  lines  PQ 


H  0 

Fig.  765.  Fig.  766. 

and  KH  meet.  The  current  PQ  flowing  from  Q  to  P  in  the  direction  of  the 
arrows,  let  us  first  consider  the  case  in  which  the  current  KH  approaches  the 
current  QP.  From  the  first  law  of  angular  currents  (860)  the  portion  PQ  of 
the  current  PQ  attracts  the  current  KH,  because  they  both  flow  towards  the 
summit  of  the  angle  formed  by  their  directions.  The  portion  PO,  on  the  con- 
trary, will  repel  the  current  KH,  for  here  the  two  currents  are  in  opposite 
directions  at  the  summit  of  the  angle.  If  then  mq  and  mp  stand  for  the  two 
forces,  one  attractive  and  the  other  repulsive,  which  act  on  the  current  KH, 
and  which  are  necessarily  of  the  same  intensity,  since  they  are  symmetrically 


812 


Dynamical  Electricity. 


[862- 


arranged  in  reference  to  the  two  sides  of  the  point  O,  these  two  forces  may 
be  resolved  into  a  single  force,  mn,  which  tends  to  move  the  current  KH 
parallel  to  the  current  QP,  but  in  a  contrary  direction. 

A  little  consideration  will  show  that  when  the  current  KH  is  below  the 
current  PQ,  its  action  will  be  the  opposite  of  what  it  is  when  above. 

On  considering  the  case  in  which  the  current  KH  moves  away  from  PQ 
(fig.  766),  it  will  be  readily  seen  from  similar  considerations  that  it  moves 
parallel  to  this  current,  but  in  the  same  direction. 

Hence  follows  this  general  principle.  A  finite  movable  current  which 
approaches  a  fixed  infinite  current  is  acted  on  so  as  to  move  in  a  direction 
parallel  and  opposite  to  that  of  the  fixed  current;  if  the  movable  current 
tends  from  the  fixed  current,  it  is  acted  on  so  as  to  move  parallel  to  the 
current  and  in  the  same  direction. 

It  follows  from  this,  that  if  a  vertical  current  is  movable  about  an  axis, 
XY,  parallel  to  its  direction  (figs.  767  and  768),  any  horizontal  current  PQ, 


Fig.  767. 


Fig.  768. 


will  have  the  effect  of  turning  the  movable  current  about  its  axis,  until  the 
plane  of  the  axis  and  of  the  current  have  become  parallel 'to  PQ  ;  the  vertical 
current  stopping,  in  reference  to  its  axis,  on  the  side  from  which  the  current 
PQ  comes  (fig.  767),  or  on  the  side  towards  which  it  is  directed  (fig.  768), 
according  as  the  vertical  current  descends  or  ascends — that  is,  according  as  it 
approaches  or  moves  from  the  horizontal  axis. 

It  also  follows  from  this  principle  that  a  system  of  two  vertical  currents 

rotating  about  a 


X 

vertical  axis 

J 

(figs.  769  and 
770)  is  directed 
by  a  horizontal 
current,  PQ,  in 
a  plane  parallel 

p 

Y 

to  this  current 

Fig.  769. 


Fig.  770. 


the 

rents  is  ascend- 
ing and  the  other  descending  (fig.  769) ;  but  that  if  they  are  both  ascending 
or  both  descending  (fig.  770),  they  are  not  directed. 

863.  Action  of  an  infinite  rectilinear  current  on  a  rectangular  or 
circular  current. —  It  is  easy  to  see  that  a  horizontal  infinite  current  exer- 
cises the  same  directive  action  on  a  rectangular  current  movable  about  a 


-864] 


Rotation  of  a  Finite  Horizontal  Current. 


813 


— TIH 


vertical  axis  (fig.  771)  as  what  has  been  above  stated.  For,  from  the-directionot 
the  currents  indicated  by  the  arrows,  the  part  QY  acts  by  attraction  not 
only  on  the  horizontal  portion  YD  (law  of  angular 
currents),  but  also  on  the  vertical  portion  AD 
(law  of  perpendicular  currents).  The  same 
action  evidently  takes  place  between  the  part 
PY  and  the  parts  CY  and  BC.  Hence,  the  fixed 
current  PQ  tends  to  direct  the  movable  rect- 
angular current  ABCD  into  a  position  parallel 
ta  PQ,  and  such  that  in  the  wires  CD  and  PQ 
the  direction  of  the  two  currents  is  the  same. 

This  principle  is  readily  demonstrated  by  p 
placing  the  circuit  ABCD  on  the  apparatus  with  ~~ 
two  supports  (fig.  771),  so  that  at  first  it  makes 
an  angle  with  the  plane  of  the  supports.  On 
passing  the  circuit  below  a  somewhat  powerful  current  in  the  same  plane  as 
the  supports,  the  movable  part  passes  into  that  plane.  It  is  best  to  use  the 
circuit  in  fig.  779,  which  is  astatic,  while  that  of  fig.  771  is  not. 

What  has  been  said  about  the  rectangular  current  in  fig.  771  applies  also 
to  circular  currents,  and  is  demonstrated  by  the  same  experiments. 


Fig.  771. 


,-  ROTATION  OF  CURRENTS   BY  CURRENTS. 

\S 

864.  Rotation  of  a  finite  horizontal  current  by  an  infinite  horizontal 
rectilinear  current. — The  attractions  and  repulsions  which  rectangular 
currents  exert  on  one  another 
may  readily  be  transformed 
into  a  continuous  circular  mo- 
tion. Let  OA  (fig.  772)  be  a 
current  movable  about  the 
point  O  in  a  horizontal  plane, 
and  let  PQ  be  a  fixed  infinite 
current  also  horizontal.  As 
these  two  currents  flow  in  the 


P    / 


direction  of  the   arrows,  it  fol- 


Fig.  772. 


Fig.  773- 


lows  that  in  the  position  OA  the  movable  current  is  attracted  by  the  current 
PQ,  for  they  are  in  the  same  direction.  Having  reached  the  position  OA', 
the  movable  current  is  attracted  by  the  part  N  Q  of  the  fixed  current,  and 
repelled  by  the  part  PN.  Similarly,  in  the  position  OA",  it  is  attracted  by 
MQ  and  repelled  by  PM,  and  so  on  ;  from  which  follows  a  continuous  rota- 
tory motion  in  the  direction  AA'A^A"'.  If  the  movable  current,  instead  of 
being  directed  from  O  towards  A,  were  directed  from  A  towards  O,  it  is 
easy  to  see  that  the  rotation  would  take  place  in  the  contrary  direction. 
Hence,  by  the  action  of  a  fixed  infinite  current,  PQ,  the  movable  current 
OA  tends  to  a  continuous  motion  in  a  direction  opposite  to  that  of  the  fixed 
current. 

If,  both  currents  being  horizontal,  the  fixed  current  were  circular  instead 
of  being  rectilinear,  its  effect  would  still  be  to  produce  a  continuous  circular 


8 14  Dynamical  Electricity.  [864- 

motion.  For,  let  ABC  (fig.  773)  be  a  fixed  circular  current,  and  mn  a  rec- 
tilinear current  movable  about  the  axis  n,  both  currents  being  horizontal. 
These  currents,  flowing  in  the  direction  of  the  arrows,  would  attract  one 
another  in  the  angle  «AC,  for  they  both  flow  towards  the  summit  (860).  In 
the  angle  TzAB,  on  the  contrary,  they  repel  one  another,  for  one  goes  towards 
the  summit  and  the  other  moves  from  it.  Both  effects  coincide  in  moving 
the  wire  mn  in  the  same  direction  ACB. 

865.  Rotation  of  a  vertical  current  by  a  Horizontal  circular  current. 
A  horizontal  circular  current,  acting  on  a  rectilinear  vertical,  also  imparts  to 
it  a  continuous  rotatory  motion.     In  order  to  show  this,  the  apparatus  repre- 
sented in  fig.  774  is  used. 

It  consists  of  a  brass  vessel,  round  which  are  rolled  several  coils  of  in- 
sulated copper  wire,  through  which  a  current  passes.  In  the  centre  of  the 
vessel  is  a  brass  support,  <z,  terminated  by  a  small  cup  containing  mercury. 
In  this  dips  a  pivot  supporting  a  copper  wire,  bb,  bent  at  its  ends  in  two  ver- 
tical branches,  which  are  soldered  to  a  very  light  copper  ring  immersed  in 
acidulated  water  contained  in  the  vessel.  A  current  entering  through  the 
wire  ;;/,  reaches  the  wire  A,  and  having  made  several  circuits,  terminates 
at  B,  which  is  connected  by  a  wire  underneath  with  the  lower  part  of 
the  column  a.  Ascending  in  this  column,  it  passes  by  the  wires  bb  into 

the  copper  ring, 
into  the  acidu- 
lated water,  and 
into  the  sides 
of  the  vessel, 
whence  it  re- 
turns to  the 
battery  by  the 
strip  D.  The 

• 
^^^     thus  closed,  the 

*=»•  774*  •         •  f       77  i 

circuit    bb    and 

the  ring  tend  to  turn  in  a  direction  contrary  to  that  of  the  fixed  current,  a 
motion  due  to  the  action  of  the  circular  current. on  the  current  in  the  vertical 
branches  bb  ;  for,  as  follows  from  the  two  laws  of  angular  currents,  the 
branch  b  on  the  right  is  attracted  by  the  portion  A  of  the  fixed  current,  and 
the  branch  b  on  the  left  is  attracted  in  the  contrary  direction  by  the  opposite 
part,  and  these  two  motions  coincide  in  giving  the  ring  a  continuous  rotatory 
motion  in  the  same  direction.  The  action  of  the  circular  current  on  the 
horizontal  part  of  the  circuit  bb  would  tend  to  turn  it  in  the  same  direction  ; 
but  from  its  distance  it  may  evidently  be  neglected. 

866.  Rotation  of  magrnets  by  currents. — Faraday  proved  that  currents 
impart  the  same  rotatory  motions  to  magnets  which  they  do  to  currents.   This 
maybe  shown  by  means  of  the  apparatus  represented  in  fig.  775.    It  consists 
of  a  large  glass  vessel,  almost  filled  with  mercury.     In  the  centre  of  this  is 
immersed  a  magnet,  A,  about  eight  inches  in  length,  which  projects  a  little 
above  the  surface  of  the  mercury,  and  is  loaded  at  the  bottom  with  a  pla- 
tinum  cylinder.     At  the  top  of  the  magnet  is  a  small   cavity  containing 
mercury  ;    the   current   ascending  the   column  m   passes   into  this   cavity 


-866] 


Rotation  of  Magnets  by  Currents. 


815 


Fig.  775- 


Fig.  776. 


by  the  rod  C.  From  the  magnet  it  passes  by  the  mercury  to  a  copper 
ring,  G,  whence  it  emerges  by  the  column  n.  When  this  takes  place 
the  magnet  begins  to  rotate  round  its  own  axis  with  a  velocity  de- 
pending on  its 
magnetic  power 
and  on  the  in- 
tensity of  the 
current. 

Instead  of 
making  the 
magnet  rotate 
on  its  axis,  it 
may  be  caused 
to  rotate  round 
a  line  parallel 
to  its  axis  by 
arranging  the 
experiment,  as 
shown  in  fig. 

779- 

This  rotatory 

motion  is  readily  intelligible  on  Ampere's  theory  of  magnetism  (879),  ac- 
cording to  which,  magnets  are  traversed  on  their  surface  by  an  infinity 
of  circular  currents  in  the  same  direction,  in  planes  perpendicular  to  the 
axis  of  the  magnet.  At  the  moment  at  which  the  current  passes  from 
the  magnet  into  the  mercury,  it  divides  on  the  surface  of  the  mercury  into 
an  infinity  of  rectilinear  currents  proceeding  from  the  axis  of  the  magnet  to 
the  circumference  of  the  glass.  Figs.  777  and  778,  which  correspond  re- 
spectively to  figs.  775  and  776,  give  on  a  larger  scale,  and  on  a  horizontal 
plane  passing  through  the  surface  of  the  mercury,  the  direction  of  the  currents 
to  which  the  rotation  is  due.  In  fig.  777  the  north  pole  being  at  the  top,  the 
Amperian  currents  pass  round  the  magnet  in  the  reverse  direction  to  that 
of  the  hands  of  a  watch,  as  indicated  by  the  arrow  f  (879),  while  the  cur- 
rents which  radiate 
from  the  rod  C 
towards  the  metal 
ring  GG',  have 
the  direction  CD, 
CE.  Thus  (860) 
any  given  element 
e  of  the  magnetic 
current  of  the  bar 
A  is  attracted  by 
the  current  CE 
and  repelled  by  the 
current  CD  ;  hence 

results  a  rotation  of  the  bar  about  its  axis  in  the  same  direction  as  the  hands 
of  a  watch. 

In  fig.  778  the  currents  CD,  CE  being  in  the  opposite  direction  to  those 


777t 


Fig.  778. 


8i6 


Dynamical  Electricity. 


[866- 


of  the  bar  would  repel  the  latter,  which  would  be  attracted  by  the  currents 
CE,  CA.  Hence  the  bar  rotates  in  a  circular  direction,  shown  by  the  arrow 
s,  about  the  vertical  axis  which  passes  through  the  rod  C. 

If  the  north  pole  is  below,  or  if  the  direction  of  the  current  be  altered,  the 
rotation  of  the  magnet  is  in  the  opposite  direction. 


ACTION   OF  THE  EARTH  AND   OF  MAGNETS   ON  CURRENTS. 

867.  Directive  action  of  magnets  on  currents. — Not  only  do  currents 
act  upon  magnets,  but  magnets  also  act  upon  currents.  In  Oersted's  funda- 
mental experiment  (fig.  719),  the  magnet  being  movable  while  the  current  is 
fixed,  the  former  is  directed  and  sets  at  right  angles  with  the  current.  If, 
on  the  contrary,  the  magnet  is  fixed  and  the  current  movable,  the  latter  is 
directed  and  sets  across  the  direction  of  the  magnet.  This  may  be  illus- 
trated by  the  apparatus  represented  in  fig.  779.  This  is  the  original  form 
of  Amperes  stand,  and  is  frequently  used  in  experimental  demonstration. 
It  needs  no  explanation.  The  circuit  which  the  current  traverses  is  movable, 
and  below  its  lower  branch  a  powerful  bar  magnet  is  placed  ;  the  circuit 
immediately  begins  to  turn,  and  stops  after  some  oscillations  in  a  plane 
perpendicular  to  the  axis  of  the  magnet. 


Fig.  779. 


Fig.  780. 


For  demonstrating  the  action  of  magnets  upon  currents,  De  la  Rive's 
floating  battery  (fig.  780)  is  well  adapted.  It  consists  of  plates  of  zinc  and 
copper  which  are  immersed  in  dilute  ^ulphuric  acid  contained  in  a  glass 
bulb  slightly  loaded  with  mercury  to  keep  it  upright,  and  which  can  float 
freely  on  water.  With  the  plates  can  be  connected  either  circular  or  rect- 
angular wires,  coils,  or  solenoids  ;  they  are  then  traversed  by  a  current,  and 
can  be  subjected  to  the  action  either  of  magnets  or  of  currents. 


-869]  Electrodynamic  and  Electromagnetic  Rotation  of  Liquids.  8 1 7 

868.  Rotation    of  currents  by  magnets.— Not    merely   can    currents 
be  directed  by  magnets,  but  they  may  also  be  made  to  rotate,  as  is  seen 
from   the   following  experiment,  devised  by 

Faraday  (fig.  781).  On  a  base  with  levelling 
screws,  and  resting  on  an  ivory  support, 
is  a  copper  rod,  BD.  It  is  surrounded  in 
part  of  its  length  by  a  bundle  of  magnetised 
wires,  AB,  and  at  the  top  is  a  mercury 
cup.  A  copper  circuit,  EF,  balanced  on  a 
steel  point,  rests  in  the  cup,  and  the  other 
ends  of  the  circuit,  which  terminate  in  steel 
points,  dip  in  an  annular  trough  full  of  mer- 
cury. 

The  apparatus  being  thus  arranged,  the 
current  from  4  or  5  Bunsen's  elements  enters 
at  the  binding  screw  b  •  it  thence  rises  in 
the  rod  D,  descends  by  the  two  branches, 
reaches  the  mercury  by  the  steel  points, 
whence  it  passes  by  the  framework,  which  is 
of  copper,  to  the  battery  by  the  binding  screw 
a.  If  now  the  magnetised  bundle  be  raised, 
the  circuit  EF  rotates,  either  in  one  direction 
or  the  other,  according  to  the  pole  by  which 
it  is  influenced.  This  rotation  is  due  to  cur- 
rents assumed  to  circulate  round  magnets  ; 
currents  which  act  on  the  vertical  branches 
EF  in  the  same  way  as  the  circular  current 
on  the  branches  bb  in  fig.  774. 

In  this  experiment  the  magnetised  bundle  Fig  ?8l 

may  be  replaced  by  a  solenoid  (874)  or  by 

an  electromagnet,  in  which  case  the  two  binding  screws  in  the  base  of  the 
apparatus  on  the  left  give  entrance  to  the  current  which  is  to  traverse  the 
solenoid  or  electromagnet. 

869.  Electrodynamic  and  electromagnetic  rotation  of  liquids. — The 
condition  of  a  linear  current  assumed  in  the  previous  experiments  is  not 
necessary.     Fig.  782  represents  an  apparatus  devised  by  Bertin  to  show  the 
electrodynamic  and  electromagnetic  rotation  of  liquids.     This   apparatus 
consists  of  an  annular  earthen  vessel,  VV  ;  that  is  to  say,  it  is  open  in  the 
centre  so  as  to  be  traversed  by  a  coil,  H.     It  rests  on  a  board  which  can  be 
raised  along  two  columns,  E  and  I,  and  which  are  fixed  by  means  of  the 
screws  KK.     Round  the  vessel  VV  is  a  second  larger  coil,  G,  fixed  on  the 
columns  SS'.      The  vessel  V  V  rests  on  the  lower  plane.    In  the  centre  of 
the  coil  is  a  bar  of  soft  iron,  .r,  which  makes  an  electromagnet. 

The  vessel  VV  contains  acidulated  water,  and  in  the  liquid  are  two 
cylindrical  copper  plates  e  and  z,  soldered  to  copper  wire's,  e'  and  /',  which 
convey  the  current  of  a  battery  of  four  cells  through  the  rods  E  and  I.  The 
whole  system  is  arranged  on  a  larger  base,  on  the  left  of  which  is  a  commu- 
tator represented  afterwards  on  a  larger  scale  (fig.  783).  With  the  base  of 
the  columns  E,  I,  S  and  S'  are  connected  four  copper  strips,  three  of  which 

3G 


8i8 


Dynamical  Electricity. 


[869- 


lead  to  the  commutator  and  the  fourth  to  the  binding  screw   A,  which 

receives  the  wire  from  the  positive  pole. 

The  following  three  effects  maybe  obtained  with  this  apparatus  : — (i),  the 

action  of  the  coil  G  alone  ;  (2),  the  action  of  the  electromagnet  H  alone  ; 

(3),  the  simultaneous  action  of  the  coil  and  of  the  electromagnet. 

I.  Fig.  782  represents  the  apparatus  arranged  for  the  first  effect.     The 

current  coming 
by  the  binding 
screw  A  attains 
the  column  S', 
which  leads  it 
to  the  coil  G, 
with  regard  to 
which  it  is  left — 
that  is,  in  a  con- 
trary direction 
to  the  hands  of 
a  watch.  'Then 
descending  by 
the  column  S,  it 
reaches  the  com 
mutator,  which 
leads  it  by  the 
plate  marked 
centripete  to  the 
column  E  and 
to  the  electrode 


Fig.  782. 


e'.  The  current  here  traverses  the  liquid  from  the  circumference  to  the 
centre,  attains  the  electrode  /,  the  column  I,  and  by  the  intervention  of  the 
plate  centrifuge  the  central  piece  of  the  commutator.  This  transmits  it 
finally  to  the  negative  binding  screw,  which  leads  it  to  the  battery.  The 
liquid  then  commences  a  direct  rotatory  motion — that  is  to  say,  in  the 
same  direction  as  the  coil.  If  the  direction  of  the  current  in  the  liquid  is 
centrifugal—  that  is,  proceeds  from  the  centre  to  the  circumference — the 
rotation  is  inverse  ;  that  is,  in  the  opposite  direction  to  that  of  the  coil. 
In  both  cases  the  rotations  may  be  shown  to  those  at  a  distance  by  means 
of  small  flags,  f,  fy  fixed  on  discs  of  cork  which  float  on  the  liquid,  and 
which  are  coated  with  lampblack  to  prevent  adherence  by  capillary  attraction 
between  the  discs  and  the  electrodes  e  and  i. 

II.  To  experiment  with  the  electromagnet  alone,  the -positive  wire  of  the 
battery  is  connected  with  the  binding  screw  C,  and  the  binding  screws  D  and 
B  are  joined  by  a  copper  wire.  The  current  first  passes  into  the  electromagnet 
H,  then,  reaching  the  commutator  by  the  binding  screw  B,  passes  into  the 
centripetal  plate,  whence  it  rises  in  the  column  E,  traverses  the  liquid  in  the 
same  direction  as  at  first,  reascends  by  the  column  I,  and  from  thence  to 
the  centre  of  the  commutator  and  the  negative  binding  screw  which  leads  it 
to  the  battery.  If  the  north  pole  of  the  electromagnet  is  at  the  same  height 
as  the  glass  vessel,  as  in  the  figure,  the  Amperian  currents  move  in  the 
opposite  direction  to  the  hands  of  a  watch,  and  the  floats  then  move  in  the 


-870]  Bertiris  Commutator.  819 

same  direction  as  above ;  and  if  the  electromagnet  is  raised  until  the  neutral 
line  is  at  the  same  height  as  the  vessel,  the  floats  stop  ;  if  it  is  above  them, 
the  floats  move  again,  but  in  the  opposite  direction. 

III.  To  cause  the  coil  and  the  electromagnet  to  act  simultaneously,  the 
positive  wire  of  the  battery  is  attached  at  C,  and  the  binding  screws  D  and 
A.  are  connected  by  a  conductor.  Hence,  after  having  traversed  the  coil  H, 
the  current  arrives  from  D,  and  the  binding  screw  A,  whence  it  traverses 
exactly  the  same  circuit  as  in  the  first  experiments.  The  effects  are  the 
same,  though  more  intense ;  the  action  of  the  coil  and  the  electromagnet 
being  in  the  same  direction. 

A  simpler  form  of  this  experiment  was  devised  by  Clerk  Maxwell.  At 
the  bottom  of  a  small  beaker,  a  copper  disc  is  placed  with  an  insulated 
tongue  bent  at  right  angles,  and  connected  with  a  similar  zinc  disc  supported 
about  an  inch  above  the  copper.  Dilute  acid  is  placed  so  as  to  cover  both 
discs,  and  some  fine  sawdust  having  been  added  to  the  liquid  the  whole  is 
placed  on  the  pole  of  an  electromagnet.  The  rotation  of  the  liquid  is  then 
shown  by  that  of  the  sawdust. 

870.  Berlin's  commutator. — Commutators  are  apparatus  by  which  the 
direction  of  currents  may  be  changed  at  pleasure,  or  by  which  they  may  be 
opened  or  closed.  Bertin's  has  the  advantage  of  at  once  showing  the  direc- 
tion of  the  current.  It  consists  of  a  small  base  of  hard  wood  on  which  is  an 
ebonite  plate,  which,  by  means  of  the  handle  m  (fig.  783),  is  turned  about  a 
central  axis,  between  two  stops,  c  and  c*.  On  the  disc  are  fixed  two  copper 
plates,  one  of  which,  o,  is  always  positive,  being  connected  by  the  axis  and 
by  a  plate,  + ,  with  the  binding  screw  P,  which  receives  the  positive  electrode 
of  the  battery  ;  the  other,  z>,  bent  in  the  form  of  a  horseshoe,  is  connected 
by  friction  below  the  disc  with  a  plate — which  passes  to  the  negative  elec- 
trode N.  On  the  opposite  side  of  the  board  are  two  binding  screws,  b  and 
b\  to  which  are  adapted  two  elastic  metal  plates,  r  and  r*. 

These  details  being 
premised,  the  disc  being 
turned  as  shown  in  the 
figure,  the  current  coming 
by  the  binding  screw  P 
passes  into  the  piece  o, 
the  plate  r  and  the  bind- 
ing screw  ^,  which  by  a 
second  plate,  or  by  a  cop- 
per wire,  leads  it  to  the 
apparatus  shown  in  fig. 
782,  or  any  other.  Then 
returning  to  the  binding  Flg>  783' 

screw  b',  the  current  attains  the  plate  r\  the  piece  zV,  and  ultimately  the 
binding  screw  N,  which  returns  it  to  the  battery. 

If  the  disc  is  turned  so  that  the  handle  is  halfway  between  c  and  c\  the 
pieces  o  and  ie  being  no  longer  in  contact  with  the  plates  r  and  r',  the  cur- 
rent does  not  pass.  If  m  is  turned  as  far  as  c,  the  plate  o  touches  r' ;  the 
current  thus  passes  first  to  b'  and  returns  by  b  ;  it  is  therefore  reversed. 

3G2 


820 


Dynam ical  Electricity. 


[871- 


871.  Directive  action  of  the  earth  on  vertical  currents. — The  earth, 
which  exercises  a  directive  action  on  magnets  (690),  acts  also  upon  currents, 
giving  them,  in  some  cases,  a  fixed  direction,  in  others  a  continuous  rotatory 
motion. 

The  first  of  these  two  actions  may  be  thus  enunciated  :  Every  vertical 
current  movable  about  an  axis  parallel  to  itself,  places  itself  under  the  direc- 
tive action  of  the  earth  in  a  plane  through  this  axis  perpendicular  to  the 
magnetic  meridian,  and  stops  after  some  oscillations,  on  the  east  of  its  axis 
of  rotation  when  it  is  descending,  and  on  the  west  when  it  is  ascending. 

This  may  be  demonstrated  by  means  of  the  apparatus  represented  in  fig. 
785,  which  consists  of  two  brass  vessels  of  somewhat  different  diameters. 


Fig.  785- 

The  larger,  a,  about  13  inches  in  diameter,  has  an  aperture  in  the  centre, 
through  which  passes  a  brass  support,  b,  insulated  from  the  vessel  a,  but 
communicating  with  the  vessel  K.  This  column  terminates  in  a  small  cup, 
in  which  a  light  wooden  rod  rests  on  a  pivot.  At  one  end  of  this  rod  a  fine 
wire  is  coiled,  each  end  of  which  dips  in  acidulated  water,  with  which  the 
two  vessels  are  respectively  filled. 

The  current  arriving  by  the  wire  m  passes  to  a  strip  of  copper,  which  is 
connected  underneath  the  base  of  the  apparatus  with  the  bottom  of  the 
column  b.  Ascending  in  this  column,  the  current  reaches  the  vessel  K,  and 
the  acidulated  water  which  it  contains  •  it  ascends  from  thence  in  the  wire 
c,  redescends  by  the  wire  e,  and  traversing  the  acidulated  water>  it  reaches 
the  sides  of  the  vessel  a,  and  so  back  to  the  battery  through  the  wire  n. 

The  current  being  thus  closed,  the  wire  e  moves  round  the  column  b,  and 
stops  to  the  east  of  it,  when  it  descends,  as  is  the  case  in  the  figure  ;  but  if 
it  ascends,  which  is  effected  by  transmitting  the  current  by  the  wire  n,  the 
wire  e  stops  to  the  west  of  the  column  b,  in  a  position  directly  opposite  to 
that  which  it  assumes  when  it  is  descending. 

If  the  rod  with  a  single  wire,  in  fig.  785,  be  replaced  by  one  with  two  wires 
as  in  fig.  786,  the  rod  will  not  move,  for  as  each  wire  tends  to  place  itself  on 
the  east  of  the  column  b,  two  equal  and  contrary  effects  are  produced,  which 
counterbalance  one  another. 


Fig.  786. 


-873]       Directive  Action  of  the  Earth  on  Closed  Currents.        821 

\  872.  Action  of  the  earth  on  horizontal  currents  movable  about  a 
vertical  axis. — The  action  of  the  earth  on  horizontal  currents  is  not  direc- 
tive, but  gives  them  a  continuous  rotatory  motion  from  the  east  to  the  west, 
when  the  horizontal  current  moves  away  from  the  axis  of  rotation,  and  from 
the  west  to  the  east  when  it  is  directed  towards  this  axis. 

This  may  be  illustrated  by  means  of  the  apparatus  represented  in  fig.  786 
which  only  differs  from  that  of  fig.  785  in  having  but  one  vessel.  The 
current,  ascending  by  the 
column  a,  traverses  the 
two  wires  cc,  and  de- 
scends by  the  wires  bb, 
from  which  it  regains 
the  pile  ;  the  circuit  bccb 
then  begins  a  continuous 
rotation  either  from  the 
east  to  the  west,  or  from 
the  west  to  the  east,  ac- 
cording as  in  the  wires 
cc  the  current  goes  from  the  centre,  as  is  the  case  in  the  figure,  or  according 
as  it  goes  towards  it,  which  is  the  case  when  the  current  enters  by  the  wire 
m  instead  of  by/z.  But  we  have  seen  (871)  that  the  action  of  the  earth  on  the 
vertical  wires  bb  is  destroyed  :  hence  the  rotation  is  that  produced  by  the 
action  on  the  horizontal  branches  cc.  This  rotatory  action  of  the  terrestrial 
current  on  horizontal  currents  is  a  consequence  of  the  rotation  of  a  finite 
horizontal  by  an  infinite  horizontal  current  (864). 

873.  Directive  action  of  the  earth  on  closed  currents  movable  about 
a  vertical  axis. —  If  the  current  on  which  the  earth  acts  is  closed,  whether 
it  be  rectangular  or  circular,  the  result  is  not  a  continuous  rotation,  but  a 
directive  action,  as  in  the  case  of  vertical  currents  (871),  in  virtue  of  which 
the  current  places  itself  in  aplane perpendicular 
to  the  magnetic  meridian,  so  that,  for  an  ob- 
server looking  at  the  north, it  is  descending  on 
the  east  of  its  axis  of  rotation,  and  ascending 
on  the  west. 

This  property,  which  can  be  shown  by 
means  of  the  apparatus  represented  in  fig. 
787,  is  a  consequence  of  what  has  been  said 
about  horizontal  and  vertical  currents.  For 
in  the  closed  circuit  BA,  the  current  in  the 
upper  and  lower  parts  tends  to  turn  in  oppo- 
site directions,  from  the  law  of  horizontal 
currents  (862),  and  hence  is  in  equilibrium  ; 
while  in  the  lateral  parts  the  current  on  the 


Fig.  787. 


one  side  tends  towards  the  east,  and  on  the  other  side  to  the  west,  from  the  law 
of  vertical  currents. 

From  the  directive  action  of  the  earth  on  currents,  it  is  necessary,  in  many 
experiments,  to  obviate  this  action.  This  is  effected  by  arranging  the 
movable  circuit  symmetrically  about  its  axis  of  rotation,  so  that  the  directive 
action  of  the  earth  tends  to  turn  them  in  opposite  directions,  and  hence 


822  Dynamical  Electricity.  [873- 

destroys  them.  This  condition  is  fulfilled  in  the  circuit  in  fig.  781.  Such 
circuits  are  hence  called  astatic  circuits. 

874.  structure  of  a  solenoid. — A  solenoid   is   a  system  of  equal  and 
parallel  circular  currents  formed  of  the  same  piece  of  covered  copper  wire 
and  coiled  in  the  form  of  a  helix  or  spiral,  as  represented  in  fig.  788.     A  sole- 
noid, however,  is  only  complete  when  part  of  the  wire  BC  passes  in  the 
direction  of  the  axis  in  the  interior  of  the  helix.     With  this  arrangement, 

when  the  circuit  is  traversed  by  a  cur- 
rent,  it  follows  from  what  has  been  said 
about  sinuous  currents  (86 1)  that  the 
action  of  a  solenoid  in  a  longitudinal 
direction,  AB,  is  counterbalanced  by  that 

of  the  rectilinear  current  BC.  This  action  is  accordingly  null  in  the  direction 
of  the  length,  and  the  action  of  a  solenoid  in  a  direction  perpendicular  to 
its  axis  is  exactly  equivalent  to  that  of  a  series  of  equal  parallel  currents. 

875.  Action  of  currents   on  solenoids. — What  has  been  said  of  the 
action  of  fixed  rectilinear  currents  on  finite  rectangular,  or  circular  currents 

(864)  applies  evidently  to 
each  of  the  circuits  of  a  sole- 
noid, and  hence  a  rectilinear 
current  must  tend  to  direct 
these  circuits  parallel  to 

^^VB^SSI^^^^SB*  itself.  To  demonstrate  this 
fact  experimentally,  a  sole- 
noid is  constructed  as  shown 
in  fig.  789,  so  that  it  can  be 
suspended  by  two  pivots  in 

the  cups  a  and  c  of  the  appa~ 

ratus  represented  in  fig.  789. 

The   solenoid  is  then  mov- 
Fig.  789.  able  about   a  vertical   axis, 

and  if  a   rectilinear  current 

QP  be  passed  beneath  it,  which  at  the  same  time  traverses  the  wires  of 
the  solenoid,  the  latter  is  seen  to  turn  and  set  at  right  angles  to  the  lower 
current — that  is,  in  such  a  position  that  its  circuits  are  parallel  to  the  fixed 
•current  ;  and,  further,  the  current  in  the  lower  part  of  each  of  the  circuits  is 
in  the  same  direction  as  in  the  rectilinear  wire. 

If,  instead  of  passing  a  rectilinear  current  below  the  solenoid,  it  is  passed 
vertically  on  the  side,  an  attraction  or  repulsion  will  take  place,  according 
as  the  two  currents  in  the  vertical  wire,  and  in  the  nearest  part  of  the 
solenoid,  are  in  the  same  or  in  contrary  directions. 

876.  Directive  action  of  the  earth    on  solenoids. — If  a  solenoid  be 
suspended  in  the  two  cups  (fig.  790),  not  in  the  direction  of  the  magnetic 
meridian,  and  a  current  be  passed  through  the  solenoid,  the  latter  will 
begin  to  move,  and  will  finally  set  in  such  a  position  that  its  axis  is  in  the 
direction  of  the  magnetic  meridian.     If  the  solenoid  be  removed,  it  will, 
after  a  few  oscillations,  return,  so  that  its  axis  is  in  the  magnetic  meridian. 
Further,  it  will  be  found  that  in  the  lower  half  of  the  coils  of  which  the 
solenoid  consists,  the  direction  of  the  current  is  from  east  to  west ;  in  other 


-879]  Ampere's  Theory  of  Magnetism.  823 

words,  the  current  is  descending  on  that  side  of  the  coil  turned  towards  the 
east   and   ascending  on   the   west.     The  directive  action   of  the  earth  on 


Fig.  790. 

solenoids  is  accordingly  a  consequence  of  that  which  it  exerts  on  circular 
currents.  In  this  experiment  the  solenoid  is  directed  like  a  magnetic  needle, 
and  the  north  pole,  as  in  magnets,  is  that  end  which  points  towards  the 
north,  and  the  south  pole  that  which  points  towards  the  south.  This  experi- 
ment may  be  made  by  means  of  a  solenoid  fitted  on  a  De  la  Rive's  floating 
battery  (867). 

V//^877.  Mutual  action  of  magnets  and  solenoids. — Exactly  the  same 
phenomena  of  attraction  and  repulsion  exist  between  solenoids  and  magnets 
as  between  magnets  themselves.  For  if  one  of  the  poles  of  a  magnet  be  pre- 
sented to  a  movable  solenoid,  traversed  by  a  current,  attraction  or  repulsion 
will  take  place,  according  as  the  poles  of  the  magnet  and  of  the  solenoid  are 
of  contrary  or  of  the  same  name.  The  same  phenomenon  takes  place 
when  a  solenoid  traversed  by  a  current  and  held  in  the  hand  is  presented  to 
.a  movable  magnetic  needle.  Hence  the  law  of  attractions  and  repulsions 
Applies  exactly  to  the  case  of  the  mutual  action  of  solenoids  and  of  magnets. 
j  878.  Mutual  action  of  solenoids.- — When  two  solenoids  traversed  by  a 
powerful  current  are  allowed  to  act  on  each  other,  one  of  them  being  held 
in  the  hand  and  the  other  being  movable  about  a  vertical  axis,  as  shown 
in  fig.  790,  attraction  and  repulsion  will  take  place  just  as  in  the  case  of  two 
magnets.  These  phenomena  are  readily  explained  by  reference  to  what  has 
been  said  about  the  mutual  action  of  the  currents,  bearing  in  mind  the  direc- 
tion of  the  currents  in  the  extremities  presented  to  each  other. 

879.  Ampere's  theory  of  magnetism. — Ampere  propounded  a  theory, 
based  on  the  analogy  between  solenoids  and  magnets,  by  which  all  magnetic 
phenomena  may  be  referred  to  electrodynamical  principles. 

Instead  of  attributing  magnetic  phenomena  to  the  existence  of  two  fluids, 
.Ampere  assumed  that  each  individual  molecule  of  a  magnetic  substance  is 
traversed  by  a  closed  electric  current,  and  further  that  these  molecular  cur- 
rents are  free  to  move  about  their  centres.  The  coercive  force,  however, 
which  is  little  or  nothing  in  soft  iron,  but  considerable  in  steel,  opposes  this 
motion,  and  tends  to  keep  them  in  any  position  in  which  they  happen  to  be. 
When  the  magnetic  substance  is  not  magnetised,  these  molecular  currents, 


824  Dynamical  Electricity.  [879- 

under  the  influence  of  their  mutual  attractions,  occupy  such  positions  that 
their  total  action  on  any  external  substance  is  nil.  Magnetisation  consists 
in  giving  to  these  molecular  currents  a  parallel  direction,  and  the  stronger 
the  magnetising  force  the  more  perfect  the  parallelism.  The  limit  of  mag- 
netisation is  attained  when  the  currents  are  completely  parallel. 

The  resultant  of  the  actions  of  all  the  molecular  currents  is  equivalent  to 
that  of  a  single  current  which  traverses  the  outside  of  a  magnet.  For  by 

inspection  of  fig.  791,  in  which 
the  molecular  currents  are  re- 
presented by  a  series  of  small 
internal  circles  in  the  two  ends 
of  a  cylindrical  bar,  it  will  be 
seen  that  the  adjacent  parts  of 
the  currents  oppose  one  another 
and  cannot  exercise  any  external 
electrodynamic  action.  This  is 
not  the  case  with  the  surface  ; 
there  the  molecular  currents  at 
ab  are  not  neutralised  by  other 
currents,  and  as  the  points  abc 
are  infinitely  near,  they  form  a  series  of  elements  in  the  same  direction 
situated  in  planes  perpendicular  to  the  axis  of  the  magnet,  and  which  con- 
stitute a  true  solenoid. 

The  direction  of  these  currents  in  magnets  can  be  ascertained  by  con- 
sidering the  suspended  solenoid  (fig.  789).  If  we  supposed  it  traversed  by  a 
current,  and  in  equilibrium  in  the  magnetic  meridian,  it  will  set  in  such  a 
position  that  in  the  lower  half  of  each  coil  the  current  flows  from  east  to 
west.  We  have  then  the  following  rule.  At  the  north  pole  of  magnet^  the 
direction  of  the  Ampcrian  currents  is  opposite  to  that  of  the  hands  of  a  watch, 
and  at  the  south  pole  the  direction  is  the  same  as  that  of  the  hands. 

880.  Terrestrial   current. — In    order   to   explain   terrestrial    magnetic 
effects  on  this  supposition,  the  existence  of  electrical  currents  is  assumed, 
which  continually  circulate  round  our  globe  from  east  to  west  perpendicular 
to  the  magnetic  meridian.     The  resultant  of  their  action  is  a  single  current 
traversing  the  magnetic  equator  from  east  to  west.     They  are  supposed  by 
some  to  be  thermoelectric  currents  due  to  the  variations  of  temperature 
caused  by  the  successive  influence  of  the  sun  on  the  different  parts  of  the 
globe  from  east  to  west. 

These  currents  direct  magnetic  needles;  for  a  suspended  magnetic 
needle  comes  to  rest  when  the  molecular  currents  on  its  under  surface  are 
parallel  and  in  the  same  direction  as  the  terrestrial  currents.  As  the 
molecular  currents  are  at  right  angles  to  the  direction  of  its  length,  the 
needle  places  its  greatest  length  at  right  angles  to  east  and  west,  or  north 
and  south.  Natural  magnetisation  is  probably  imparted  in  the  same  way  to 
iron  minerals. 

88 1.  Kail's  experiment. — In  the  action  of  magnets  on  currents  which 
have  been  described  in  the  foregoing  sections,  we  have  been  concerned  with 
the  action  of  the  magnet  on  the  body  conveying  the  current. 

Professor   Hall   of  Baltimore  has   made   the   following  experiment  ta 


-881]  Hall's  Experiment.  82$ 

determine  whether  the  path  of  a  current  in  the  body  of  a  conductor  is  or  is 
not  deflected  when  it  is  exposed  to  the  direct  action  of  a  magnetic  field. 
A  strip  of  gold  leaf,  9  centimetres  in  length  by  2  centimetres  broad,  was 
fastened  on  a  glass  plate,  which  was  placed  between  the  poles  of  an  electro- 
magnet in  such  a  manner  that  the  plane  of  the  strip  was  at  right  angles  to 
the  lines  of  force  of  the  magnetic  field.  The  ends  of  this  strip  were  in 
connection  with  the  poles  of  a  Bunsen's  cell.  Two  wires  leading  to  a 
Thomson's  galvanometer  were  connected  with  two  equipotential  points  at 
the  opposite  edges  of  the  strip  ;  that  is  to  say,  in  two  points,  found  by  trial, 
in  which  there  was  no  deflection  of  the  galvanometer  (738).  When  now  the 
electromagnet  was  excited  by  passing  a  current  through  it,  a  distinct  deflec- 
tion was  produced  in  the  galvanometer,  showing  that  the  path  of  the  current 
in  the  conducting  strip  had  been  deflected.  This  deflection  was  permanent,, 
and  could  not  therefore  be  due  to  induction,  and  its  direction  was  reversed 
when  the  current  in  the  magnet  was  reversed. 

The  magnetic  field  acts  thus  upon  the  current  in  the  gold  leaf  in  such  a 
manner  as  to  displace  it  from  one  edge  towards  the  other,  and  to  cause  a 
small  portion  to  pass  through  the  circuit  of  the  galvanometer. 

This  experiment  has  greatly  interested  physicists  from  its  theoretical 
bearings,  as  leading  to  a  method  of  determining  the  velocity  of  electricity  in 
absolute  measure. 


826 


Dynamical  Electricity. 


[882- 


CHAPTER  V. 

MAGNETISATION   BY   CURRENTS.    ELECTROMAGNETS. 
ELECTRIC  TELEGRAPHS. 

882.  Magnetisation  by  currents. — From  the  influence  which  currents 
exert  upon  magnets,  turning  the  north  pole  to  the  left  and  the  south  pole  to 
the  right,  it  is  natural  to  think  that  by  acting  upon  magnetic  substances  in 
the  natural  state  the  currents  would  tend  to  separate  the  two  magnetisms. 
In  fact,  when  a  wire  traversed  by  a  current  is  immersed  in  iron  filings,  they 
adhere  to  it  in  large  quantities,  but  become  detached  as  soon  as  the  current 
ceases,  while  there  is  no  action  on  any  other  non-magnetic  metal. 

The  action  of  currents  on  magnetic  substances  is  well  seen  by  coiling  an 
insulated  copper  wire  round  a  glass  tube,  in  which  there  is  an  unmagnetised 
steel  bar.  If  a  current  be  passed  through  the  wire,  even  for  a  short  time, 
the  bar  becomes  strongly  magnetised. 

If,  as  we  have  already  seen  (791),  the  discharge  of  a  Leyden  jar  be  trans- 
mitted through  the  wire,  by  connecting  one  end  with  the  outer  coating,  and 


Fig.  792. 

the  other  with  the  inner  coating,  the  bar  is  also  magnetised.     Hence  both 
-voltaic  and  frictional  electricity  can  be  used  for  magnetising. 

If  in  this  experiment  the  wire  be  coiled  on  the  tube  in  such  a  manner 
that  when  it  is  held  vertically  the  downward  direction  of  the  coils  is  from 
right  to  left  on  the  side  next  the  observer,  this  constitutes  a  right-handed  or 
dextrorsal  spiral  or  helix  (fig.  792),  of  which  the  ordinary  screw  is  an 
•example.  In  a  left-handed  or  sinistrorsal  heli.r  the  coiling  is  in  the  opposite 
direction,  that  is  from  left  to  right  (fig.  793). 


Fig.  793- 

In  a  right-handed  spiral  the  north  pole  is  at  the  end  at  which  the  current 
•emerges,  and  the  south  pole  at  the  end  at  which  it  enters  ;  the  reverse  is  the 
•case  in  a  left-handed  spiral.  But  whatever  the  direction  of  the  coiling,  the 
polarity  is  easily  found  by  the  following  rule  :  If  a  person  swimming  in  the 
current  look  at  the  axis  of  the  spiral,  the  north  pole  is  always  on  his  left.  If 
the  wire  be  not  coiled  regularly,  but  if  its  direction  be  reversed,  at  each 


-833] 


Electromagnets. 


827 


change  of  direction  a  consequent  pole  (68 1)  is  formed  in  the  magnet.  The 
simplest  method  of  remembering  the  polarity  produced  is  as  follows  :  What- 
ever be  the  nature  of  the  helix,  either  right  or  left  handed,  if  the  end  facing 
the  observer  has  the  current  flowing  in  the  direction  of  the  hands  of  a  watch, 
it  is  a  south  pole,  and  "vice  versa.  The  same  polarity  is  produced  whether 
or  not  there  is  an  iron  core  within  the  helix. 

The  nature  of  the  tube  on  which  the  helix  is  coiled  is  not  without  influence. 
Wood  and  glass  have  no  effect,  but  a  thick  cylinder  of  copper  may  greatly 
affect  the  action  of  the  current  unless  the  copper  be  slit  longitudinally.  This 
action  will  be  subsequently  explained.  The  same  is  the  case  with  iron, 
silver,  and  tin. 

In  order  to  magnetise  a  steel  bar  by  means  of  electricity,  it  need  not  be 
placed  in  a  tube,  as  shown  in  figs.  792  and  793.  It  is  sufficient  to  coil  round 
it  a  copper  wire,  covered  with  silk,  cotton,  or  gutta-percha,  in  order  to  insu- 
late the  circuits  from  one  another.  The  action  of  the  current  is  thus  multi- 
plied, and  a  feeble  current  is  sufficient  to  produce  a  powerful  magnetising 
effect. 

Y  883.  Electromagnets. — Electromagnets  are  bars  of  soft  iron  which,  under 
•the  influence  of  a  voltaic  current,  become  magnets  ;  but  this  magnetism  is 
only  temporary,  for  the  coercive  force 
of  perfectly  soft  iron  is  nil,  and  the 
two  magnetisms  neutralise  each  other 
as  soon  as  the  current  ceases  to  pass 
through  the  wire.  If,  however,  the 
iron  is  not  quite  pure,  it  retains  more 
or  less  traces  of  magnetisation.  Elec- 
tromagnets have  the  horse-shoe  form, 
as  shown  in  fig.  794,  and  a  copper  wire, 
covered  with  silk  or  cotton,  is  rolled 
several  times  round  them  on  the  two 
branches  so  as  to  form  two  bobbins, 
A  and  B.  In  order  that  the  two  ends 
of  the  horse-shoe  may  be  of  opposite 
polarity,  the  winding  on  the  two  limbs 
A  and  B  must  be  such  that  if  the 
horse-shoe  were  straightened  out,  it 
would  be  in  the  same  direction. 

Electromagnets,  instead  of  being 
made  in  one  piece,  are  frequently  con- 
structed of  two  cylinders,  firmly  screwed 
to  a  stout  piece  of  the  same  metal. 
Such  are  the  electromagnets  in  Morse's 
telegraph  (889)  and  the  electromag- 
netic motor  (899).  The  helices  on 
them  must  be  such  that  the  current  Fig-  794- 

shall  flow  in  the  same  direction  as  the  hands  of  a  watch  as  seen  from  the 
south  pole,  and  against  the  hands  of  a  watch  as  seen  from  the  north  pole. 

The  results  at  which  various  experimenters  have  arrived  as  regards  the 
force  of  electromagnets  are  often  greatly  divergent,  which  is  partly  due  to 


828  Dynamical  Electricity.  [833- 

the  different  senses  they  have  attached  to  the  notion  of  electromagnetic  force. 
For  this  may  mean  (I.)  the  induction  current  which  the  development  and 
disappearance  of  the  magnetism  of  an  iron  core  indicate  in  a  spiral  which 
surrounds  it;  this  is  the  excited  magnetism;  or  (II.)  the  free  magnetism 
measured  by  the  action  on  a  magnetic  needle,  oscillating  at  a  distance  ; 
(III.)  the  attractive  force,  or  the  force  required  to  hold  an  armature  at  a 
distance  from  the  electromagnet ;  (IV.)  the  lifting  power  measured  by  the 
force  with  which  an  armature  is  held  in  direct  contact  with  the  pole. 

The  most  important  results  which  have  been  arrived  at  are  the  following : — 

(i.)  Using  the  term  'electromagnetic  force'  in  the  first  two  senses,  it  is 
proportional  to  the  strength  of  the  current.  This  only  applies  when  the  cur- 
rents are  not  very  powerful,  and  to  stout  bars  ;  for  in  each  bar  there  is,  as 
Miiller  has  found,  a  maximum  of  magnetisation  which  cannot  be  exceeded. 

(ii.)  Taking  into  account  the  resistance,  the  electromagnetic  force  is  in- 
dependent of  the  nature  and  thickness  of  the  wire.  Thus,  the  strength  of  the 
current,  and  the  number  of  coils  being  the  same,  thick  and  thin  wires  produce 
the  same  effect. 

(iii.)  With  the  same  current  the  electromagnetic  force  is  independent  oj 
the  width  of  the  coils,  provided  the  iron  projects  beyond  the  coils,  and  the 
diameter  of  the  coil  is  small  compared  with  its  length. 

(iv.)  The  temporary  magnetic  moment  of  an  iron  bar  is,  within  certain 
limits,  proportional  to  the  number  of  windings.  The  product  of  the  intensity 
into  the  number  of  turns  is  usually  spoken  of  as  the  magnetising  power  of 
the  spiral.  The  greatest  magnetising  power  is  obtained  when  the  resistance 
in  the  magnetising  spiral  is  equal  to  the  sum  of  the  other  resistances  in  the 
circuit,  those  of  the  battery  included,  and  the  length  and  diameter  of  the 
wire  must  be  so  arranged  as  to  satisfy  these  conditions. 

(v.)  The  magnetism  in  solid  and  in  hollow  cylinders  of  the  same  dia- 
meters is  the  same,  provided  in  the  latter  case  there  is  sufficient  thickness 
of  iron  for  the  development  of  the  magnetism.  With  currents  below  a  certain 
strength,  wide  tubes  of  sheet  iron  are  far  more  powerfully  magnetised  than 
solid  rods  of  the  same  length  and  weight ;  but  with  more  powerful  currents 
the  magnetisation  of  the  latter  preponderates. 

(vi.)  The  attraction  of  an  armature  by  an  electromagnet  is  proportional 
to  the  square  of  the  strength  of  the  current  so  long  as  the  magnetic  moment 
does  not  attain  its  maximum.  Two  unequally  strong  electromagnets  attract 
each  other  with  a  force  proportional  to  the  square  of  the  sum  of  both  currents, 

(vii.)  For  powerful  currents  the  length  of  the  branches  of  an  electro- 
magnet is  without  influence  on  the  weight  which  it  can  support. 

Beetz  observed  that,  for  the  same  strength  of  current,  electromagnetism 
is  produced  more  rapidly  in  circuits  with  great  resistance  and  great  electro- 
motive force  than  in  circuits  with  small  resistance  and  correspondingly 
smaller  electromotive  force  ;  in  the  latter  case  the  reverse  currents  which 
occur  in  the  coils  of  the  electromagnet  come  into  play  more  than  in  the 
former. 

During  magnetisation  the  volume  of  a  magnet  does  not  vary.  This  has- 
been  established  by  placing  the  bar  to  be  magnetised  with  its  helix  in  a  sort 
of  water  thermometer,  consisting  of  a  flask  provided  with  a  capillary  tube. 
On  magnetising,  no  alteration  in  the  position  of  the  water  is  observed.  But. 


-884]     Vtbratoi y  Motion  and  Sounds  produced  by  Currents.     829 

the  dimensions  vary  ;  the  diameter  is  somewhat  lessened,  and  the  length 
increased  :  according  to  Joule  to  the  extent  of  about  of^uuo'  ^  tne  bar  ^s 
magnetised  to  saturation. 

As  regards  the  quality  of  the  iron  used  for  the  electromagnet,  it  must  be 
pure,  and  be  made  as  soft  as  possible  by  being  reheated  and  cooled  a  great 
many  times  ;  it  is  polished  by  means  of  a  file,  so  as  to  avoid  twisting.  If 
this  is  not  the  case,  the  bar  retains,  even  after  the  passage  of  the  current,  a 
quantity  of  magnetism  which  is  called  the  remanent  magnetism.  A  bundle 
of  soft  iron  wires  loses  its  magnetism  more  rapidly  than  a  massive  bar  of 
the  same  size.  According  to  Stone,  iron  wires  may  be  materially  improved 
for  electromagnetic  experiments  by  forming  them  into  bundles  by  tying 
them  round  with  wire  ;  these  bundles  are  then  dipped  in  melted  paraffine 
and  set  fire  to. 

Remanent  magnetism  is  greater  in  long  magnets — those,  that  is  to  say,  in 
which  the  diameter  is  small  in  proportion  to  the  length.  It  is  decidedly 
greater  in  soft  iron  when  the  magnetising  current  is  not  opened  suddenly,  as 
is  usually  the  case,  but  is  gradually  brought  to  zero  by  inserting  successively 
greater  resistances.  By  suddenly  opening  the  current  it  has  occasionally 
been  found  with  thick  rods  of  very  soft  iron  that  a  reversed  remanent  mag- 
netism is  met  with,  which  is  called  abnormal  magnetisation. 

This  is  easily  understood  from  the  tendency  of  molecular  magnets  to  re- 
vert to  this  primitive  condition  (879).  In  doing  this  they  experience  a  certain 
friction  or  resistance,  and  when  the  magnetisation  gradually  diminishes  this 
hinders  the  complete  reversal  of  the  molecules  ;  but  with  a  sudden  cessation 
the  molecules,  from  the  greater  vis  viva  of  their  reversal,  will  sooner  come 
back  to  their  original  position,  or  even  pass  it,  and  come  to  rest  on  the 
opposite  side. 

884.  Vibratory  motion  and  sounds  produced  by  currents. — When  a 
rod  of  soft  iron  is  magnetised  by  a  strong  electric  current,  it  gives  a  very 
distinct  sound,  which,  however,  is  only  produced  at  the  moment  of  closing 
•or  opening  the  current.  This  phenomenon,  first  observed  by  Page  in 
America,  and  by  Delezenne  in  France,  was  particularly  investigated  by 
De  la  Rive,  who  attributed  it  to  a  vibratory  motion  of  the  molecules  of 
iron  in  consequence  of  a  rapid  succession  of  magnetisations  and  demag- 
netisations. 

When  the  current  is  broken  and  closed  at  very  short  intervals,  Dela  Rive 
observed  that,  whatever  be  the  shape  or  magnitude  of  the  iron  bars,  two 
sounds  may  always  be  distinguished  ;  one,  which  is  musical,  corresponds  to 
that  which  the  rod  would  give  by  vibrating  transversely  ;  the  other,  which 
consists  of  a  series  of  harsh  sounds,  corresponding  to  the  interruptions  of 
the  current,  was  compared  by  De  la  Rive  to  the  noise  of  rain  falling  on  a 
metal  roof.  The  most  marked  sound  is  that  obtained  by  stretching,  on  a 
sounding-board,  pieces  of  soft  iron  wire,  well  annealed,  from  i  to  2  mm.  in 
diameter  and  i  to  2  yards  long.  These  wires  being  placed  in  the  axis  of  one 
or  more  bobbins  traversed  by  powerful  currents,  send  forth  a  number  of 
sounds,  which  produce  a  surprising  effect,  and  much  resemble  that  of  a 
number  of  church  bells  heard  at  a  distance. 

Wertheim  obtained  the  same  sounds  by  passing  a  discontinuous  cur- 
rent, not  through  the  bobbins  surrounding  the  iron  wires,  but  through  the 


830 


Dynamical  Electricity. 


[884- 


wires  themselves.  The  musical  sound  is  then  stronger  and  more  sonorous 
in  general  than  in  the  previous  experiment.  The  hypothesis  of  a  molecular 
movement  in  the  iron  wires  at  the  moment  of  their  magnetisation,  and  of 
their  demagnetisation,  is  confirmed  by  the  researches  of  Wertheim,  who 
found  that  their  elasticity  is  then  diminished. 

885.  Reis's  telephone.  —  The  essential  features  of  this    instrument  (fig. 
795)  are  a  sort  of  box,  B,  one  side  of  which  is  closed  by  a  membrane  C, 

while  there  is 
a  mouthpiece, 
A,  in  another 
side.  On  the 
membrane  is  a 
piece  of  thin 
metal-foil  C, 
which  is  con- 
nected with  a. 
wire  leading  to 
one  pole  of  the 
battery  G,  the 
other  pole  of 

which  is  put  to  earth.  Just  above  the  foil,  and  almost  touching  it,  is  a  metal 
point  D,  which  is  connected  by  the  line  wire  (886)  with  one  end  of  a  coil  of 
insulated  wire  surrounding  an  iron  wire,  the  other  end  of  which  is  put  to  earth. 
When  the  mouthpiece  is  spoken  or  sung  into,  the  sounds  set  the  mem- 
brane in  vibration  ;  this  alternately  opens  and  closes  the  current,  and  these 
makes  and  breaks  being  transmitted  through  the  circuit  to  the  electromagnet. 
F,  produce  the  corresponding  sounds. 


. 


ELECTRIC  TELEGRAPH. 


886.  Electric  telegraphs. — These  are  apparatus  by  which  signals  can  be 
transmitted  to  considerable  distances  by  means  of  voltaic  currents  propa- 
gated in  metallic  wires.  Towards  the  end  of  the  last  century,  and  at  the 
beginning  of  the  present,  many  philosophers  proposed  to  correspond  at  a 
distance  by  means  of  the  effects  produced  by  electrical  machines  when  pro- 
pagated in  insulated  conducting  wires.  In  1811,  Scemmering  invented  a 
telegraph,  in  which  he  used  the  decomposition  of  water  for  giving  signals,. 
In  1820,  at  a  time  when  the  electromagnet  was  unknown,  Ampere  proposed 
to  correspond  by  means  of  magnetic  needles,  above  which  a  current  was  sent, 
as  many  wires  and  needles  being  used  as  letters  were  required.  In  1834. 
Gauss  and  Weber  constructed  an  electromagnet  telegraph,  in  which  a  voltaic 
current  transmitted  by  a  wire  acted  on  a  magnetised  bar,  the  oscillations  of 
which  under  its  influence  were  observed  by  a  telescope.  They  succeeded  in 
thus  sending  signals  from  the  Observatory  to  the  Physical  Cabinet  in  Got- 
tingen,  a  distance  of  a  mile  and  a  quarter,  and  to  them  belongs  the  honour  ot 
having  first  demonstrated  experimentally  the  possibility  of  electrical  com- 
munication at  a  considerable  distance.  In  1837,  Steinheil  in  Miinich,  and 
Wheatstone  in  London,  constructed  telegraphs  in  which  several  wires  each. 


Electric  Telegraph. 


831 


acted  on  a  single  needle  ;  the  current  in  the  first  case  being  produced  by  an 
electromagnetic  machine,  and  in  the  second  by  a  constant  battery. 

Every  electric  telegraph  consists  essentially  of  three  parts  ;  I,  a  circuit 
consisting  of  a  metallic  connection  between  two  places,  and  an  electromotor 
for  producing  the  current ;  2,  a  communicator  for  sending  the  signals  from 
the  one  station  ;  and,  3,  an  indicator  for  receiving  them  at  the  other  station. 
The  manner  in  which  these  objects,  more  especially  the  last  two,  are  effected 
can  be  greatly  varied,  and  we  shall  limit  ourselves  to  a  description  of  the 
three  principal  methods. 

One  form  of  electromotor  still  sometimes  used  in  England  is  a  modifica- 
tion of  Wollaston's  battery.  It  consists  of  a  trough  divided  into  compart- 
ments in  each  of  which  is  an  amalgamated  zinc  plate  and  a  copper  plate  ; 
these  plates  are  usually  about  4|  inches  in  height  by  3^  in  breadth.  The 
compartments  are  filled  with  sand,  which  is  moistened  with  dilute  sulphuric 
acid.  This  battery  is  inexpensive  and  easily  worked,  only  requiring  from 
time  to  time  the  addition  of  a  little  acid  ;  but  it  has  very  low  electromotive 
force  and  considerable  resistance,  and  when  it  has  been  at  work  for  some 
time  the  effects  of  polarisation  begin  to  be  perceived.  On  the  telegraphs  of 
the  South-Eastern  Railway,  the  plati- 
nised graphite  (811)  battery,  invented  by 
Mr.  C.  V.  Walker,  has  been  used  with 
success.  On  circuits  on  which  there  is 
constant  work  some  form  of  DanielFs 
battery  is  used,  and  for  other  circuits 
Leclanche's  cell  is  coming  into  more  ex- 
tended use.  In  France,  Daniell's  bat- 
tery is  used  for  telegraphic  purposes. 

The  connection  between  two  stations 
is  made  by  means  of  galvanised  iron 
wire  suspended  by  porcelain  supports 
(fig.  796),  which  insulate  and  protect 
them  against  the  rain,  either  on  posts  or  against  the  sides  of  buildings.  In 
England  and  other  moist  climates  special  attention  is  required  to  be  paid  to 
the  perfection  of  the  insulation.  In  towns,  wires  covered  with  gutta-percha 
are  placed  in  tubes  laid  in  the  ground.  Submarine  cables,  where  great 
strength  is  required  combined  with  lightness  and  high  conducting  power, 


Fig.  797. 


Fig.  798. 


are  formed  on  the  general  type  of  one  of  the  Atlantic  cables,  a  longitudinal 
view  of  which  is  given  in  fig.  797,  while  fig.  798  represents  a  cross  section. 
In  the  centre  is  the  core,  which  is  the  conductor ;  it  consists  of  seven  copper 


832 


Dynamical  Electricity. 


[886- 


wires,  each  I  mm.  in  diameter,  twisted  in  a  spiral  strand  and  covered  with 
several  layers  of  gutta-percha,  between  each  of  which  is  a  coating  of  Chat- 
tertoris  compound— a.  mixture  of  tar,  resin,  and  gutta-percha.  This  forms 
the  insulator  proper,  and  it  should  have  great  resistance  to  the  passage  of 
electricity,  combined  with  low  specific  inductive  capacity  (748).  Round  the 
insulator  is  a  coating  of  hemp,  and  on  the  outside  is  wound  spirally  a  pro- 
tecting sheath  of  steel  wire,  each  of  which  is  spun  round  with  hemp. 

At  the  station  which  sends  the  despatch,  the  line  is  connected  with  the 
positive  pole  of  a  battery,  the  current  passes  by  the  line  to  the  other  station, 
and  if  there  were  a  second  return  line,  it  would  traverse  it  in  the  opposite 
direction  to  return  to  the  negative  pole.  In  1837,  Steinheil  made  the  very 
important  discovery  that  the  earth  might  be  used  for  the  return  conductor, 
thereby  saving  the  expense  of  the  second  line.  For  this  purpose  the  end  of 
the  conductor  at  the  one  station,  and  the  negative  pole  of  the  battery  at  the 

other,  are  connected  with 
large  copper  plates,  which 
are  sunk  to  some  depth  in 
the  ground.  The  action 
is  then  the  same  as  if  the 
earth  acted  as  a  return 
wire.  The  earth  is,  in- 
deed, far  superior  to  a 
return  wire ;  for  the  added 
resistance  of  such  a  wire 
would  be  considerable, 
whereas  the  resistance  of 
the  earth  beyond  a  short 
distance  is  absolutely  nil. 
The  earth  really  dissi- 
pates the  electricity  and 
does  not  actually  return 
the  same  current  to  the 
battery. 

887.  Wheatstone 

and  Cooke's  single 
needle  telegraph. — This 
consists  essentially  of  a 
vertical  multiplier  (821) 
with  an  astatic  needle, 
the  arrangement  of  which 
is  seen  in  fig.  800,  while 
fig.  799  gives  a  front  view 
of  the  case  in  which  the  apparatus  is  placed.  A  (fig.  800)  is  the  bobbin, 
consisting  of  about  400  feet  of  fine  copper  wire,  wound  in  a  frame  in  two 
connected  coils.  Instead  of  an  astatic  needle,  Mr.  Walker  has  found  it  ad- 
vanta°"eous  to  use  a  single  needle  formed  of  several  pieces  of  very  thin  steel 
strongly  magnetised  ;  it  works  with  the  bobbin,  and  a  light  index  joined  to 
it  by  a  horizontal  axis  indicates  the  motion  of  the  needle  on  the  dial. 

The  signs  are  made  by  transmitting  the  current  in  different  directions 


799- 


-887] 


WJieatstone  and  Cooke's  Telegraph. 


833 


through  the  multiplier,  by  which  the  needle  is  deflected  either  to  the  right 
or  left,  according  to  the  will  of  the  operator.  The  instrument  by  which  this 
is  effected  is  a  commutator  or  key,  G,  fig.  80 1  ;  its  action  is  shown  in  fig.  80 1, 
while  fig.  800  shows  on  a  large  scale  how  two  stations  are  connected.  It 
consists  of  a  cylinder  of  boxwood  with  a  handle,  which  projects  in  front  of 
the  case  (fig.  800;.  On  its  circumference  parallel  to  the  axis  are  seven  brass 
strips  (fig.  801),  the  spaces  between  which  are  insulated  by  ivory ;  these 
strips  are  connected  at  the  end  by  metallic  wires,  also  insulated  from  each 
other,  in  the  following  manner  :  a  with  b  and  c,f  with  d,  and  e  with  g.  Four 
springs  press  against  the  cylinder  ;  x  and  y  are  connected  with  the  poles  of 
the  battery,  m,  with  the  earth  plate,  and  n  with  one  end  of  the  multiplier,  N. 

When  not  at  work  the  cylin- 
der and  the  handle  are  in  a 
vertical  position,  as  seen  on  the 
left  of  the  diagram.  The  circuit 
is  thus  open,  for  the  pole  springs, 
x  and  j,  are  not  connected  with 
the  metal  of  the  commutator. 
But  if,  as  in  the  figure  on  the 
right,  the  key  is  turned  to  the 
right,  the  battery  is  brought  into 
the  circuit,  and  the  current 
passes  in  the  following  direc- 
tion :  +  pole,  jrV^VM'f 'Nj 
conductor  yflMnacmlLfl,  earth 
p'Wm'e'g'y',  -  pole.  The  coils  N 
and  N'  are  so  arranged  that  by 
the  action  of  the  current  the  mo- 
tion of  the  needle  corresponds 
to  the  motion  of  the  handle.  By 
turning  the  handle  to  the  left  the 
current  would  have  the  following 
direction  :  +  pole  x*d'fm'Y,'p', 
earth  p^LmcabnM.q,  conductor 
p'q'Wn'b'a'y',  —  pole,  and  thus  the 
needle  would  be  deflected  in  the 
opposite  direction. 

The  signs  are  given  by  differ- 
ently combined  deflections  of  the 
needle,  as  represented  in  the  alphabet  on  the  dial  (fig.  799).  \  denotes  a 
deflection  of  the  upper  end  of  the  needle  to  the  left,  and  /  a  deflection  to 
the 'right  ;  I,  for  instance,  is  indicated  by  two  deflections  to  the  left,  and  M 
by  two  to  the  right.  Some  of  the  marks  on  the  alphabet  are  only  half  as 
long  as  the  others  ;  this  indicates  that  the  shortest  of  the  connected  marks 
must  first  be  signalled.  Thus,  D  is  expressed  by  right-left-left,  and  C  by 
right-left-right-left,  etc. 

These  signs  are  somewhat  complicated  and  require  great  practice  ; 
usually  not  more  than  12  to  20  words  can  be  sent  in  a  minute.  The  single- 
needle  telegraph  was  formerly  sometimes  replaced  by  the  double -needle  one, 

3H 


834 


Dynamical  Electricity. 


[887- 


which  is  constructed   on  the  same  principle,  but  there  are  two  needles  and 
two  wires  instead  of  one. 


Fig.  801. 

888.  Dial  telegraphs. — Of  these  many  kinds  exist.  Figs.  803  and  804 
represent  a  lecture-model  of  one  form,  constructed  by  Froment,  and 
which  will  serve  to  illustrate  the  principle.  It 
consists  of  two  parts — the  key  for  transmitting 
signals  (fig.  803,  and  the  indicator  (fig.  804)  for 
receiving  them.  The^first  apparatus  is  connected 
with  a  battery,  O,  and  the  two  apparatus  are 
in  communication  by  means  of  metal  wires,  one 
of  which,  AOD  (fig.  803),  goes  from  the  departure 
to  the  arrival  station,  and  the  other,  HKLI  (fig. 
804),  from  the  arrival  to  the  departure.  In  practice, 
the  latter  is  replaced  by  the  earth  circuit.  Each 
apparatus  is  furnished  with  a  dial  with  25  of  the 
letters  of  the  alphabet,  on  which  a  needle  moves. 
The  needle  at  the  departure  station  is  moved  by 
hand,  that  of  the  arrival  by  electricity. 

The  path  of  the  current  and  its  effects  are  as  follows  :  from  the  battery  it 
passes  through  a  copper  wire,  A  (fig.  803),  into  a  brass  spring,  N,  which 
presses  against  a  metal  wheel,  R,  then  by  a  second  spring,  M,  into  the  wire 
O,  which  joins  the  other  station.  Thence  the  current  passes  into  the  bobbin 
of  an  electromagnet,  b,  not  fully  shown  in  fig.  804,  but  of  which  fig.  802 
represents  a  section,  showing  the  front  of  the  apparatus.  This  electromagnet 
is  fixed  horizontally  at  one  end,  and  at  the  other  it  attracts  an  armature  of 
soft  iron,  #,  which  forms  part  ofa  bent  lever,  movable  about  its  axis,  0,  while 
a  spring,  r,  attracts  the  lever  in  the  opposite  direction. 


-888] 


Dial  Telegraphs. 


835 


When  the  current  passes,  the  electromagnet  attracts  the  lever  aC,  which 
by  a  rod,  /,  acts  on  a  second  lever,  d,  fixed  to  a  horizontal  axis,  itself  con- 


nected with  a  fork,  F.     When  the  current  is  broken  the  spring  r  draws  the 
lever  aC,  and  therewith  all  the  connected  pieces  ;  a  backward-and-forward 

3H2 


836  Dynamical  Electricity.  [888- 

motion  is  produced,  which  is  communicated  to  the  fork  F  ;  this  transmits 
it  to  a  toothed  wheel,  G,  on  the  axis  of  which  is  the  needle.  From  the 
arrangement  of  its  teeth,  the  wheel  G  is  always  moved  in  the  same  direction 
by  the  fork. 

To  explain  the  intermittent  action  of  the  magnet,  we  must  refer  to  fig. 
803.  The  toothed  wheel,  R,  has  26  teeth,  of  which  25  correspond  to  letters 
of  the  alphabet,  and  the  last  to  the  interval  reserved  between  the  letters  Z 
and  A.  When  holding  the  knob  P  in  the  hand  the  wheel  R  is  turned,  the  end 
of  the  plate  N  from  its  curvature  is  always  in  contact  with  the  teeth  ;  the 
plate  M,  on  the  contrary,  terminates  in  a  catch  cut  so  that  contact  is  alter- 
nately made  and  broken.  Hence,  the  connections  with  the  battery  having 
been  made,  if  the  needle  P  is  advanced  through  four  letters,  for  example,  the 
current  passes  four  times  in  N  and  M,  and  is  four  times  broken.  The  electro- 
magnet of  the  arrival  station  will  then  have  attracted  four  times,  and  have 
ceased  to  do  so  four  times.  Lastly,  the  wheel  G  will  have  turned  by  four 
teeth,  and  as  each  tooth  corresponds  to  a  letter,  the  needle  of  the  arrival 
station  will  have  passed  through  exactly  the  same  number  of  letters  as  that 
of  the  departure  station.  The  piece  S,  represented  in  the  two  figures,  is  a 
copper  plate,  movable  on  a  hinge,  which  serves  to  make  or  to  break  the 
current  at  will. 

From  this  explanation  it  will  be  readily  intelligible  how  communications 
are  made  between  different  places.  Suppose,  for  example,  that  the  first  ap- 
paratus being  at  London  and  the  second  at  Brighton,  there  being  metallic 
connection  between  the  two  towns,  it  is  desired  to  send  the  word  signal  to 
the  latter  town  :  as  the  needles  correspond  on  each  apparatus  to  the  interval 
retained  between  Z  and  A,  the  person  sending  the  despatch  moves  the 
needle  P  to  the  letter  S,  where  it  stops  for  a  very  short  time  ;  as  the  needle 
in  Brighton  accurately  reproduces  the  motion  of  the  London  needle,  it  stops 
at  the  same  letter,  and  the  person  who  receives  the  despatch  notes  this  letter. 
The  one  at  London,  always  continuing  to  turn  in  the  same  direction,  stops 
at  the  letter  I,  the  second  needle  immediately  stops  at  the  same  letter  ;  and 
continuing  in  the  same  manner  with  the  letters  G,  N,  A,  L,  all  the  word  is 
soon  transmitted  to  Brighton.  The  attention  of  the  observer  at  the  arrival 
station  is  attracted  by  means  of  an  electric  alarum.  Each  station  must 
further  be  provided  with  the  two  apparatus  (figs.  803  and  804),  without  which 
it  would  be  impossible  to  answer. 

\  889.  Morse's  telegraph. — The  telegraphs  hitherto  described  leave  no 
trace  of  the  despatches  sent,  and  if  any  errors  have  been  made  in  copying 
the  signals  there  is  no  means  of  remedying  them.  These  inconveniences 
are  not  met  with  in  the  case  of  the  writing  telegraphs,  in  which  the  signs 
themselves  are  printed  on  a  strip  of  paper  at  the  time  at  which  they  are 
transmitted. 

Of  the  numerous  printing  and  writing  telegraphs  which  have  been  devised, 
that  of  Morse,  first  brought  into  use  in  North  America,  is  best  known.  It 
has  been  almost  universally  adopted  on  the  Continent.  In  this  instrument 
there  are  three  distinct  parts  :  the  receiver,  the  sender,  and  the  relay ;  figs. 
805,  806,  807,  and  808  represent  these  apparatus. 

Receiver.  We  will  first  describe  the  receiver  (fig.  805),  leaving  out  of  sight 
for  the  moment  the  accessory  pieces,  G  and  T,  placed  on  the  right  of  the 


-889]  Morse's  Telegraph.  837 

figure.  The  current  which  enters  the  indicator  by  the  wire,  C,  passes  into  an 
electro-magnet,  E,  which,  when  the  current  is  closed,  attracts  an  armature  of  soft 
iron,  A,  fixed  at  the  end  of  a  horizontal  lever  movable  about  an  axis,  x ;  when 
the  current  is  open  the  lever  is  raised  by  a  spring,  r.  By  means  of  two  screws, 
m  and  v,  the  amplitude  of  the  oscillations  is  regulated.  At  the  other  end  of 
the  lever  there  is  a  pencil,  a,  which  writes  the  signals.  For  this  purpose  a 
long  band  of  strong  paper,  hp,  rolled  round  a  drum,  R,  passes  between  two 
copper  rollers  with  a  rough  surface,  u,  and  turning  in  contrary  directions. 
Drawn  in  the  direction  of  the  arrows,  the  band  of  paper  becomes  rolled  on  a 
second  drum,  Q,  which  is  turned  by  hand.  A  clockwork  motion  placed  in 
the  box,  BD,  works  the  rollers,  between  which  the  band  of  paper  passes. 

The  paper  being  thus  set  in  motion,  whenever  the  electromagnet  works, 
the  point  o  strikes  the  paper,  and,  without  perforating  it,  produces  an  inden- 


Fig.  805 

tation  the  shape  ot  which  depends  on  the  time  during  which  the  point  is  in 
contact  with  the  paper.'  If  it  only  strikes  it  instantaneously,  it  makes  a  dot 
(-)  or  short  stroke  ;  but  if  the  contact  has  any  duration,  a  dash  ( — )  of  corre- 
sponding length  is  produced.  Hence,  by  varying  the  length  of  contact  of 
the  transmitting  key  at  one  station,  a  combination  of  dots  and  dashes  may 
be  produced  at  another  station,  and  it  is  only  necessary  to  give  a  definite 
meaning  to  these  combinations. 

In  order  to  make  an  indentation  a  considerable  pressure  is  required,  which 
necessitates  the  employment  of  a  strong  current,  and  the  newer  instruments 
(fig.  806)  are  based  on  the  use  of  ink-writers.  The  paper  band  passes 
close  to,  but  not  touching,  a  metal  disc  with  a  fine  edge,  c,  which  turns 
against  a  small  ink-roller,  a,  all  being  rotated  by  the  same  mechanism. 
When  the  end  A  is  attracted,  the  bent  plate  at  the  other  end  presses  the 


838 


Dynamical  Electricity. 


[889 


paper  against  the  disc  which  is  inked  by  contact  with  the  ink-roller,  and 
thus  produces  a  mark  on  the  paper,  which  is  either  short  or  long  according 

to  the  duration 

1(\\      \  J^     of  the  contact. 

The  signs  are 
thus  more  le- 
gible and  are 
produced  by 
far  weaker  cur- 
rents. 

The  same 
telegraphic  al- 
phabet is  now 
universally 
used  wherever 


Fig.  806. 


telegraphic  communication  exists  ;  and  the  signals  for  the  single-needle  instru- 
ment (fig.  799)  as  well  as  those  used  for  printing  have  been  modified,  so  that 
they  now  correspond  to  each  other.  Thus  a  beat  of  the  top  of  the  needle  to 
the  left  \  is  equivalent  to  a  dot  :  and  a  beat  to  the  right  /  to  a  dash.  The 
following  figure  gives  the  alphabet. 


SIN'GIE 

SLVGfi 

PRINTING. 

XEEDLE. 

FB1NIING. 

XEEDLE. 

A       

v/ 

N       

A 

B      

Ax, 

0      

1/1 

C      

AA 

p     

Jk 

D      

As 

Q         

IU 

E      - 

\ 

R      

vA 

F      

SNA 

S 

X\N 

G     

/A 

T        — 

/ 

H     

x\x\ 

U       

XN/ 

I     -- 

x\ 

y        

XXX/ 

J    

x/// 

w     

X// 

K      

IJ 

X       

Ax/ 

L      

J* 

Y       

A// 

M     

//   <** 

Z        

The  flag  signals  used  in  military  operations  are  similarly  used.  A  swing 
of  the  flag  from  its  upright  vertical  position  to  the  right  or  left  has  the  same 
mean  ing  as  the  corresponding  motion  of  the  top  end  of  the  needle.  So  too 
long  or  short  obscurations  of  the  limelight  used  in  signalling  by  night,  or  of 
the  heliograph  (523),  correspond  to  dashes  and  dots. 

Sender  or  key.     This  consists  of  a  small  mahogany  base,  which  acts  as 


889]  Morses  Telegraph.  839 

support  for  a  metal  lever  ab  (fig.  807),  movable  in  its  middle  on  a  horizontal 
axis.  The  extremity  a  of  this  lever  is  always  pressed  upwards  by  a  spring 
beneath,  so  that  it  is  only  by  pressing  with  the  finger  on  the  key  B  that  the 
lever  sinks  and  strikes  the  button  x.  Round  the  base  are  three  binding 
screws,  one  connected  with  the  wire  P,  which  comes  from  the  positive  pole 
of  the  battery  ;  the  second  connected  with  L,  the  line  wire ;  and  the  third 
with  the  wire  A,  which  passes  to  the  indicator,  for  of  course  two  places  in 
communication  are  each  provided  with  an  indicator  and  communicator. 

These  details  known,  there  are  two  cases  to  be  considered.  I.  The  key 
arranged  so  as  to  receive  a  message  from  a  distant  station  ;  the  end 
b  is  then  down,  as  represented  in  the  figure,  so  that  the  current  which 
arrives  by  the  line  wire  L, 
and  ascends  in  the  me- 
tallic  piece  ;;z,  descends 
in  the  wire  A,  which  leads 
it  to  the  indicator  of  the 
station  at  which  the  ap- 
paratus is  placed.  2.  A 
message  is  to  be  trans- 
mitted ;  in  this  case  the 
key  B  is  pressed  so  that 
the  lever  comes  in  contact  Fig.  8o7. 

with  the  button  x.     The 

current  of  the  local  battery,  which  comes  by  the  wire  P,  ascending  then  in 
the  lever,  descends  by  m  and  joins  the  wire  L,  which  conducts  it  to  the 
station  to  which  the  despatch  is  addressed.  According  to  the  length  of  time 
during  which  B  is  pressed,  a  dot  or  a  line  is  produced  in  the  receiver  to 
which  the  current  proceeds. 

Relay.  In  describing  the  receiver  we  have  assumed  that  the  current  of 
the  line  coming  by  the  wire  C  (fig.  805)  entered  directly  into  the  electro- 
magnet, and  worked  the  armature  A,  producing  a  despatch  ;  but  when  the 
current  has  traversed  a  distance  of  a  few  miles  its  strength  has  diminished 
so  greatly  that  it  cannot  act  upon  the  electromagnet  with  sufficient  force  to 
print  a  despatch.  Hence  it  is  necessary  to  have  recourse  to  a  relay — that  is, 
to  an  auxiliary  electromagnet  which  is  still  traversed  by  the  current  of  the 
line,  but  which  serves  to  introduce  into  the  communicator  the  current  of  a 
local  battery  of  four  or  five  elements  placed  at  the  station,  and  which  is  only  used 
to  print  the  signals  transmitted  by  the  wire. 

For  this  purpose  the  current  entering  the  relay  by  the  binding  screw,  L 
(fig.  808),  passes  into  an  electromagnet,  E,  whence  it  passes  into  the  earth 
by  the  binding  screw  T.  Now,  each  time  that  the  current  of  the  line  passes 
into  the  relay,  the  electromagnet  attracts  an  armature,  A,  fixed  at  the  bottom 
of  a  vertical  lever,/,  which  oscillates  about  a  horizontal  axis. 

At  each  oscillation  the  top  of  the  lever  p  strikes  against  a  button  71, 
and  at  this  moment  the  current  of  the  local  battery  which  enters  by  the  bind- 
ing screw  c,  ascends  the  column  m,  passes  into  the  lever/,  descends  by  the  rod 
£>,  which  transmits  it  to  the  screw  Z  :  thence  it  enters  the  electromagnet  of  the 
indicator,  whence  it  emerges  by  the  wire  Z,  to  return  to  the  local  battery  from 
which  it  started.  Then,  when  the  current  of  the  line  is  open,  the  electro- 


840 


Dynamical  Electricity. 


[889- 


magnet  of  the  relay  does  not  act,  and  the  lever/,  drawn  by  a  spring  r,  leaves 
the  button  /z,  as  shown  in  the  drawing,  and  the  local  current  no  longer 
passes.  Thus  the  relay  transmits  to  the  indicator  exactly  the  same  phases  of 
passage  and  intermittence  as  those  effected  by  the  manipulator  in  the  station 
which  sends  the  despatch. 

With  a  general  battery  of  25  Daniell's  elements  the  current  is  usually 
strong  enough  at  upwards  of  90  miles  from  its  starting-point  to  work  a  relay. 
For  a  longer  distance  a  new  current  must  be  taken,  as  will  be  seen  in  the 
paragraph  on  the  change  of  current  (vide  infra). 

Working  of  the  three  apparatus.  The  three  principal  pieces  of  Morse's 
apparatus  being  thus  known,  the  following  is  the  actual  path  of  the  current. 

The  current  of 
the  line  coming  by 
the  wire  L  (fig.  805) 
passes  at  first  to 
the  piece  T  intended 
to  serve  as  light- 
n  i n g-c  onductor 
when,  from  the  in- 
fluence of  atmos- 
pheric electricity  in 
time  of  storm,  the 
conducting  wires 
become  charged 
with  so  much  elec- 
tricity as  to  give 
dangerous  sparks. 
This  apparatus  consists  of  two  copper  discs,  </and/  provided  with  teeth  on 
the  sides  opposite  each  other,  but  not  touching.  The  disc  d  is  connected 
with  the  earth  by  a  metal  plate  at  the  back  of  the  stand  which  supports  this 
lightning  conductor,  while  the  disc/ is  in  the  current.  The  latter  coming  by 
the  line  L  enters  the  lightning-conductor  by  the  binding  screw  fixed  at  the 
lower  part  of  the  stand  on  the  left ;  then  rises  to  a  commutator,  «,  which  con- 
ducts it  to  a  button,  c,  whence  it  reaches  the  disc  f  by  a  metal  plate  at  the 
back  of  the  stand  ;  in  case  a  lightning  discharge  should  pass  along  the  wire, 
it  would  now  act  inductively  on  the  disc  d,  and  emerge  by  the  points  without 
'danger  to  those  about  the  apparatus.  Moreover,  from  the  disc/  the  current 
passes  into  a  very  fine  wire  insulated  on  a  tube,  e.  As  the  wire  is  melted 
when  the  discharge  is  too  strong,  the  electricity  does  not  pass  into  the 
apparatus,  which  still  further  removes  any  danger. 

Lastly,  the  current  proceeds  from  the  foot  of  the  support  to  a  screw  on 
the  right,  which  conducts  it  to  a  small  galvanometer,  G,  serving  to  indicate 
by  the  deflection  of  the  needle  whether  the  current  passes.  From  this 
galvanometer  the  current  passes  to  a  key  (fig.  807),  which  it,  enters  at  L, 
whence  it  emerges  at  A  to  go  to  the  relay  (fig.  808).  Entering  this  at 
L,  it  works  the  electromagnet,  and  establishes  the  communication  necessary 
for  the  passage  of  the  current  of  the  local  battery,  as  has  been  said  in 
speaking  of  the  relay. 

Change  of.  current.     To  complete  this  description  of  Morse's  apparatus  it 


-890]  Cowpers  Writing  Telegraph.  841 

must  be  observed  that  in  general  the  current  which  arrives  at  L,  after  having 
traversed  several  miles,  has  not  sufficient  force  to  register  the  despatch,  nor 
to  proceed  to  a  new  distant  point.  Hence  in  each  telegraphic  station  a 
new  current  must  be  taken,  that  of  \htpostal  battery,  which  consists  of  20  to 
30  DanielPs  elements,  and  is  not  identical  with  the  local  battery. 

This  new  current  enters  at  P  (fig,  805),  reaches  a  binding  screw  which 
conducts  it  to  the  column  H,  and  thence  only  proceeds  further  when  the 
armature  A  sinks.  A  small  contact  placed  under  the  lever  then  touches  the 
button  v ;  the  current  proceeds  from  the  column  H  to  the  metallic  mass 
BD,  whence  by  a  binding  screw  and  a  wire,  not  represented  in  the  figure,  it 
reaches,  lastly,  the  wire  of  the  line,  which  sends  it  to  the  following  post,  and 
so  on  from  one  point  to  another. 

890.  Cowper's  writing:  telegraph. — This  very  remarkable  invention  is 
a  true  telegraph,  in  that  it  faithfully  reproduces  at  a  distance  an  exact  facsimile 
of  a  person's  handwriting.  The  following  is  a  general  idea  of  the  principle 
of  the  instrument. 

Two  line  wires  are  required,  which  are  severally  connected  at  the  re- 
ceiving station  with  two  galvanometers,  whose  coils  are  at  right  angles  to 
each  other.  At  the  sending  station  is  a  vertical  pencil  with  two  light  rods, 
jointed  to  it  at  right  angles  to  each  other.  One  of  these  contact  rods  guides 
a  contact  piece  which  is  Connected  by  a  wire  with  one  pole  of  a  battery,  the 
other  pole  of  which  is  to  earth.  This  contact  piece  slides  over  the  edges  of 
a  series  of  contact  plates  insulated  from  each  other,  between  each  of  which 
a  special  resistance  is  interposed,  and  the  last  of  the  contact  plates  is  con- 
nected with  one  line  wire.  The  other  contact  piece  slides  over  a  second 
series  of  such  plates  connected  with  the  other  line  wire. 

Let  us  consider  one  contact  alone ;  as  it  moves  over  the  contact  plates  in 
one  direction  or  the  other,  it  brings  less  or  more  resistance  into  the  circuit, 
and  thereby  alters  the  strength  of  the  current.  The  effect  of  this  is  that  the 
needle  of  the  corresponding  galvanometer  is  less  or  more  deflected.  Now  the 
end  of  this  needle  is  connected  by  a  light  thread  with  a  receiving  pen,  which 
is  a  capillary  tube  full  of  ink.  An  oscillation  of  the  needle  would  produce  an 
up  and  down  motion  of  the  pen,  and  if  simultaneously  a  band  of  paper  passed 
under  the  pen,  being  moved  regularly  by  clockwork,  there  would  be  produced 
on  it  a  series  of  up  and  down  strokes.  A  corresponding  effect  would  be  pro- 
duced by  the  action  of  the  needle  of  the  other  galvanometer,  except  that  its 
strokes  would  be  backwards  and  forwards  instead  of  up  and  down. 

Now  the  action  of  the  writing  pen  is  that  it  varies  simultaneously  the 
strengths  of  the  two  currents,  and  they  produce  a  motion  of  the  receiving 
pen  which  is  compounded  of  the  two  movements  described  above,  and 
which  is  an  exact  reproduction,  on  a  smaller  scale,  of  the  original  motion. 
The  following  line  is  a  facsimile. 

. Jfcfrtfd dtfCLlfy^f^^  — 

Both  the  paper  written  in  pencil  at  the  sending  station  and  that  written 
in  ink  at  the  receiving  station  move  along  as  the  writing  proceeds,  and  the 
messages  have  only  to  be  cut  off  from  time  to  time. 


842  Dynamical  Electricity.  [890- 

Experiments  made  with  this  instrument  show  that  it  will  write  through 
resistances  equal  to  36  miles. 

891.  Induction  in  telegraph  cables. — In  the  earliest  experiments  on  the 
use  of  insulated  subterranean  wires  for  telegraphic  communication  it  was 
found  that  difficulties  occurred  in  their  use  which  were  not  experienced  with 
overhead  wires.  This  did  not  arise  from  defective  insulation,  for  the  better 
the  insulation  the  greater  the  difficulty.  It  was  suspected  by  Siemens  and 
others  that  the  retardation  was  due  to  statical  induction,  taking  place  be- 
tween the  inner  wire  through  the  insulator  and  the  external  moisture  ;  and 
Faraday  proved  that  this  was  the  case  by  the  following  experiments  among 
others.  A  length  of  about  100  miles  of  gutta-percha-covered  copper  wire 
was  immersed  in  water,  the  ends  being  led  into  the  chamber  of  observation. 
When  the  pole  of  a  battery  containing  a  large  number  of  cells  was  momen- 
tarily connected  with  one  end  of  the  wire,  the  other  end  being  insulated,  and 
a  person  simultaneously  touched  the  wire  and  the  earth  contact,  he  obtained 
a  violent  shock. 

When  the  wire,  after  being  in  momentary  contact  with  the  battery,  was 
placed  in  connection  with  a  galvanometer,  a  considerable  deflection  was 
observed ;  there  was  a  feebler  one  3  or  4  minutes  after,  and  even  as  long  as 
20  or  30  minutes  afterwards. 

When  the  insulated  galvanometer  was  permanently  connected  with  one 
end  of  the  wire,  and  then  the  free  end  of  the  galvanometer  wire  joined  to  the 
pole  of  the  battery,  a  rush  of  electricity  through  the  galvanometer  into  the 
wire  was  perceived.  This  speedily  diminished  and  the  needle  ultimately 
came  to  rest.  When  the  galvanometer  was  detached  from  the  battery  and 
put  to  earth,  the  electricity  flowed  as  rapidly  out  of  the  wire,  and  the  needle 
was  momentarily  deflected  in  the  opposite  direction. 

These  phenomena  are  not  difficult  to  explain.  The  wire  with  its  thin 
insulating  coating  of  gutta-percha  becomes  statically  charged  with  electricity 
from  the  battery.  The  coating  of  gutta-percha  through  which  the  inductive 
action  takes  place  is  only  i  of  an  inch  in  thickness,  and  the  extent  of  the 
coatings  is  very  great.  The  surface  of  the  copper  wire  amounts  to  8,300 
square  feet,  and  that  of  the  outside  coating  is  four  times  as  much.  The 
potential  can  only  be  as  great  as  that  of  the  battery,  but  from  the  enormous 
surface  the  capacity,  and  therefore  the  quantity,  is  very  great.  Thus  the 
wires,  after  being  detached  from  the  battery,  showed  all  the  actions  of  a 
powerful  electric  battery.  These  effects  take  place,  but  to  a  less  extent  with 
wires  in  air  ;  the  external  coating  is  here  the  earth,  which  is  so  distant  that 
induction  and  charge  are  very  small. 

Hence  the  difficulty  in  submarine  telegraphy.  The  electricity  which 
enters  the  insulating  wire  must  first  be  used  in  charging  the  large  Leyden 
jar  which  it  constitutes,  and  only  after  this  has  happened  can  the  current 
reach  the  distant  end  of  the  circuit.  The  current  begins  later  at  the  distant 
end,  and  ceases  sooner.  If  the  electrical  currents  follow  too  rapidly,  an 
uninterrupted  current  will  appear  at  the  other  end,  which  indicates  small 
differences  in  strength,  but  not  with  sufficient  clearness  differences  in  dura- 
tion or  direction.  Hence  in  submarine  wires  the  signals  must  be  slower 
than  in  air  wires  to  obtain  clear  indications.  By  the  use  of  alternating 
currents — that  is,  of  currents  which  are  alternately  positive  and  negative — 


-893]  Duplex  Telegraphy.  843 

these  disturbing  influences  may  be  materially  lessened,  and  communication  be 
accelerated  and  made  more  certain,  but  they  can  never  be  entirely  obviated. 

In  the  Atlantic  Cable,  instruments  on  the  principle  of  Thomson's  reflect- 
ing galvanometer  (822)  are  used  for  the  reception  of  signals  ;  the  motions  of 
the  spot  of  light  to  the  right  and  left  forming  the  basis  of  the  alphabet. 
^"892.  Sypbon  recorder. — Sir  W.  Thomson  has  invented  an  extremely 
ingenious  instrument  called  the  syphon  recorder,  by  which  the  very  feeble 
signals  transmitted  through  long  lengths  of  submarine  cables  are  observed 
and  also  recorded. 

Its  construction  is  somewhat  complicated,  but  the  essential  features  are 
as  follows.  A  light  flat  coil  of  insulated  wire,  which  is  connected  with  the 
line  wire,  is  suspended  by  a  bifilar  suspension  between  the 
two  poles  of  a  powerful  horseshoe  magnet.  When  no  current 
passes,  its  plane  is  in  the  right  line  joining  the  poles.  When  a 
current  is  passed,  this  coil,  becoming  thereby  a  magnet,  is  de- 
flected either  to  the  right  or  to  the  left,  according  to  the  direction 
of  the  current.  It  is,  in  short,  the  reverse  of  the  arrangement 
in  (882),  for  here  the  coil  is  movable  and  the  magnets  fixed  ; 
there  the  magnet  is  movable  and  the  coil  fixed. 

A  very  light  capillary  glass  tube,  shaped  as  represented  'in  Flg*  8o9' 
fig.  809,  dips  with  its  short  end  in  a  reservoir  of  ink,  while  the  other  end  is 
in  front  of  a  paper  ribbon,  which  is  moved  along  at  a  uniform  rate,  like  a 
ribbon  in  a  Morse's  recorder.  When  this  ink  is  electrified,  it  spurts  out  in  a 
continuous  series  of  fine  drops  against  the  paper,  and  marks  on  it  a  straight 
line  so  long  as  no  current  passes  in  the  coil.  This  syphon  is,  however,  con- 
nected by  a  system  of  silk  threads  with  the  coil,  and  according  as  this  is 
deflected  either  to  the  right  or  the  left,  the  end  of  the  syphon  is  deflected  too, 
and  accordingly  traces  a  wavy  line  on  the  paper  which  represents  deflections 
right  or  left  of  the  central  line,  that  are  in  short  the  Morse  signals. 

The  electrification  of  the  ink  is  effected  by  a  small  electrostatic  induction 
machine  ;  this  is  worked  by  clockwork,  which  at  the  same  time  pays  out  the 
paper  ribbon. 

V  893.  Duplex  telegraphy.— By  this  is  meant  a  system  of  telegraphy  by 
which  messages  may  be  simultaneously  sent  in  opposite  directions  on  one  and 
the  same  wire,  whereby  the  working  capacity  of  a  line  is  practically  doubled. 

Several  plans  have  been  devised  for  accomplishing  this  very  important 
improvement  ;  no  more  can  here  be  attempted  than  to  give  a  general  account 
of  the  principle  of  the  method  in  one  case. 

Let  m,  fig.  810,  represent  the  electromagnet  of  a  Morse's  instrument 
which  is  wound  round  with  two  equal  coils  in  opposite  directions  ;  these  coils 
are  represented  by  the  full  and  dotted  lines,  and  one  of  them,  which  may  be 
called  the  line  coil,  is  joined  to  the  line  LL',  which  connects  the  two  stations. 
The  other  coil,  that  represented  by  the  dotted  line,  which  maybe  called  the 
equating  coil,  is  in  connection  with  the  earth  at  E  by  means  of  an  adjustable 
resistance,  or  artificial  line,  R.  By  this  means  the  resistance  of  the  branch 
«RE  may  be  made  equal  to  that  of  the  branch  #LLV.  The  battery  b  has 
one  pole  to  earth  at  E,  and  the  other  pole,  by  means  of  a  make-and-break 
key,  c,  can  be  connected  at  a,  where  the  two  oppositely  wound  coils  bifurcate. 
The  back  contact  of  the  key  is  also  connected  with  earth. 


S44 


Dynamical  Electricity. 


[893- 


The  station  at  B  is  arranged  in  a  similar  manner,  as  is  represented  by 
corresponding  letters  with  affixes. 

Now  when  B  depresses  his  key  and  sends  a  current  into  the  line,  inasmuch 

as  the  electromagnet  of  his  instrument  is  wound  with  equal  coils  in  opposite 

directions,  the  armature  is  not  attracted,  for  the  core  is  not  magnetised  because 

the  currents  in  the  two  coils  counteract  one  another.     Thus,  although  a 

^  _  current  passes 


R 

I 
i 

!' 

~~\     ;L                                   —  "S'\     )  —  1       ^~~\         is  no  indication 
[**                                               /^p                   x        of  it  in  his  own 
instrument  —  a 
condition     es- 
sential   in    all 
^^e*^                                       «*4**t_£  °r              systems  of  du- 
!       p  1  e  x     tele- 
^S                                                                  =r     /        graphy. 
,                                           \                     /'               But      with 
/                                            v^  --"'           regard   to   the 
E                                                                    B/                effect     on     A, 
there   are   two 

t 

j                                                                  l^j              vN  cases     accord- 
^                    ing  as  he  is  or 
Fig-  8l°-                                                  is  not  sending 

a  message  at  the  same  time.  If  A's  key  is  not  down,  then  the  current  will 
circulate  round  the  core  of  the  electromagnet  and  will  reach  the  earth  by  the 
path  L  a  c  E  ;  the  core  will  therefore  become  magnetised,  the  armature 
attracted,  and  a  signal  produced  in  the  ordinary  way. 

If,  however,  at  the  moment  at  which  B  has  his  key  down,  A.  also  depresses 
his,  then  it  will  be  seen  that,  as  currents  are  sent  in  opposite  directions  from 
both  A  and  B,  they  neutralise  one  another,  no  current  passes  in  the  line 
a\3Jaf :  it  is,  as  it  were,  blocked.  But  though  no  current  passes  in  the  line 
coil,  a  current  does  pass  at  each  station  to  earth,  through  the  equating  coil, 
which  being  no  longer  counterbalanced  by  any  opposite  current  in  the  line 
coil,  magnetises  the  core  of  the  electromagnet,  which  thus  attracts  the  arma- 
ture and  produces  a  signal. 

We  have  here  supposed  that  A  and  B  both  send,  for  instance,  the  same 
currents  to  line  :  the  final  effect  is  not  different  if  they  send  opposite  currents 
at  the  same  time.  For  then,  as  they  neutralise  each  other  in  the  line  LL', 
the  effect  is  the  same  as  if  the  resistance  of  the  line  were  diminished.  More 
electricity  flows  at  line  from  each  station  through  the  line  coil  being  no  longer 
balanced  by  the  equating  coil ;  the  current  of  the  line  coil  preponderates  and 
then  works  the  electromagnet. 

Hence,  in  both  these  cases,  each  station,  so  to  speak,  produces  the  signal 
which' the  other  one  wishes  to  send. 

Other  methods  of  duplex  telegraphy  are  based  on  the  principle  of 
Wheatstone's  Bridge  (955),  and  on  the  principle  of  leakage ;  but  for  these, 
as  well  as  for  quadruplex  telegraphy,  special  manuals  must  be  consulted. 

894.  Earth  currents. — In  long  telegraph  circuits  more  or  less  powerful 
currents  are  produced,  even  when  the  battery  is  not  at  work.  This  arises 


-896]  The  Sounder.  845 

from  a  difference  of  potential  being  established  in  the  earth  at  the  two  places 
between  which  the  communication  is  established.  These  currents  are  some- 
times in  one  direction  and  sometimes  in  another,  and  are  at  times  so  power- 
ful and  irregular  as  quite  to  interfere  with  the  working  of  the  lines.  Lines 
running  NE  and  SW  are  most  frequently  affected  ;  lines  running  NW  and 
SE  are  less  so,  and  the  currents  are  far  weaker.  Their  strength  often 
amounts  to  as  much  as  40  millamperes,  which  is  a  stronger  current  than  is 
necessarily  required  for  working  telegraph  instruments. 

These  currents  do  not  seem  to  be  due  to  atmospheric  electricity,  for  they 
cease  if  a  wire  be  disconnected  at  one  of  its  ends,  and  they  appear  in  under- 
ground wires. 

According  to  Wild,  they  are  the  prime  cause  of  magnetic  storms,  but  not 
of  the  periodical  variations  in  the  magnetic  elements. 

895.  Bain's  electrochemical  telegraph.— If  a  strip  of  paper  be  soaked 
in  a  solution  of  ferrocyanide  of  potassium  and  be  placed  on  a  metal  surface 
connected  with  the  negative  pole  of  a  battery,  on  touching  the  paper  with  a 
steel  pointer  connected  with  the  positive  pole,  a  blue  mark  due  to  the  forma- 
tion of  some  Prussian  blue  will  be  formed  about  the  iron,  so  long  as  the  current 
passes.     The  first  telegraph  based  on  this  principle  was  invented  by  Bain. 
The  alphabet  is  the  same  as  Morse's,  but  the  despatch  is  first  composed  at 
the  departure  station  on  a  long  strip  of  ordinary  paper.     It  is  perforated 
successively  by  small  round  elongated  holes,   which   correspond    respec- 
tively to  the  dots  and  marks.     This  strip  of  paper  is  interposed  between  a 
small  metal  wheel  and  a  metal  spring,  both  forming  part  of  the  circuit.    The 
wheel,  in  turning,  carries  with  it  the  paper  strip,  all  parts  of  which  pass 
successively  between  the  wheel  and  the  plate.     If  the  strip  were  not  per- 
forated, it  would,  not  being  a  conductor,  constantly  offer  a  resistance  to  the 
passage  of  the  current  ;  but,  in  consequence  of  the  holes,  every  time  one  of 
them  passes,  there  is  contact  between  the  wheel  and  the  plate.     Thus  the 
current  works  the  relay  of  the  station  to  which  it  is  sent,  and  traces  in  blue, 
on  a  paper  disc,  impregnated  with  ferrocyanide  of  potassium,  the  same  series 
of  points  and  marks  as  those  on  the  perforated  paper. 

896.  The   sounder. — The  sound  produced  when  the  armature   of  the 
electromagnet  in  a  Morse's  instrument  is  attracted  by  the  passage  of  the 
current  is  so  distinct  and  clear  that  many  telegraph  operators  have  been 
in  the  habit  of  reading  the  messages  by  the  sounds  thus  produced,  and  at 
most  of  checking  their  reading  by  comparison  with  the  signs  produced  on  the 
paper. 

Based  on  this  fact  a  form  of  instrument  invented  in  America  has  come 
into  use  for  the  purpose  of  reading  by  sound.  The  sounder,  as  it  is  called,, 
is  essentially  a  small  electromagnet  on  an  ebonite  base,  resembling  the  relay 
in  fig.  808.  The  armature  is  attached  to  one  end  of  a  lever,  and  is  kept  at 
a  certain  distance  from  the  electromagnet  by  a  spring.  When  the  current 
passes,  the  armature  is  attracted  against  the  electromagnet  with  a  sharp 
click,  and  when  the  current  ceases  it  is  withdrawn  by  the  spring.  Hence 
the  interval  between  the  sounds  is  of  longer  or  shorter  duration  according 
to  the  will  of  the  sender,  and  thus  in  effect  a  series  of  short  and  long  sounds 
can  be  produced  which  correspond  to  the  dots  and  dashes  of  the  Morse 
alphabet. 


846 


Dynamical  Electricity. 


[896- 


Such  instruments  are  simple,  easily  adjusted,  and  portable,  not  occupy- 
ing more  space  than  an  ordinary  field-glass.  They  are  coming  into  extended 
use,  especially  for  military  telegraph  work. 

897.  Electric  alarum. — One  form  of  these  instruments  is  represented  in 
fig.  811.  On  a  wooden  board  arranged  vertically  is  fixed  an  electromagnet, 

E  ;  the  line  wire  is  connected  with  the  bind- 
ing screw,  W  with  which  is  also  connected 
one  end  of  \he  wire  of  the  electromagnet ; 
the  other  end  is  connected  with  a  spring,  c, 
to  which  is  attached  the  armature,  a  ;  this 
again  is  pressed  against  by  a  spring,  C,  which 
in  turn  is  connected  with  the  binding  screw 
.  from  which  the  wire  leads  to  earth. 

Whenever  the  current  passes,  the  arma- 
ture a  is  attracted,  carrying  with  it  a  hammer, 
P,  which  strikes  against  the  bell  T  and  makes 
it  sound.  The  moment  this  takes  place,  con- 
tact is  broken  between  the  armature  a  and 
the  spring  C,  and  the  current  being  stopped 
the  electromagnet  does  not  act ;  the  spring 
c,  however,  in  virtue  of  its  elasticity,  brings 
the  armature  in  contact  with  the  spring  C, 
the  current  again  passes,  and  so  on  as  long 
as  the  current  continues  to  pass. 

898.  Electrical  clocks.  —  Electrical 
clocks  are  clockwork  machines,  in  which  an 
electromagnet  is  both  the  motor  and  the  regulator,  by  means  of  an  electric 
current  regularly  interrupted,  in  a  manner  resembling  that  described  in  the 
preceding  paragraph.  Fig.  812  represents  the  face  of  such  a  clock,  and  fig. 
813  the  mechanism  which  works  the  needles. 

An  electromagnet,  B,  attracts  an  armature  of  soft  iron,  P,  movable  on  a 
pivot,  a.  The  armature  P  transmits  its  oscillating  motion  to  a  lever,  s,  which 
by  means  of  a  ratchet,  n,  turns  the  wheel  A.  This,  by  the  pinion,  D,  turns 
the  wheel  C,  which  by  a  series  of  wheels  and  pinions  moves  the  hands.  The 
small  one  marks  the  hours,  the  large  one  the  minutes  ;  but  as  the  latter  does 
not  move  regularly,  but  by  sudden  starts  from  second  to  second,  it  follows 
that  it  may  also  be  used  to  indicate  the  seconds. 

It  is  obvious  that  the  regularity  of  the  motion  of  the  hands  depends  on 
the  regularity  of  the  oscillations  of  the  piece  P.  For  this  purpose,  the  oscil- 
lations of  the  current,  before  passing  into  the  electromagnet  B,  are  regulated 
by  a  standard  clock,  which  itself  has  been  previously  regulated  by  a  seconds 
pendulum.  At  each  oscillation  of  the  pendulum  there  is  an  arrangement  by 
which  it  opens  and  closes  the  current,  and  thus  the  armature  P  beats  seconds 
exactly. 

To  illustrate  the  use  of  these  electrical  clocks,  suppose  that  on  the  railway 
from  London  to  Birmingham  each  station  has  an  electric  clock,  and  that 
from  the  London  station  a  conducting  wire  passes  to  all  the  clocks  on  the 
line  as  far  as  Birmingham.  When  the  current  passes  in  this  wire  all  the 
clocks  will  simultaneously  indicate  the  same  hour,  the  same  minute,  and  the 


Fig.  811. 


-899] 


Electromagnetic  Machines. 


847 


same  second  ;  for  electricity  takes  an  inappreciable  time  to  go  from  London 
to  Birmingham. 


Fig.  812. 


Fig.  813. 


899.  Electromagnetic  machines. — Numerous  attempts  have  been  made 
to  apply  electromagnetism  as  a  motive  power  in  machinery.  Fig.  814  repre- 
sents an  engine  of  this  kind  constructed  by  Froment.  It  consists  of  four 
powerful  electromagnets,  ABCD,  fixed  on  an  iron  frame,  X.  Between  these 
electromagnets  is  a  system  of  two  iron  wheels  movable  on  the  same  hori- 
zontal axis,  with  eight  soft  iron  armatures,  M,  on  their  circumference. 

The  current  arrives  at  K,  ascends  in  the  wire  E,  and  reaches  a  metallic 
arc,  O,  which  serves  to  pass  the  current  successively  into  each  electromagnet, 
so  that  the  attractions  exerted  on  the  armatures  M  shall  always  be  in  the 
same  direction.  Now  this  can  only  be  the  case  provided  the  current  is 
broken  in  each  electromagnet  just  when  an  armature  comes  in  front  of  the 
axis  of  the  bobbin.  To  produce  this  interruption  the  arc  O  has  three  branches 
<?,  each  terminating  with  a  steel  spring,  to  which  a  small  sheave  is  attached. 
Two  of  these  establish  the  communication  respectively  with  one  electro- 
magnet, and  the  third  with  two.  On  a  central  wheel,  a,  there  are  cogs,  on 
which  the  sheaves  alternately  rest.  Whenever  one  of  them  rests  on  a  cog, 
the  current  passes  into  the  corresponding  electromagnet,  but  ceases  to  pass 
when  there  is  no  longer  contact.  On  emerging  from  the  electromagnets  the 
current  passes  to  the  negative  pole  of  the  battery  by  the  wire  H. 

In  this  manner,  the  armatures  M  being  successively  attracted  by  the  four 
electromagnets,  the  system  of  wheels  which  carries  them  assumes  a  rapid  rota- 
tory motion,  which  by  the  wheel  P  and  an  endless  band  is  transmitted  to  a 
sheave,  O,  which  sends  it  finally  to  any  machine,  a  grinding-mill  for  example. 

In  his  workshops  Froment  had  an  electromotive  engine  of  one-horse 
power.  But,  though  an  interesting  application  of  the  transformation  ot 
energy,  there  is  no  expectation  that  these  machines  will  ever  be  practically 
applied  in  manufactures,  for  the  expense  of  the  acids  and  the  zinc  which 
they  use  very  far  exceeds  that  of  the  coal  in  steam-engines  of  the  same  force. 


848 


Dynamical  Electricity. 


[899- 


Thus  a  machine  devised  by  Kravogl  produces  about  17  per  cent,  of  the 
useful  effect  due  to  the  chemical  combination  of  the  zinc  with  the  acid  in  the 
battery,  and  therefore  in  utilising  this  force  they  are  about  equal  to  the  best 
steam-engines.  But  a  pound  of  coal  yields  7,200  thermal  units,  and  a  pound 
of  zinc  only  1,200  (484)  ;  and  as  zinc  is  ten  times  as  dear  as  coal,  engines 
worked  by  electricity,  independently  of  any  question  as  to  the  cost  of  con- 


Fig.  8i4. 

struction,  or  of  the  cost  of  the  acids,  are  sixty  times  as  dear  to  work  as 
steam-engines. 

The  energy  of  the  electrical  current  may  be  compared  with  the  iris  viva 
of  a  small  mass  which  moves  with  very  great  velocity.  Hence  it  can  be 
understood  that  at  present  the  most  advantageous  employment  of  electricity 
is  to  be  found,  not  so  much  in  the  transformation  of  its  vis  viva  into  the 
relatively  slow  movement  of  large  masses,  as  in  the  rapid  transmission  of 
a  small  power  to  great  distances,  as  in  the  electric  telegraph. 


-900] 


Induction  by  Currents. 


849 


CHAPTER  VI. 

VOLTAIC   INDUCTION. 

v  900.  Induction  by  currents. — We  have  already  seen  (744)  that  by 
induction  is  meant  the  action  which  electrified  bodies  exert  at  a  distance 
on  bodies  in  the  natural  state.  Hitherto  we  have  only  had  to  deal  with 
electrostatical  induction  ;  we  shall  now  see  that  dynamical  electricity  pro- 
duces analogous  effects. 

Faraday  discovered  this  class  of  phenomena  in  1832,  and  he  gave  the 
name  of  currents  of  induction  or  induced  currents  to  instantaneous  currents 
developed  in  metallic  conductors  under  the  influence  of  metallic  conductors 
traversed  by  electric  currents,  or  by  the  influence  of  powerful  magnets,  or 
even  by  the  magnetic  action  of  the  earth  ;  and  the  currents  which  give  rise 
to  them  he  called  inducing  currents. 

The  inductive  action  of  a  current  at  the  moment  of  opening  or  closing 
may  be  shown  by  means  of  a  bobbin  with  two  wires.  This  consists  (fig.  815) 


of  a  cylinder  of  wood  or  of  cardboard,  on  which  a  quantity  of  silk-covered 
No.  1 6  copper  wire  is  coiled  ;  on  this  is  coiled  a  considerably  greater  length 
of  fine  copper  wire,  about  No.  35,  also  insulated  by  being  covered  with  silk. 
This  latter  coil,  which  is  called  the  secondary  coil,  is  connected  by  its  ends 
with  two  binding  screws,  «,  b,  from  which  wires  pass  to  a  galvanometer, 
while  the  thicker  wire,  the  primary  coil,  is  connected  by  its  extremities  with 
two  binding  screws,  c  and  d.  One  of  these,  d,  being  connected  with  one  pole 
of  a  battery,  when  a  wire  from  the  other  pole  is  connected  with  c,  the  current 
passes  in  the  primary  coil,  and  in  this  alone.  The  following  phenomena  are 
then  observed  : — 

31 


850 


Dynamical  Electricity. 


[900- 


i.  At  the  moment  at  which  the  thick  wire  is  traversed  by  the  current 
the  galvanometer,  by  the  deflection  of  the  needle,  indicates  the  existence  in 
the  secondary  coil  of  a  current  inverse  to  that  in  the  primary  coil,  that  is, 
in  the  contrary  direction  ;  this  is  only  instantaneous,  for  the  needle  imme- 
diately reverts  to  zero,  and  remains  so  as  long  as  the  inducing  current  passes 
through  cd. 

ii.  At  the  moment  at  which  the  current  is  opened— that  is,  when  the  wire 
cd  ceases  to  be  traversed  by  a  current — there  is  again  produced  in  the  wire 
ab  an  induced  current  instantaneous  like  the  first,  but  direct,  that  is,  in  the 
same  direction  as  the  inducing  current. 

901.  Production  of  induced  currents  by  continuous  ones. — Induced 
currents  are  also  produced  when  a  primary  coil  traversed  by  a  current  is 
approached  to  or  removed  from  a  secondary  one  ;  this  may  be  shown  by  the 
following  apparatus  (fig.  816),  in  which  B  is  a  hollow  coil  consisting  of  a 


Fig.  8 1 6. 

great  length  of  fine  wire,  and  A  a  coil  consisting  of  a  shorter  and  thicker 
wire,  and  of  such  dimensions  that  it  can  be  placed  in  the  secondary  coil. 
The  coil  A  being  traversed  by  a  current,  if  it  is  suddenly  placed  in  the  coil 
B,  a  galvanometer  connected  with  the  latter  indicates  by  the  direction  of  its 
deflection  the  existence  in  it  of  an  inverse  current ;  this  is  only  instantaneous  ; 
the  needle  rapidly  returns  to  zero,  and  remains  so  as  long  as  the  small 
bobbin  is  in  the  large  one.  If  it  is  rapidly  withdrawn,  the  galvanometer 
shows  that  the  wire  is  traversed  by  a  direct  current.  If,  instead  of  rapidly 
introducing  or  replacing  the  primary  coil,  this  is  done  slowly,  the  galvano- 
meter only  indicates  a  weak  current,  and  which  is  the  feebler  the  slower  the 
motion. 

If,  instead  of  varying  the  distance  of  the  inducing  current,  its  intensity 
be  varied,  that  is,  either  increased  by  bringing  additional  battery  power  into 


-903]  Inductive  Action  of  the  Ley  den  Discharge,  851 

the  circuit,  or  diminished  by  increasing  the  resistance,  an  induced  current 
is  produced  in  the  secondary  wire,  which  is  inverse  if  the  intensity  of  the 
inducing  current  increases,  and  direct  if  it  diminishes. 

902.  Conditions  of  induction.  Xienz's  law. — From  the  experiments 
which  have  been  described  in  the  previous  paragraphs  the  following  prin- 
ciples may  be  deduced  : — 

I.  The  distance  remaining  the  same,  a  continuous  and  constant  current 
does  not  induce  any  current  in  an  adjacent  conductor. 

II.  A  current,  at  the  moment  of  being  closed,  produces  in  an  adjacent  con- 
ductor an  inverse  current. 

III.  A  current,  at  the  moment  it  ceases,  produces  a  direct  ctirrent. 

IV.  A  current  'which  is  removed,  or  whose  strength  diminishes,  gives 
rise  to  a  direct  induced  current. 

V.  A  current  which  is  approached,  or  whose  strength  increases,  gives  rise 
to  an  inverse  induced  current. 

VI.  On  the  induction  produced  between  a  closed  circuit  and  a  current 'in 
activity,  when  their  relative  distance  varies,  Lenz  has  based  the  following 
1  aw,  which  is  known  as  Lenz*s  law  : — 

If  the  relative  position  of  two  conductors  A  and  B  be  changed,  of  which 
A  is  traversed  by  a  current,  a  current  is  induced  in  B  in  such  a  direction 
that,  by  its  electrodynamic  action  on  the  curre?itinA,  it  would  have  imparted 
to  the  conductors  a  motion  of  the  contrary  kind  to  that  by  which  the  inducing 
action  was  produced. 

Thus,  for  instance,  inV.,  when  a  current  is  approached  to  a  conductor,  an 
inverse  current  is  produced  ;  but  two  conductors  traversed  by  currents  in 
opposite  directions  repel  one  another,  according  to  the  received  laws  of 
electrodynamics  (858).  Conversely  when  a  current  is  moved  away  from  a 
conductor,  a  current  of  the  same  direction  is  produced  ;  now  two  currents  in 
the  same  direction  attract  one  another. 

On  bringing  the  inducing  wire  near  the  induced  as  well  as  in  i  amoving  it 
away,  work  is  required ;  hence  a  quantity  of  heat  proportional  to  the  work 
consumed  must  result,  as  Edlund's  investigations  have  shown.  On  the 
other  hand,  when  induction  results  from  the  opening  and  closing  of  the  cir- 
cuit (II.  and  III.)  no  work  is  lost,  but  the  inducing  current  loses  as  much 
heat  as  is  produced  in  the  induced  circuit. 

903.  Inductive  action  of  the  Ley  den  discharge. — Figure  817  represents 
an  apparatus  devised  by  Matteucci,  which  is  very  well  adapted  for  showing 
the  development  of  induced  currents  produced  either  by  the  discharge  of  a 
Leyden  jar  or  by  the  passage  of  a  voltaic  current. 

It  consists  of  two  glass  plates  about  12  inches  in  diameter,  fixed  vertically 
on  the  two  supports  A  and  B.  These  supports  are  on  movable  feet,  and 
can  either  be  approached  or  removed  at  will.  On  the  anterior  face  of  the 
plate  A  are  coiled  about  30  yards  of  copper  wire  C,  a  millimetre  in  diameter. 
The  two  ends  of  this  wire  pass  through  the  plate,  one  in  the  centre,  the  other 
near  the  edge,  terminating  in  two  binding  screws,  like  those  represented  in 
m  and  //,  on  the  plate  B.  To  these  binding  screws  are  attached  two  copper 
wires,  c  and  d,  through  which  the  inducing  current  is  passed. 

On  the  face  of  the  plate  B,  which  is  towards  A,  is  enrolled  a  spiral  of 
finer  copper  wire  than  the  wire  C.  Its  extremities  terminate  in  the  binding 

3  12 


852  Dynamical  Electricity.  [903- 

screws  m  and  «,  on  which  are  fixed  two  wires,  h  and  /,  intended  to  transmit 
the  induced  current.  The  two  wires  on  the  plates  are  not  only  covered  with 
silk,  but  each  circuit  is  insulated  from  the  next  one  by  a  thick  layer  of  shellac 
varnish. 

In  order  to  show  the  production  of  the  induced  current  by  the  discharge 
of  a  Leyden  jar,  one  end  of  the  wire  C  is  connected  with  the  outer  coating, 
and  the  other  end  with  the  knob  of  the  Leyden  jar,  as  shown  in  the  figure. 
When  the  spark  passes,  the  electricity  traversing  the  wire  C  acts  by  induc- 
tion on  the  wire  on  the  plate  B,  and  produces  an  instantaneous  current 
in  this  wire.  A  person  holding  two  copper  handles  connected  with  the 
wires  i  and  h  receives  a  shock,  the  intensity  of  which  is  greater  in  pro- 
portion as  the  plates  A  and  B  are  nearer. 


The  experiment  may  also  be  made  by  simply  twisting  together  two 
lengths  of  a  few  feet  of  gutta-purcha-covered  copper  wire.  The  ends  of  one 
length  being  held  in  the  hand,  an  electric  discharge  is  passed  through  the 
other  length. 

The  above  apparatus  can  also  be  used  to  show  the  production  of  induced 
currents  by  the  influence  of  voltaic  currents.  For  this  purpose  the  current 
of  a  battery  is  passed  through  the  inducing  wire  C,  while  the  ends  of  the 
other  wire,  h  and  z,  are  connected  with  a  galvanometer.  At  the  moment  at 
which  the  current  commences  or  finishes,  or  when  the  distance  of  the  two 
conductors  is  varied,  the  same  phenomena  are  observed  as  in  the  case  of  the 
apparatus  represented  in  fig.  816. 

904.  Induction  by  magnets. — It  has  been  seen  that  the  influence  of  a 
current  magnetises  a  steel  bar  ;  in  like  manner  a  magnet  can  produce  induced 
currents  in  metal  circuits.  Faraday  showed  this  by  means  of  a  coil  with  a 
single  wire  of  200  to  300  yards  in  length.  The  two  ends  of  the  wire  being 
connected  with  a  galvanometer,  as  shown  in  fig.  818,  a  strongly  magnetised 
bar  is  suddenly  inserted  in  the  bobbin,  and  the  following  phenomena  are 
observed  : — 

i.  At  the  moment  at  which  the  magnet  is  introduced,  the  galvanometer 
indicates  in  the  wire  the  existence  of  a  current,  the  direction  of  which  is 
opposed  to  that  which  circulates  round  the  magnet,  considering  the  latter  as 
a  solenoid  on  Ampere's  theory  (879). 


-905]     Inductive  Action  of  Magnets  on  Bodies  in  Motion.        853 

ii.  When  the  magnet  is  withdrawn,  the  needle  of  the  galvanometer,  which 
has  returned  to  zero,  indicates  the  existence  of  a  direct  current. 

The  inductive  action  of  magnets  may  also  be  illustrated  by  the  follow- 
ing experiment  :  a  bar  of  soft  iron  is  placed  in  the  above  bobbin  and  a  strong 
magnet  suddenly  brought  in  contact  with  it ;  the  needle  of  the  galvanometer 
is  deflected,  but  returns  to  zero  when  the  magnet  is  stationary,  and  is  de- 
flected in  the  opposite  direction  when  it  is  removed.  The  induction  is  here 
produced  by  the  magnetisation  of  the  soft  iron  bar  in  the  interior  of  the 
bobbin  under  the  influence  of  the  magnet. 

The  same  inductive  effects  are  produced  in  the  wires  of  an  electromagnet, 
if  a  strong  magnet  be  made  to  rotate  rapidly  in  front  of  the  extremities  of 


Fig.  8 1 8. 

..the  wire  in  such  a  manner  that  its  poles  act  successively  by  influence  on  the 
two  branches  of  the  electromagnet ;  or  also  by  forming  two  coils  round  a 
horseshoe  magnet,  and  passing  a  plate  of  soft  iron  rapidly  in  front  of  the 
poles  of  the  magnet  ;  the  soft  iron  becoming  magnetic  reacts  by  influence  on 
the  magnet,  and  induced  currents  are  produced  in  the  wire  alternately  in 
different  directions. 

The  inductive  action  of  magnets  is  a  confirmation  of  Ampere's  theory 
of  magnetism.  For  as,  on  this  theory,  magnets  are  solenoids,  all  the  ex- 
periments which  have  been  mentioned  may  be  explained  by  the  inductive 
action  of  currents  which  traverse  the  surface  of  magnets  ;  the  induction  of 
magnets  is,  in  short,  an  induction  of  currents.  And  it  is  a  useful  exercise 
to  see  how  on  this  view  the  inductive  action  of  magnets  falls  under  Lenz's 
law  (902). 

905.  Inductive  action  of  magnets  on  bodies  in  motion. — Arago  was 
the  first  to  observe,  in  1824,  that  the  number  of  oscillations  which  a  mag- 
netised needle  makes  in  a  given  time,  under  the  influence  of  the  earth's 
magnetism,  is  very  much  lessened  by  the  proximity  of  certain  metallic 
masses,  and  especially  of  copper,  which  may  reduce  the  number  in  a  given 
time  from  300  to  4.  This  observation  led  Arago  in  1825  to  the  discovery  of 


854  Dynamical  Electricity.  [905- 

an  equally  unexpected  fact — that  of  the  rotative  action  which  a   plate  of 
copper  in  motion  exercises  on  a  magnet. 

This  phenomenon  may  be  shown  by  means  of  the  apparatus  represented 
in  fig.  819.  It  consists  of  a  copper  disc,  M,  movable  about  a  vertical  axis. 
On  this  axis  is  a  sheave,  B,  round  which  is  coiled  an  endless  cord,  passing 
also  round  the  sheave  A.  By  turning  this  with  the  hand,  the  disc  M  may 
be  rotated  with  great  rapidity.  Above  the  disc  is  a  glass  plate,  on  which  is 


Fig.  819. 

a  small  pivot  supporting  a  magnetic  needle,  ab.  If  the  disc  be  now  rotated 
with  a  slow  and  uniform  velocity,  the  needle  is  deflected  in  the  direction  of 
the  motion,  and  stops  at  an  angle  of  from  20°  to  30°  with  the  direction  of  the 
magnetic  meridian,  according  to  the  velocity  of  the  rotation  of  the  disc. 
But  if  this  velocity  increases,  the  needle  is  ultimately  deflected  more  than 
90° ;  it  is  then  carried  along,  describes  an  entire  revolution,  and  follows  the 
motion  of  the  disc  until  this  stops. 

Babbage  and  Herschel  modified  Arago's  experiment  by  causing  a  horse- 
shoe magnet  placed  vertically  to  rotate  below  a  copper  disc  suspended  on 
silk  threads  without  torsion  ;  the  disc  rotated  in  the  same  direction  as  the 
magnets.  The  effect  decreases  with  the  distance  of  the  disc,  and  varies 
with  its  nature.  The  maximum  effect  is  produced  with  metals  ;  with  wood, 
glass,  water,  &c.  it  disappears.  Babbage  and  Herschel  found  that,  represent- 
ing this  action  on  copper  at  100,  the  action  on  other  metals  is  as  follows  : 
zinc  95,  tin  46,  lead  25,  antimony  9,  bismuth  2.  Lastly,  the  effect  is  enfeebled 
if  there  are  non-conducting  breaks  in  the  disc,  especially  in  the  direction  of 
the  radii ;  but  it  is  the  same  if  these  breaks  are  soldered  with  any  metal. 

Faraday  made  an  experiment  the  reverse  of  Arago's  first  observation  ; 
since  the  presence  of  a  metal  at  rest  stops  the  oscillations  of  a  magnetic 
needle,  the  neighbourhood  of  a  magnet  at  rest  ought  to  stop  the  motion  of  a 
rotating  mass  of  metal.  Faraday  suspended  a  cube  of  copper  to  a  twisted 
thread,  which  was  placed  between  the  poles  of  a  powerful  electromagnet. 
When  the  thread  was  left  to  itself,  it  began  to  spin  round  with  great  velocity, 
but  stopped  the  moment  a  powerful  current  passed  through  the  electromagnet. 

Faraday  was  the  first  to  give  an  explanation  of  all  these  phenomena  of 
magnetism  by  rotation.  They  depend  on  the  circumstances  that  a  magnet 


-906]  Induction  by  tJie  Action  of  the  Earth.  855 

or  a  solenoid  can  induce  currents  in  a  solid  mass  of  metal.  In  the  above  case 
the  magnet  induces  currents  in  the  disc  when  the  latter  is  rotated  ;  and  con- 
versely when  the  magnet  is  rotated  while  the  disc  is  primarily  at  rest.  Now 
these  induced  currents,  by  their  electrodynamic  action,  tend  to  destroy  the 
motion  which  gave  rise  to  them  ;  they  are  simple  illustrations  of  Lenz's  law  ; 
they  act  in  the  same  way  as  friction  would  do. 

i.  For  instance,  let  AB  (fig.  820)  be  a  needle  oscillating  over  a  copper 
disc,  and  suppose  that  in  one  of  its  oscillations  it  goes  in  the  direction  of  the 
arrows  from  N  to  M.  In  approaching  the  point  M,  for 
instance,  it  develops  there  a  current  in  the  opposite 
direction,  and  which  therefore  repels  it ;  in  moving  away 
from  N  it  produces  currents  which  are  of  the  same  kind, 
and  which  therefore  attract,  and  both  these  actions 
concur  in  bringing  it  to  rest. 

ii.  Suppose  the  metallic  mass  turns  from  N  towards 
M,  and  that  the  magnet  is  fixed  ;  the  magnet  will  repel 
by  induction  points  such  as  N  which  are  approaching  A, 
and  will  attract  M  which  is  moving  away  ;  hence  the  motion  of  the  metal 
stops,  as  in  Faraday's  experiment. 

iii.  If  in  Arago's  experiment  the  disc  is  moving  from  N  to  M,  N  ap- 
proaches A  and  repels  it,  while  M,  moving  away,  attracts  it  ;  hence  the  needle 
moves  in  the  same  direction  as  the  disc. 

If  this  explanation  is  true,  all  circumstances  which  favour  induction  will 
increase  the  dynamic  action  ;  and  those  which  diminish  the  former  will 
also  lessen  the  latter.  We  know  that  induction  is  greater  in  good  conductors, 
and  that  it  does  not  take  place  in  insulating  substances ;  but  we  have  seen 
that  the  needle  is  moved  with  a  force  which  is  less,  the  less  the  conducting 
power  of  the  disc,  and  it  is  not  moved  when  the  disc  is  of  glass.  Dove  found 
that  there  is  no  induction  on  a  tube  split  lengthwise  in  which  a  coil  is 
introduced. 

In  order  to  bring  the  oscillations  of  the  needle  of  a  galvanometer  more 
quickly  to  rest,  the  wire  is  coiled  upon  a  copper  frame.  Such  an  arrange- 
ment is  called  a  damper,  and  in  practice  it  is  frequently  used. 

The  strength  of  the  induction  currents  is  proportional  to  their  relative 
velocities,  and  therefore  the  amplitudes  of  the  vibration  diminish  according 
to  the  law  of  a  geometrical  series.  The  greater  the  masses  of  metal  and 
the  more  closely  they  surround  the  magnet,  the  stronger  is  the  damping ;  it 
is  approximately  according  to  the  inverse  square  of  the  distance. 
^906.  Induction  by  the  action  of  the  earth. — Faraday  discovered  that 
terrestrial  magnetism  can  develop  induced  currents  in  metallic  bodies  in 
motion^  acting  like  a  powerful  magnet  placed  in  the  interior  of  the  earth  in 
the  direction  of  the  dipping  needle,  or,  according  to  the  theory  of  Ampere, 
like  a  series  of  electrical  currents  directed  from  east  to  west  parallel  to  the 
magnetic  equator.  He  first  proved  this  by  placing  a  long  helix  of  copper 
wire  covered  with  silk  (such  as  A,  fig.  816)  in  the  plane  of  the  magnetic 
meridian  parallel  to  the  dipping  needle  ;  by  turning  this  helix  180°  about  an 
axis  perpendicular  to  its  length  in  its  middle,  he  observed  that  at  each  turn 
a  galvanometer  connected  with  the  two  ends  of  the  helix  was  deflected.  The 
apparatus  depicted  in  fig.  821,  and  known  as  Deleze.nnds  circle,  serves  for 


856 


Dynamical  Electricity. 


[906 


showing  the  currents  produced  by  the  inductive  action  of  the  earth.  It 
consists  of  a  wooden  ring,  RS.  about  two  feet  in  diameter,  fixed  to  an  axis,, 
oa,  about  which  it  can  be  turned  by  means  of  a  handle,  M.  The  axis  oa  is 
itself  fixed  in  a  frame  PQ,  movable  about  a  horizontal  axis.  By  pointers 
fixed  to  these  two  axes*  the  inclination  towards  the  horizon  of  the  frame  PO, 
and  therefore  of  the  axis  oa,  is  indicated  on  a  dial,  b,  while  a  second  dial,  c\ 
gives  the  angular  displacement  of  the  ring.  This  ring  has  a  groove  in  which 
is  coiled  a  great  length  of  insulated  copper  wire.  The  two  ends  of  the  wire 
terminate  in  a  commutator  analogous  to  that  in  Clarke's  apparatus  (912),  the 
object  of  which  is  to  pass  the  current  always  in  the  same  sense,  although  its 
direction,  SR,  changes  at  each  half-turn  of  the  ring.  On  each  of  the  rings 
of  the  commutator  are  two  brass  plates,  which  transmit;  the  current  to  two- 
wires  in  contact  with  the  galvanometer.  Suppose  that  the  ends  of  the 


Fig.  821. 

wire  on  the  coil  are  directly  connected  with  wires  leading  to  a  galvanometer 
at  some  distance,  and  the  apparatus  so  placed  that  its  axis  of  rotation  oa 
is  at  right  angles  to  the  magnetic  meridian,  and  the  plane  of  the  ring,  RS, 
at  right  angles  to  the  line  of  dip.  If,  now,  the  frame  be  quickly  turned 
through  1 80°,  the  needle  will  be  momentarily  deflected,  to  the  right  for 
instance  ;  if,  while  the  needle  on  its  return  is  just  passing  its  position  ot 
rest,  the  frame  is  rapidly  turned  to  its  original  position,  it  will  be  deflected 
to  the  left  to  a  greater  angle  than  at  first,  for  the  needle  is  already  in  motion  ; 
by  repeating  the  operation,  that  is,  reversing  the  swing  when  the  needle  is 
passing  its  position  of  rest,  the  deflections  will  increase  to  a  maximum,  which 
is  a  measure  of  the  earth's  magnetism.  This  method  of  amplifying  an 
originally  small  motion  is  known  as  the  method  of  multiplication. 

If  the  axis  of  rotation,  oa,  is  vertical  and  the  ring  is  rotated  as  above 
described,  only  the  horizontal  component  of  the  earth's  magnetism  can  act, 
and  the  angular  deflection  is  then  a  measure  of  the  horizontal  component  H. 
Similarly,  if  the  axis  is  horizontal  and  in  the  plane  of  the  magnetic  meridian, 
and  if  the  rotation  is  made  through  180°  from  the  horizontal  position,  only 
the  vertical  component  V  acts,  and  is  thus  measured  by  the  deflection. 


-907]      Induction  of  a  Ctirrent  on  itself.     Extra  Current.         857 
Hence,  from  two  such  sets  of  observations  we  may  determine  the  inclina- 
tion in  any  place,  for  tan  i-  — . 

rl 

To  experiment  with  the  currents  produced  by  continuous  rotation  the 
wires  are  connected  with  the  commutator. 

"Y9O7.  Induction  of  a  current  on  itself.  Extra  current. — If  a  closed 
circuit  traversed  by  a  voltaic  current  be  opened,  a  scarcely  perceptible  spark 
is  obtained  if  the  wire  joining  the  two  poles  be  short.  Further,  if  the  ob- 
server himself  form  part  of  the  circuit  by  holding  a  pole  in  each  hand,  no 
shock  is  perceived  unless  the  current  is  very  strong.  If,  on  the  contrary, 
the  wire  is  long,  and  especially  if  it  makes  a  great  number  of  turns  so  as  to 
form  a  bobbin  with  very  close  folds,  the  spark,  which  is  inappreciable  when 
the  current  is  closed,  acquires  a  great  intensity  when  it  is  opened,  and  an 
observer  in  the  circuit  receives  a  shock  which  is  the  stronger  the  greater  the 
number  of  turns. 

Faraday  referred  this  strengthening  of  the  current  when  it  is  broken  to 
an  inductive  action  which  the  current  in  each  coil  exerts  upon  the  adjacent 
coils  :  an  action  in  virtue  of  which  there  is  produced  in  the  bobbin  a  direct 
induced  current — that  is,  one  in  the  same  direction  as  the  principal  one. 
This  is  known  as  the  extra  current.  :  : 

To  show  the  existence  of  this  current,  at  the  moment  of  opening,  Fara- 


Fig.  822. 

day  arranged  the  experiment  as  seen  in  fig.  822.  Two  wires  from  the  poles 
E  E'  of  a  battery  are  connected  with  two  binding  screws,  D  and  F,  with 
'which  are  also  connected  the  two  ends  of  a  bobbin,  B,  with  a  long  fine  wire 
which  offers  therefore  a  great  resistance .  On  the  path  of  the  wires  at  the 
points  A  and  C  are  two  other  wires,. which  are  connected  with  a  galvano- 
meter, G.  Hence  the  current  from  the  pole  E  branches  at  A  into  two  cur- 
rents, one  which  traverses  the  galvanometer,  the  other  the  bobbin,  and  both 
oining  the  negative  pole  E'. 

The  needle  of  the  galvanometer  being  then  deflected  from  G  to  a'  by  the 
current  which  goes  from  A  to  C,  it  is  brought  back  to  zero,  and  kept  there  by 
an  obstacle  which  prevents  it  from  turning  in  the  direction  Gd/,  but  leaves  it 


858  Dynamical  Electricity.  [907- 

free  in  the  opposite  direction.  On  breaking  contact  at  E,  it  is  seen  that  the 
moment  the  circuit  is  open  the  needle  is  deflected  in  the  direction  Ga  ; 
showing  a  current  contrary  to  that  which  passed  during  the  existence  of  the 
current — that  is,  showing  the  current  from  C  to  A.  But  the  battery  current 
having  ceased,  the  only  remaining  one  is  the  current  AFBCDA  ;  and  since  in 
the  part  CA  the  current  goes  from  C  to  A,  it  must  traverse  the  entire  circuit 
in  the  direction  AFBDC — that  is,  the  same  as  the  principal  current.  This 
current,  which  thus  appears  when  the  circuit  is  opened,  is  the  extra  current, 
or  current  of  self-induction. 

908.  Extra  current  on  opening:  and  on  closing-. — The  coils  of  the  spiral 
act  inductively  on  each  other,  not  merely  on  opening  but  also  on  closing 
the  current.  Hence,  in  accordance  with  the  general  law  of  induction,  each 
spiral  acting  on  each  succeeding  one  induces  a  current  in  the  opposite 
direction  to  its  own — that  is,  an  inverse  current :  this,  which  is  the  extra 
cttrrent  on  closing,  or  the  inverse  extra  current,  being  of  contrary  direction 
to  the  principal  one,  diminishes  its  intensity  and  lessens  or  suppresses  the 
spark  on  closing. 

When,  however,  the  current  is  opened,  each  turn  then  acts  inductively 
on  each  succeeding  one,  producing  a  current  in  the  same  direction  as  its  own, 
and  which  therefore  greatly  heightens  the  intensity  of  the  principal  current. 
This  is  the  extra  current  on  opening,  or  direct  extra  current. 

To  observe  the  direct  extra  current,  the  conductor  on  which  its  effect  is 
to  be  traced  may  be  introduced  into  the  circuit,  by  being  connected  in  any 
suitable  manner  with  the  binding  screws  A  and  C  in  the  place  of  the  galvano- 
meter. It  can  thus  be  shown  that  the  direct  extra  current  gives  violent 
shocks  and  bright  sparks,  decomposes  water,  melts  platinum  wires,  and 
magnetises  steel  needles.  The  shock  produced  by  the  current  may  be 
tried  by  attaching  the  ends  of  the  wire  to  two  files,  which  are  held  in  the 
hands.  On  moving  the  point  of  one  file  over  the  teeth  of  the  other,  a  series 
of  shocks  is  obtained,  due  to  the  alternate  opening  and  closing  of  the  current. 

The  above  effects  acquire  greater  intensity  when  a  bar  of  soft  iron  is 
introduced  into  the  bobbin,  or,  what  is  the  same  thing,  when  the  current  is 
passed  through  the  bobbin  of  an  electromagnet ;  and  still  more  is  this  the 
case  if  the  core,  instead  of  being  massive,  consists  of  a  bundle  of  straight 
wires.  Faraday  explained  this  strengthening  action  of  soft  iron  as  follows  : 
If  inside  the  spiral  there  is  an  iron  bar,  on  opening  the  circuit  when  the 
principal  current  disappears,  the  magnetism  which  it  evokes  in  the  bar 
disappears  too  ;  but  the  disappearance  of  this  magnetism  acts  like  the  dis- 
appearance of  the  electrical  current,  and  the  disappearing  magnetism  in- 
duces a  current  in  the  same  direction  as  the  disappearing  principal  current, 
the  effect  of  which  is  thus  heightened. 

In  the  experiments  just  described  the  effects  of  the  two  extra  currents 
accompany  those  of  the  principal  current.  Edlund  has  devised  an  in- 
genious arrangement  of  apparatus  by  which  the  action  of  the  principal  cur- 
rent on  the  measuring  instruments  can  be  completely  avoided,  so  that  only 
that  of  the  extra  current  remains.  In  this  way  -he  has  arrived  at  the  follow- 
ing laws  : — 

i.  The  strength  of  the  currents  tised  being  the  same,  the  extra  currents 
obtained  on  opening  and  closing  Jiave  the  same  electromotive  force. 


-911]  Magneto -electrical  Apparatus.  859 

ii.  The  electromotive  force  of  the  extra  current  is  proportional  to  the 
strength  of  the  primary  current. 

909.  Induced  currents  of  different  orders. — Spite  of  their  instantaneous 
character,  induced  currents  can  themselves,  by  their  action  on  closed  circuits, 
give  rise  to  new  induced  currents,  these  again  to  others,  and  so  on,  producing 
induced  currents  of  different  orders. 

These  currents,  discovered  by  Henry,  may  be  obtained  by  causing  to 
act  on  each  other  a  series  of  bobbins,  each  formed  of  a  copper  wire  covered 
with  silk,  and  coiled  spirally  in  one  plane,  like  that  represented  in  plate  A, 
fig.  817.  The  currents  thus  produced  are  alternately  in  opposite  directions, 
and  their  intensity  decreases  in  proportion  as  they  are  of  a  higher  order. 

910.  Properties  of  induced  currents. — Notwithstanding  their  instan- 
taneous character,  it  appears  from  the  preceding  experiments  that  induced 
currents  have  all  the  properties  of  ordinary  currents.     They  produce  violent 
physiological,  luminous,  calorific,  and  chemical  effects,  and  finally  give  rise 
to  new  induced  currents.     They  also  deflect  the  magnetic  needle  and  mag- 
netise steel  bars  when  they  are  passed  through  a  copper  wire  coiled  in  a 
helix  round  the  bars. 

The  intensity  of  the  shock  produced  by  induced  currents  renders  their 
effects  comparable  to  those  of  electricity  at  high  potential. 

The  direct  induced  current  and  the  inverse  induced  current  have  been 
compared  as  to  their  chemical  action  ;  the  violence  of  the  shock  ;  the  deflec- 
tion of  the  galvanometer  \  and  the  magnetising  action  on  steel  bars.  In  these 
respects  they  differ  greatly  :  they  are  equal  in  their  chemical  action  ;  they  are 
about  equal  in  their  action  on  the  galvanometer  ;  but  while  the  shock  of  the 
direct  current  is  very  powerful,  that  of  the  inverse  current  is  scarcely  percept- 
ible. The  same  difference  prevails  with  reference  to  the  magnetising  force. 
The  direct  current  magnetises  to  saturation,  while  the  inverse  current  does 
notjnagnetise. 

1  911.  Magneto-electrical  apparatus. — After  the  discovery  of  magneto- 
electrical  induction,  several  attempts  were  made  to  produce  an  uninterrupted 
series  of  sparks  by  means  of  a  magnet.  Apparatus  for  this  purpose  were 
devised  by  Pixii  and  Ritchie,  and  subsequently  by  Saxton,  Ettingshausen, 
and  Clarke.  Fig.  824  represents  that  invented  by  Clarke.  It  consists  of 
a  powerful  horseshoe  magnetic  battery,  A,  fixed  against  a  vertical  wooden 
support.  In  front  of  this  are  two  bobbins,  B  B',  movable  round  a  hori- 
zontal axis.  These  bobbins  are  coiled  on  two  cylinders  of  soft  iron  joined 
at  one  end  by  a  plate  of  soft  iron,  V,  and  at  the  other  by  a  similar  plate 
of  brass.  These  two  plates  are  fixed  on  a  copper  axis,  terminated  at 
one  end  by  a  commutator,  qi^  and  at  the  other  by  a  pulley,  which  is  moved  by 
an  endless  band  passing  round  a  large  wheel,  which  is  turned  by  a  handle. 

Each  bobbin  consists  of  about  1,500  turns  of  very  fine  copper  wire 
covered  with  silk.  One  end  of  the  wire  of  the  bobbin  B  is  connected  on 
the  axis  of  rotation  with  one  end  of  the  wire  of  the  bobbin  B7,  and  the  two 
other  ends  of  these  wires  terminate  in  a  copper  ferrule  or  washer,  ^,  which 
is  fixed  to  the  axis,  but  is  insulated  by  a  cylindrical  envelope  of  ivory.  In 
order  that  in  each  wire  the  induced  current  may  be  in  the  same  direction,  it 
is  coiled  on  the  two  bobbins  in  different  directions— that  is,  one  is  right- 
handed,  the  other  left-handed. 


86o  Dynamical  Electricity.  [911- 

When  now  the  electromagnet  turns,  its  two  branches  become  alternately 
magnetised  in  contrary  directions  under  the  influence  of  the  magnet  A,  and 
in  each  wire  an  induced  current  is  produced,  the  direction  of  which  changes 
at  each  half-turn. 

Let  us  follow  one  of  the  bobbins — B,  for  instance — while  it  makes  a  com- 
plete revolution  in  front  of  the  poles  a  and  b  of  the  magnet  ;  calling  the 
poles  of  the  electromagnet  successively  a'  and  b'.  Let  us  further  consider 
the  latter  when  it  passes  in  front  of  the  north  pole  of  the  magnetic  battery 
(fig.  824).  The  iron  has  then  a  south  pole  in  which,  as  we  know,  the  Am- 
perian currents  move  like  the  hands  of  a  watch.  The  contrary  seems  to  be 


Fig.  824. 

represented  in  fig.  825,  but  it  must  be  remembered  that  the  bobbins  are 
seen  here  as  they  are  in  fig.  824  ;  and  hence,  when  viewed  at  the  end  which 
faces  the  magnet,  the  Amperian  currents  seem  to  turn  like  the  hands  of  a 
watch.  These  currents  act  inductively  on  the  wire  of  the  bobbin,  producing 
a  current  in  the  same  direction  (902,  iii.),  for  the  bobbin  moves  away  from 
the  pole  #,  its  soft  iron  is  demagnetised,  and  the  Amperian  currents  cease. 
The  intensity  of  the  induced  current  in  the  bobbin  decreases,  until  the 
right  line  joining  the  axes  of  the  two  bobbins  is  perpendicular  to  that  which 
joins  the  poles  a  and  b  of  the  bar.  There  is  now  no  magnetisation  in  the  bar, 
but  quickly  approaching  the  pole  b,  its  soft  iron  is  then  magnetised  in  the 
opposite  direction — that  is,  becomes  a  north  pole  (fig.  826).  The  Amperian 
currents  are  then  in  the  direction  of  the  arrow  af ;  and  as  they  are  com- 
mencing, they  develop  in  the  wire  of  the  bobbin  an  inverse  current  (901) 


-912]  Commutator.  86 1 

which  is  in  the  same  direction  as  that  developed  in  the  first  quarter  of  the 
turn.  Moreover,  this  second  current  adds  itself  to  the  first  ;  for  while  the 
bobbin  moves  away  from  a,  it  approaches  b.  Hence,  during  the  lower  half- 
turn  from  a  to  b,  the  wire  was  successively  traversed  by  two  induced  currents 
in  the  same  direction,  and  if  the  rotatory  motion  is  sufficiently  rapid,  we 
might  admit  during  this  half-turn  the  existence  of  a  single  current  in  the  wire. 
The  same  reasoning  applied  to  the  figures  827  and  828  will  show  that 
•during  the  upper  half-turn  the  wire  of  the  bobbin  B  is  still  traversed  by 


Fig.  825. 


Fig.  826. 


Fig.  827. 

a.  single  current,  but  in  the  opposite  direction  to  that  of  the  lower  half-turn. 
What  has  been  said  about  the  bobbin  B  applies  obviously  to  the  bobbin 
B';  yet,  as  one  of  these  is  right-handed  and  the  other  left-handed,  the 
•currents  are  constantly  in  the  same  direction  in  the  two  bobbins  during 
each  upper  or  lower  half-revolution.  At  each  successive  half-turn  they  both 
•change,  but  are  in  the  same  direction  as  regards  each  other  ;  the  term 
'direction'  having  here  reference  to  figs.  825-828. 

N/9i2.  Commutator. — The  object  of  this  apparatus  (fig.  829),  of  which  fig. 
830  is  a  section,  is  to  bring  the  two  alternating  currents  always  in  the  same 
direction.  It  consists  of  an  insulating  cylinder  of  ivory  or  ebony,  J,  in  the 
axis  of  which  is  a  copper  cylinder,  k,  of  smaller  diameter,  fixed  to  the  arma- 
ture V,  and  turning  with  the  bobbins.  On  the  ivory  cylinder  is  first  a  brass 
ferrule,  g,  and  in  front  of  it  two  half-ferrules,  o  and  o',  also  of  brass  and 
completely  insulated  from  one  another.  The  half-ferrule  o  is  connected  with 
>the  ferrule  q  by  a  tongue,  x.  On  the  sides  of  a  block  of  wood,  M,  there  are 


862 


Dynamical  Electricity. 


[912- 


two  brass  plates,  ;//,  ;/,  on  which  are  screwed  two  elastic  springs,  b  and  r,which 
press  successively  on  the  half-ferrules  o  and  <?',  when  rotation  takes  place. 

We  have  al- 
ready seen  that 
the  two  ends  of 
the  wire  of  the 
bobbin,  those  in 
the  same  direc- 
tion with  respect 
to  the  currents 
passing  through 
them  at  any 
time,  which  will 
be  found  to  be 
those  farthest 
away  from  the 
armature  V,  ter- 
minate in  the 
metallic  axis  k, 
and  therefore  on 
the  half-ferrule 
o'\  while  the 
other  two  ends, 


Fig.  829. 


Jill 


both  in  the  same  direction  with  respect  to  the  current,  are  joined  to  the 
ferrule  g,  and  therefore  to  the  half-ferrule  o.  It  follows  that  the  pieces 
o  o'  are  always  poles  of  alternating  currents  which  are  developed  in  the 

bobbins  :  and,  as  these  are 
alternately  in  contraiy  direc- 
tions, the  pieces  o  and  o' 
are  alternately  positive  and 
negative.  Now,  taking  the 
case  in  which  the  half-ferrule 
o'  is  positive,  the  current 
descends  by  the  spring  b, 
follows  the  plate  ?;z,  arrives 
at  n  by  the  joining  wire  p, 
ascends  in  ^,  and  is  closed 
by  contact  with  the  piece  o  ; 
then  when,  in  consequence 
of  rotation,  o  takes  the  place  ot  o',  the  current  retains  the  same  direction  ; 
for,  as  it  is  then  reversed  in  the  bobbins,  o  has  become  positive  and  o' 
negative,  and  so  forth  as  long  as  the  bobbin  is  turned. 

With  the  two  springs  b  and  c  alone,  the  opposite  currents  from  the  two 
pieces  o  and  o'  could  not  unite  when  m  and  n  are  not  joined  ;  this  is  effected 
by  means  of  a  third  spring,  a  (fig.  832),  and  of  two  appendices,  /,  only  one  of 
which  is  visible  in  the  figure.  These  two  pieces  are  insulated  from  one 
another  on  an  ivory  cylinder,  but  communicate  respectively  with  the  pieces 
o  and  o'.  As  often  as  the  spring  a  touches  one  of  these  pieces  it  is  connected 
with  the  spring  6,  and  the  current  is  closed,  for  it  passes  from  b  to  a,  and 


-913]  Magneto-electrical  Machine.  863 

then  reaches  the  spring  c  by  the  plate  n.     On  the  contrary,  as  long  as  the 
spring  a  does  not  touch  one  of  these  appendices  the  current  is  broken. 

For  physiological  effects  the  use  of  the  spring  a  greatly  increases  the 
intensity  of  the  shocks.  For  this  purpose  two  long  spirals  of  copper  wire 
with  handles,/  and/',  are  fixed  at  n  and  m.  Holding  the  handles  in  the 
hands,  so  long  as  the  spring  a  does  not  touch  the  appendices  z,  the  current 
passes  through  the  body  of  the  experimenter,  but  without  appreciable  effect  ; 
while  each  time  that  the  plate  a  touches  one  of  the  appendices  z,  the  current, 
as  we  have  seen  above,  is  closed  by  the  pieces  £,  <z,  and  c,  and  ceasing  then 
to  pass  through  the  wires  np,  mp' ',  there  is  produced  in  this  and  through  the 
body  a  direct  extra  current  which  causes  a  violent  shock. 

This  is  renewed  at  each  half-turn  of  the  electromagnet,  and  its  intensity 
increases  with  the  velocity  of  the  rotation.  The  muscles  contract  with  such 
force  that  they  do  not  obey  the  will,  and  the  two  hands  cannot  be  detached. 
With  an  apparatus  of  large  dimen- 
sions a  continuance  of  the  shock 
is  unendurable. 

All  the  effects  of  voltaic  cur- 
rents may  be  produced  by  the  in- 
duced current  of  Clarke's  machine. 
Fig.  823  shows  how  the  apparatus 
is  to  be  arranged  for  the  decom- 
position of  water.  The  spring  a 
is  suppressed,  the  current  being 
closed  by  the  two  wires  which  re-  Fig.  831.  Fig.  832. 

present  the  electrodes. 

For  physiological  and  chemical  effects  the  wire  rolled  on  the  bobbins  is 
fine,  and  each  about  500  or  600  yards  in  length.  For  heating  effects,  on  the 
contrary,  the  wire  is  thick,  and  there  are  about  25  to  35  yards  on  each  bobbin. 
Figs.  831  and  832  represent  the  arrangement  of  the  bobbins  and  the  com- 
mutator in  each  case.  The  first  represents  the  inflammation  of  ether,  and 
the  second  the  incandescence  of  a  metallic  wire,  a,  in  which  the  current  from 
the  plate  a  to  the  plate  c  always  passes  in  the  same  direction. 

Pixii's  and  Saxton's  electromagnetic  machine  differs  from  Clarke's  in 
having  the  electromagnet  fixed  while  the  magnet  rotates. 

Wheatstone  devised  a  compendious  form  of  the  magneto-electrical 
machine,  for  the  purpose  of  using  the  induced  spark  in  firing  mines  (794). 

Breguet's  apparatus  for  the  same  purpose  consists  of  a  powerful  horse- 
shoe magnetic  battery,  to  the  ends  of  which  are  screwed  soft  iron  cores, 
round  which  are  coils  of  fine  wires ;  to  these  are  connected  the  wires  leading 
to  the  mine  to  be  fired.  The  ends  of  the  soft  cores  are  connected  by  a 
soft  iron  keeper;  and  when,  by  a  suitable  mechanism,  this  is  suddenly 
detached  from  the  cores,  a  powerful  momentary  induction  current  is  pro- 
duced in  the  bobbins,  which  is  sufficient  to  fire  more  than  one  fuse,  through 
even  a  considerable  length  of  wire. 

913.  Magneto-electrical  machine. — The  principle  of  Clarke's  apparatus 
has  received  in  the  last  few  years  a  remarkable  extension  in  large  magneto- 
electrical  machines,  by  means  of  which  mechanical  work  is  transformed  into 
powerful  electric  currents  by  the  inductive  action  of  magnets  on  coils  in  motion. 


864 


Dynamical  Electricity. 


[913 


The  first  machine  of  this  kind  was  invented  by  Nollet,  in  Brussels,  in 
1850.  It  consists  (fig.  833),  of  a  cast-iron  frame,  5^  feet  in  height,  on  the 
circumference  of  which  eight  series  of  five  powerful  horseshoe  magnetic 
batteries,  A,  A,  A,  are  arranged  in  a  parallel  order  on  wooden  cross-pieces. 
These  batteries,  each  of  which  can  support  from  120  to  130  pounds,  are  so 


Fig.  833. 

arranged  that  if  they  are  considered  either  parallel  to  the  axis  of  the  frame, 
or  in  a  plane  perpendicular  to  this  axis,  opposite  poles  always  face  one 
another.  In  each  series  the  outside  batteries  consist  of  three  magnetised 
plates,  while  the  three  middle  ones  have  six  plates,  because  they  act  by  both 
faces,  while  the  first  only  acts  by  one. 

On  a  horizontal  iron  axis  going  from  one  end  to  the  other  of  the  frame 
four  bronze  wheels  are  fixed,  each  corresponding  to  the  intervals  between 
the  magnetic  batteries  of  two  vertical  series.  There  are  16  coils  on  the 


913]  Magneto-electrical  Machine.  865 

circumference  of  each  of  these — that  is,  as  many  as  there  are  magnetic  poles 
in  each  vertical  series  of  magnets.  These  coils,  represented  in  fig.  834,  differ 
from  those  of  Clarke's  apparatus  in  having  12  wires,  each  1 1^  yards  in  length, 
instead  of  a  single  wire,  by  which  the  resistance  is  diminished.  The  wires 
of  these  coils  are  insulated  by  means  of  bitumen  dissolved  in  oil  of  turpentine. 
They  are  not  wound  upon  solid  cylinders  of  iron,  but  on  iron  tubes,  split 
longitudinally  ;  this  device  renders  the  magnetisation  and  demagnetisation 
more  rapid  when  the  coils  pass  in  front  of  the  poles  of  the  magnet.  Further, 
the  discs  of  copper  which  terminate  the  coils  are  slit  in  the  direction  of  the 
radius,  in  order  to  prevent  the  formation  of  induced  currents  in  these  discs. 
The  four  wheels  being  respectively  provided  with  16  coils  each,  there  are 
altogether  64  coils  arranged  in  16  horizontal  series  of  four,  as  seen  at  D,  on  the 
left  of  the  frame.  The  length  of  the  wire  on  each  coil  being  12  times  n£ 
yards,  or  138  yards,  the  total  length  in  the  whole  apparatus  is  64  times 
138  yards,  or  8,832  yards. 

The  wires  are  wound  on  all  the  coils  in  the  same  direction  ;  and  not  only 
on  the  same  wheel,  but  on  all  four,  all  wires  are  connected  with  one  another. 
For  this  purpose  the  bobbins  are  joined,  as  shown  in  fig.  835  :  on  the  first 
wheel  the  twelve  wires  of  the  first  coil,  x,  are  connected  on  a  piece  of 
mahogany  fixed  on  the  front  face  of  the  wheel  with  a  plate  of  copper,  m, 


Fig.  834-  Fig.  835. 

connected  by  a  wire,  O,  with  the  centre  of  the  axis  which  supports  the 
wheels.  At  the  other  end,  on  the  other  face  of  the  wheel,  the  same  wires  are 
soldered  to  a  plate  indicated  by  a  dotted  line  which  connects  them  with  the 
coil  y ;  from  this  they  are  connected  with  the  coil  z  by  a  plate,  /,  and  so  on 
for  the  coils  /,  a,  ...  up  to  the  last,  v.  The  wires  of  this  coil  terminate  in 
a  plate,  »,  which  traverses  the  first  wheel,  and  is  soldered  to  the  wires  of  the 
first  coil  of  the  next  wheel,  on  which  the  same  series  of  connections  is  re- 
peated ;  these  wires  pass  to  the  third  wheel,  thence  to  the  fourth,  and  so  on 
to  the  end  of  the  axis. 

The  coils  being  thus  arranged,  one  after  another,  like  the  elements  of  a 
battery  connected  in  a  series  (825),  the  electricity  is  of  high  potential.  But 
they  may  also  be  arranged  by  connecting  the  plates  alternately,  not  with 
each  other,  but  with  two  metal  rings  in  such  a  manner  that  all  the  ends  of 
the  same  name  are  connected  with  the  same  ring.  Each  of  these  rings 
is  then  a  pole,  and  this  arrangement  may  be  used  where  a  high  degree  of 
potential  is  not  required. 

From  these  explanations  it  will  be  easy  to  understand  the  manner  in 

3K 


866 


Dynamical  Electricity. 


[913- 


which  electricity  is  produced  and  propagated  in  this  apparatus.  An  endless 
band,  receiving  its  motion  from  a  steam-engine,  passes  round  a  pulley  fixed 
at  the  end  of  the  axis  which  supports  the  wheels  and  the  coils,  and  moves 
the  whole  system  with  any  desired  rapidity.  Experience  has  shown  that  to 
obtain  the  greatest  degree  of  light,  the  most  suitable  velocity  is  235  revolu- 
tions in  a  minute.  During  this  rotation,  if  we  at  first  consider  a  single 
coil,  the  tube  of  soft  iron  on  which  it  is  coiled,  in  passing  in  front  of  the 
poles  of  the  magnet,  undergoes  at  its  two  ends  an  opposite  induction,  the 
effects  of  which  are  added,  but  change  from  one  pole  to  another.  As  these 
tubes,  during  one  rotation,  pass  successively  in  front  of  sixteen  poles 
alternately  of  different  names,  they  are  magnetised  eight  times  in  one  di- 
rection and  eight  times  in  the  opposite  direction.  In  the  same  time  there 
are  thus  produced  in  the  bobbin  eight  direct  induced  currents  and  eight 
inverse  induced  currents  ;  in  all,  sixteen  currents  in  each  revolution.  With 
a  velocity  of  235  turns  in  a  minute,  the  number  of  currents  in  the  same  time 
is  235  x  16  =  3,760  alternately  in  opposite  directions.  The  same  phe- 
nomenon is  produced  with  each  of  the  64  coils  ;  but  as  they  are  all  wound 
in  the  same  direction,  and  are  connected  with  each  other,  their  effects  accu- 
mulate, and  there  is  the  same  number  of  currents,  but  they  are  more  intense. 
To  utilise  these  currents  in  producing  the  electric  light,  the  connections 
are  made  as  shown  in  fig.  836.  On  the  posterior  side  the  last  coil,  .r\  of 
the  fourth  wheel  terminates  by  a  wire,  G  on  the  axis  MN,  which  supports 


w 


Fig.  836. 

the  wheels :  the  current  thus  passes  to  the  axis,  and  thence  over  all 
the  machine,  so  that  it  can  be  taken  from  any  desired  point.  In  the 
front  the  first  coil,  .r,  of  the  first  wheel  communicates,  by  the  wire  O,  not 
with  the  axis  itself  but  with  a  steel  cylinder,  £,  fitted  in  the  axis,  from  which 
however,  it  is  insulated  by  an  ivory  collar.  The  screw  *,  to  which  the  wire 
O  is  attached,  is  likewise  insulated  by  a  piece  of  ivory.  From  the  cylinder 
c  the  current  passes  to  a  fixed  metallic  piece,  K,  from  which  it  passes  to 
the  wire  H,  which  transmits  it  to  the  binding  screw  a  of  fig.  833.  The 
binding  screw  b  communicates  with  the  framework,  and  therefore  with  the 
wire  of  the  last  coil  xf  (fig.  836).  From  the  two  binding  screws  a  and  b 
the  current  passes  by  two  copper  wires  to  two  carbons,  the  distance  of 
which  is  regulated  by  means  of  an  apparatus  analogous  in  principle  to  that 
already  described  (835) 

In  this  machine  the  currents  are  not  rectified  so  as  to  be  in  the  same 
direction — it  produces  alternate  currents  ;  hence  each  carbon  is  alternately 


-914]  Siemens'  Armature.  867 

positive  and  negative,  and  in  fact  they  are  consumed  with  equal  rapidity 
When  these  currents  are  applied  to  produce  the  electric  light,  it  is  not 
necessary  they  should  be  in  the  same  direction  if  a  suitable  lamp  be  used  : 
but  when  they  are  to  be  used  for  electro-metallurgy,  or  for  magnetising,  they 
must  be  rectified,  which  is  effected  by  means  of  a  suitable  commutator. 

This  type  of  machine  may  claim  a  description  here  as  that  by  which 
magneto-electrical  currents  were  first  applied  on  a  large  scale  for  technical 
purposes.  Such  machines,  are,  however,  being  superseded  by  various  im- 
proved forms  of  machines,  which  for  the  same  power  are  simpler,  less  costly, 
and  occupy  a  smaller  space.  Of  the  newer  forms  of  magneto-electrical 
machine  that  of  Meriten's  is  stated  to  give  the  best  results. 

914.  Siemens'  armature. — Dr.  Siemens  devised  a  cylindrical  armature 
for  magneto-electrical  machines,  in  which  the  insulated  wire  is  wound  length- 
wise on  the  core,  instead  of  transversely,  as  is  usually  the  case. 

It  consists  of  a  soft  iron  rod  or  cylinder,  AB  (fig.  837),  from  one  foot  to 
three  feet  in  length.  A  deep  groove  is  cut  in  this  cylinder  and  on  the  ends, 
in  which  is  coiled  the  insulated  wire,  as  shown  in  section  in  fig.  839.  To 


Fig.  837. 

the  two  ends  of  the  cylinder,  brass  discs,  E  and  D,  are  secured.  With  E  is 
connected  a  commutator  C,  consisting  of  two  pieces  of  steel  insulated  from 
each  other,  and  connected  respectively  with  the  two  ends  of  the  wire.  On 
the  other  disc  is  a  pulley,  /,  round  which  passes  a  cord,  so  that  the  bobbin 
moves  very  rapidly  on  the  two  pivots. 

When  a  voltaic  current  circulates  in  the  wire,  the  two  cylindrical  seg- 
ments ^  and  B  are  immediately  magnetised,  one  with  one  polarity  and  the 
other  with  the  opposite.  On  the  other  hand,  if  instead  of  passing  a  voltaic 
current  through  the  wire  of  the  bobbin,  the  bobbin  itself  be  made  to  rotate 
rapidly  between  the  opposite  poles  of  magnetised  masses,  as  the  segments 
A  and  B  become  alternately  magnetised  and  demagnetised,  their  induction 
produces  in  the  wire  a  series  of  currents  alternately  positive  and  negative, 
as  in  Clarke's  apparatus  (910).  When  these  currents  are  collected  in  a  com- 
mutator which  adjusts  them — that  is,  sends  all  the  positive  currents  on  one 
spring  and  all  the  negative  on  another — these  springs  become  electrodes, 
from  one  of  which  positive  electricity  starts,  and  from  the  other  negative.  If 
these  springs  are  connected  by  a  conductor,  the  same  effects  are  obtained  as 
when  the  two  poles  of  a  battery  are  united. 

This  armature  has  the  great  .advantage  that  a  large  number  of  com- 
paratively small  magnets  may  be  used  instead  of  one  large  one.  As,  weight 
for  weight,  the  former  possess  greater  magnetic  force  than  the  latter,  they 
can  be  made  more  economically.  And  as  the  armature  is  enclosed  by  and 
is  very  near  the  magnets,  it  experiences  the  action  of  the  field  in  its  greatest 
strength. 

3K2 


868 


Dynamical  Electricity. 


[915 


915.  Wild's  magneto-electrical  machine. — Mr.  Wild  constructed  a 
magneto-electrical  machine  in  which  Siemens'  armature  is  used  along  with 
a  new  principle — that  of  the  multiplication  of  the  current.  Instead  of  uti- 
lising directly  the  current  produced  by  the  induction  of  a  magnet,  Mr.  Wild 
passes  it  into  an  electromagnet,  and  by  the  induction  of  this  latter  a  more 


Fig.  838. 

energetic  current  is  obtained ;  the  electromagnet  thus  excited  plays  the  part 
of  the  permanent  magnets,  but  is  more  powerful. 

This  machine  consists  first  of  a  battery  of  12  to  16  magnets,  P  (fig.  838), 
each  of  which  weighs  about  3  pounds,  and  can  support  about  20  pounds. 
Between  the  poles  of  the  magnets  two  soft  iron  keepers  CC,  are  arranged, 


915]  Wild's  Magneto-electrical  Machine.  869 

separated  by  a  brass  plate,  O.  These  three  pieces  are  joined  by  bolts,  and 
the  whole  compound  keeper  is  perforated  longitudinally  by  a  cylindrical 
cavity,  in  which  works  a  Siemens'  armature,  n,  about  2  inches  in  diameter. 
The  wire  of  this  armature  terminates  in  a  commutator,  which  leads  the 
positive  and  negative  currents  to  two  binding  screws,  a  and  b.  This  com- 
mutator is  represented  on  a  larger  scale  in  fig.  839.  At  the  other  end  is  a 
pulley  by  which  the  armature  can  be  turned  at  the  rate  of  25  turns  in  a  second. 
The  wire  on  the  armature  is  20  yards  long. 

Below  the  support  for  the  magnets  and  their  armatures  are  two  large 
electromagnets,  BB,  which  are  called  \h.z  field  magnets ,  since  to  them  is  due 
the  production  of  the  magnetic  field.  Each  consists  of  a  rectangular  soft 
iron  plate,  36  inches  in  length  by  26  in  breadth  and  i£  inch  thick,  on  which 
are  coiled  about  1,610  feet  of  insulated  copper  wire.  The  wires  of  these 
electromagnets  are  joined  at  one  end,  so  as  to  form  a  single  circuit  of  3,200 
feet.  One  of  the  other  ends  is  connected  with  the  binding  screw  a,  and  the 
other  with  b.  At  the  top  the  two  plates  are  joined  by  a  transverse  plate  of 
iron,  so  as  to  form  a  single  electromagnet. 

At  the  bottom  of  the  electromagnets  B  B  are  two  iron  armatures,  separated 
by  a  brass  plate,  O,  and  in  the  entire  length  is  a  cylindrical  channel  in  which 
works  a  Siemens'  armature,  ?;/,  as  above  :  this  armature,  however,  is  above  a 
yard  in  length,  nearly  6  inches  in  diameter,  and  its  wire  is  100  feet  long. 
The  ends  are  connected  with  a  commutator,  from  which  the  adjusted  currents 
pass  to  two  wires,  r  and  s.  The  armature  m  is  rotated  at  the  rate  of  1,700 
turns  in  a  minute- 


Fig.  839.  Fig.  840. 

Fig.  839  shows  on  a  larger  scale  a  cross  section  of  the  coil  of  the  armatures" 
C  C,  and  of  the  plates  AA,  on  which  the  wire  of  the  electro-magnets  B  B  is 
coiled. 

These  details  being  premised,  the  following  is  the  working  of  the 
machine: — When  the  armatures  n  and  m  are  rotated  by  means  of  a  steam- 
engine  with  the  velocity  mentioned,  the  magnets  produce  in  the  first  arma- 
ture induced  currents,  which,  adjusted  by  the  commutator,  pass  into  the 
electromagnet  B  B,  and  magnetise  it.  But  as  these  impart  to  the  lower 
armatures,  C  C,  opposite  polarities,  the  induction  of  these  latter  produces  in 
the  armature  m  a  series  of  positive  and  negative  currents  far  more  powerful 
than  those  of  the  upper  armature  ;  so  that  when  these  are  adjusted  by  a 


870  Dynamical  Electricity.  [915- 

commutator  and  directed  by  the  wires  r  and  j,  very  powerful  effects  are 
obtained. 

These  effects  are  still  further  intensified  if,  as  Mr.  Wild  has  done,  the 
adjusted  current  of  the  armature  m  is  passed  into  a  second  electro-magnet, 
whose  armatures  surround  a  third  and  larger  Siemens'  armature  turning  with 
the  two  others.  Mr.  Wild  thus  produced  currents  of  a  strength  far  exceeding 
anything  which  up  to  that  time  had  been  attained  ;  he  was  able,  for  instance, 
to  melt  easily  an  iron  wire  a  foot  long  and  more  than  0-2  inch  in  diameter. 

916.  Dynamo-electrical  machines. — A  great  advance  was  made  by  the 
discovery  of  the  principle  of  the  reaction  of  a  current  on  itself — a  discovery 
made  by  Dr.  Werner  Siemens  and  Sir  C.  Wheatstone  independently  of  each 
other,  and  almost  simultaneously.  If  a  momentary  voltaic  current  be  passed 
through  the  wires  of  the  rotating  armature  of  such  a  machine  as  the  above, 
a  trace  of  residual  magnetism  will  be  left  in  the  core.  The  rotation  of  this 
armature  induces  a  current  in  the  electromagnets  B  B  :  this  in  turn  reacts  on 
the  armature,  increases  its  magnetism,  which  again  increases  the  strength  of 
the  electromagnets,  and  so  forth.  We  have  in  this  an  analogy  with  Holtz's 
machine  (759),  in  which  the  electricity  of  the  plate  and  the  conductors  reci- 
procally strengthen  each  other.  It  is  not  even  necessary  to  specially  magnetise 
the  iron  at  the  outset ;  the  trace  of  residual  magnetism  always  present  in  iron 
(715)  is  sufficient  to  start  the  apparatus,  which  then  goes  on  increasing  with 
the  velocity  of  the  rotation,  and  which  indeed  is  only  limited  by  the  heating 
of  the  wires  and  the  bearings,  and  by  the  difficulty  of  properly  insulating  the 
coils  when  such  powerful  currents  are  used. 


Fig.  841. 

Apparatus  which  transform  mechanical  work  into  electricity  without  the 
use  of  permanent   magnets,  or  of  extraneous  electro-magnets,   are  known 


-916] 


Dynamo-electrical  Machine. 


87 


as  dynamo-electrical  machines,  in  contradistinction  to  magneto-electrical 
machines,  in  which  the  magnetism  is  not  furnished  by  the  play  of  the 
machine  itself,  but  is  got  from  permanent  magnets.  It  must  not,  however, 
be  supposed  that  in  the  one  the  electricity  is  produced  at  the  expense  of  the 
magnetism,  and  in  the  other  at  the  expense  of  the  work.  There  is  really  no 
distinction  of  this  kind  between  them  ;  in  both  kinds  of  machine  electricity 
is  produced  at  the  cost  of  work,  and  for  this  reason  both  are  indeed  dynamo- 
electrical  machines. 

The  earliest  machine  of  this  kind  was  that  invented  by  Mr.  Ladd.  It  con- 
sists essentially  of  two  Siemens'  armatures,  rotating  with  great  velocity,  and 
of  two  iron  plates,  A  A  (fig.  841),  surrounded  by  an  insulated  copper  wire. 

The  electromagnets  B  B  are  not  joined  so  as  to  form  a  single  one,  but 
are  two  distinct  electromagnets,  each  having  at  the  end  two  hollow  cylin- 
ders, C  C',  in  which  are  fitted  two  Siemens'  armatures,  m  and  n  :  the  current 
of  the  armature  n  passing  round  the  electromagnets  reverts  to  itself.  The 
wire  of  the  armature  m  passes  into  the  apparatus  which  is  to  utilise  the 
current — for  instance,  two  carbon  points,  D. 

The  residual  magnetism  in  the  armature  plates  and  their  keepers  is  sufficient 
to  start  the  machine.  If,  then,  the  armatures  wand  n  be  rotated  by  means  of 
two  bands  passing  round  a  common  drum,  the  magnetism  of  the  hollow  cylin- 
ders C  C',  acting  upon  the  armature  n,  excites  induction  currents,  which,  ad- 
justed by  a  commutator,  pass  round  the  electromagnets  B  B,  and  more  strongly 
magnetise  the  cylinders  or  shoes  C  C'.  These,  in  their  turn  reacting  more 
powerfully  on  the  armature  «,  strengthen  the  current ;  we  thus  see  that  n  and 
B  continually  and  mutually  strengthen  each  other  as  the  velocity  of  the  rota- 
tion increases.  Hence,  as  the  ron  of  the  armature  m  becomes  more  and 
more  strongly  magnetised 
under  the  influence  of  the 
electro-magnets  B  B,  a 
gradually  more  powerful 
induced  current  is  de- 
veloped in  this  armature, 
which  is  directed,  corn- 
mutated  or  not,  according 
to  the  use  for  which  it  is 
designed. 

In  a  machine  ex- 
hibited at  the  Paris  Exhi- 
bition of  1867  the  plates 
A  A  were  only  24  inches 
in  length  by  12  inches  in 
width.  With  these  small 
dimensions  the  current  is 
equal  to  that  of  25  to  30 
Bunsen's  cells.  It  can 

work  the  electric  light  and  keep  incandescent  a  platinum  wire  a  metre  in 
length  and  0-5  mm.  in  diameter. 

The  above  form  of  the  machine  is  worked  by  steam  power.  Mr. 
Ladd  devised  a  more  compact  form,  which  may  be  worked  by  hand.  This 


872 


Dynamical  Electricity. 


[916- 


be 


is  represented  in  fig.  842.  The  two  armatures  are  fixed  end  to  end,  and 
the  coils  are  wound  on  it  at  right  angles  to  each  other,  as  shown  in  the  figure. 
The  current  from  this  can  raise  to  white  heat  18  inches  of  platinum  wire  croi 

in.  in  thickness,  and  with 
an  inductorium  (921)  con- 
taining 3  miles  of  second- 
ary wire  2-in.  sparks  can 
obtained. 

Pacinotti's  ring-. 
Gramme's  magneto- 

electrical  machine. — A 
remarkable  improvement 
in  magneto-  and  dynamo- 
electric  machines  is 
the  application  of  a  ring 
inductor.  This  was  in- 
vented by  Prof.  Pacinotti 
in  1862,  and  is  known 
as  Pacinotti's  ring.  It 
was  applied  by  him  to 
an  electromagnetic  motor, 
but  he  showed  that  it 
could  be  used  as  a 
magneto-electrical  motor. 
The  same  principle  was 
discovered  several  years 
later,  it  would  appear 
Fig  843  quite  independently,  by 

M.  Gramme,  and  utilised 

by  him  in  the  construction  of  a  new  form  of  magneto-electrical  machine. 
This  differed  from  all  previous  forms  in  giving  at  once  direct,  and  what  are 

practically  continuous  currents,  and 
which,  having  regard  to  the  size  of  the 
machine,  were  more  powerful  than  any 
hitherto  obtained.  A  laboratory  form 
of  Gramme's  machine  is  represented  in 
fig.  843,  in  about  \  of  the  real  size.  On 
a  base  is  fixed  vertically  a  powerful 
Jamin's  magnetic  battery,  A  (fig.  843} 
constructed  of  24  steel  plates,  each  i  mm. 
in  thickness,  then  separately  magnetised 
to  saturation.  To  the  two  poles  are 
affixed  two  soft  iron  armatures  a  and  by 
between  which  an  axle  is  rotated  by 
means  of  a  wheel  and  rackwork.  On 
this  axle  is  a  ring  on  which  are  wound 
a  series  of  thirty  coils.  The  ring  or 
core  is  not  solid,  but  itself  consists  of  a  coil  of  a  number  of  turns  of  soft  iron 
wire,  as  seen  in  fig.  844,  and  in  this  way  the  changes  in  its  magnetisation 


Fig.  844- 


-917J  Pacinotti's  Ring.     Gramme's  Machine.  873 

which  take  place  are  far  more  rapid,  and  the  heating  effect  due  to  these  rapid 
changes  is  less  ;  the  wire  is  continuous,  and  the  two  ends  are  soldered 
together. 

On  this  core  are  wound  the  coils  BCD;  they  are  united  by  thin  brass 
knee-plates  m  «,  to  each  of  which  are  soldered  the  copper  wires  of  two  suc- 
cessive coils,  so  as  to  form  a  continuous  whole.  The  plates  are  insulated 
from  each  other,  and  are  fixed  on  a  wooden  block  <?,  mounted  on  the  axis 
of  rotation.  The  branches  m  n  of  the  knee-plates  form  a  sheath  about 
this  axis,  and  two  flat  brushes  of  copper  wire,  fixed  to  the  binding  screws 
c  and  z,  are  in  contact  with  the  upper  and  lower  parts  of  this  sheath,  and 
receive  the  currents  which  originate  in  the  coils. 

In  order  to  understand  the  action  of  Gramme's  machine,  let  us  now  con- 
sider the  condition  of  a  soft  iron  ring  which  is  placed  between  the  two 
opposite  poles  of  a  powerful  permanent  magnet,  at  the  opposite  ends  of 
a  diameter  of  the  ring  (fig.  845).  The  parts  nearest  the  ring  will  be  of  trie 
opposite  polarity  to  that  of  the  inducing  magnet.  We  may  consider  that 
under  its  influence  each  half  of  the  ring  is  converted  into  a  magnet  with  its 
two  poles  and  neutral  line.  The  same  poles  of  the  ring  face  each  other,  and 
the  effect  is  not  altered  if  the  ends  touch.  Let  us  now  suppose  the  ring 
fixed,  and  that  a  thin  coil  moves  round  it,  starting  from  the  neutral  line.  As 
it  nears  the  pole  s,  a  current  on  approach  will  be  induced 
in  the  coil  in  the  opposite  direction  to  that  which,  on 
Ampere's  hypothesis,  circulates  round  the  end  of  the 
pole  s  ;  as  it  passes  over  the  other  half  s,  a  leaving  cur- 
rent is  produced,  which  is  in  the  same  direction  as  that 
which  circulates  round  s  ;  but  it  must  be  remembered 
that  as  these  poles  face  one  another,  their  Amperian  cur- 
rents are  in  opposite  directions,  the  result  of  which  is 
that  the  currents  induced  on  approaching  s  and  on  leav- 
ing s  are  in  the  same  direction ;  in  other  words,  as  the 
coil  circulates  in  front  of  the  double  pole  it  will  be  tra- 
versed by  a  continuous  current  in  the  same  direction, 
the  strength  of  which  increases  from  the  neutral  point 
till  it  comes  in  front  of  the  poles,  and  then  diminishes 
until  it  is  at  the  neutral  point  again.  The  same  process  repeats  itself  in  the 
coil  as  it  approaches  the  other  pole,  except  that  the  current  is  negative,  so 
that  if  the  collectors  are  adjusted  on  one  side  of  the  neutral  point  they  will 
collect  the  opposite  currents,  and  they  can  be  utilised  in  an  external  circuit. 
What  is  here  true  of  one  coil  is  true  of  all  others  as  they  pass  in  front  of 
the  poles  ;  and  as  they  are  all  connected  together  we  get,  not  so  much  a 
series  of  separate  impulses,  as  a  continuous  series  of  currents.  This  con- 
tinuous character  of  the  currents  is  improved  by  the  fact  that  the  collector 
brushes  are  so  arranged  as  to  touch  more  than  one  of  the  knee-pieces  at 
once. 

The  ring  of  course  does  actually  rotate  with  the  coils,  and  the  polarity  of 
each  part  is  continually  changing  ;  but  although  this  is  the  case,  the  position  of 
the  poles  remains  fixed  in  space,  and  the  effect  is  as  we  have  said.  It  must 
be  added  that  the  poles  of  the  magnet  also  act  directly  on  the  coils  ; .  and  if  we 
consider  the  ring  as  non-magnetic,  and  only  the  direct  action  of  the  poles  on 


8/4 


Dynamical  Electricity. 


[917- 


the  coil  to  operate,  it  will  be  seen  to  be  in  the  same  direction  as  the  action 
of  the  ring.  Both  effects  concur  then  in  increasing  the  strength  and  also 
continuity  of  the  currents. 

This  apparatus  is  very  powerful ;  the  smallest  size  made  can  decompose 
water,  and  heat  to  redness  an  iron  wire  20  centimetres  in  length  and  a 
millimetre  in  diameter.  Mascart  and  Angot  determined  the  electromotive 
force  of  different  Gramme's  machines  by  placing  in  the  circuit  of  the 
machine,  but  in  opposition  to  it,  a  number  of  DanielFs  elements.  The 
velocity  of  rotation  was  then  increased  until  a  galvanometer  in  the  circuit 
was  not  deflected.  When  this  was  the  case,  seeing  that  the  resistance 
traversed  by  the  opposing  currents  was  the  same,  it  is  clear  that  the  electro- 
motive force  due  to  the  machine  rotating  at  a  given  speed  is  exactly  equi- 
valent to  that  of  the  corresponding  number  of  elements.  Thus,  for  instance, 
the  current  from  3  DanielPs  cells  was  found  to  neutralise  that  of  a  particular 
hand  Gramme's  machine  rotating  with  a  velocity  of  10*2  turns  per  second. 
The  average  electromotive  force  due  to  this  machine  was  found  equal  to  0-27 
of  a  Daniell  for  a  velocity  of  I  turn  per  second.  With  another  the  ratio 
was  o'3i,  and  with  others  again  as  much  as  0*8  of  a  Daniell. 

It  will  be  seen  from  the  description  that  the  action  of  the  ring  inductor  is 
not  inconsistent  with  the  application  of  the  dynamo-electrical  principle  ;  and 
in  the  larger  machines  it  is  applied,  and  the  rotation  effected  by  steam  or 
gas  engines  or  by  water  power.  The  dimensions  and  details  of  the  construc- 
tion vary  with  the  purpose  for  which  the  machine  is  designed.  Thus  in  a 
machine  which  is  to  be  used  for  electrolysis,  the  coils  in  the  ring  inductor 

are  made  up  of  a  comparatively 
short  length  of  insulated  upper 
bands,  while  for  the  electric 
light  a  long  length  of  fine  insu- 
lated wire  is  used. 

Gramme's  machine  is  rever- 
sible ;  for  while  by  its  means 
motion  is  converted  into  elec- 
tricity, it  can  in  like  manner 
convert  electricity  into  motion. 
This  may  be  seen  by  connecting 
the  binding  screws  c  and  i  with 
the  poles  of  a  Grove's  battery. 
This  iron  core  then  becomes 
magnetised  by  the  action  of  the 
current  passing  through  the 
coils  ;  the  whole  system  rotates 
rapidly  under  the  influence  of 
the  magnetised  bundle. 


Fig.  846. 


V9i8.  Siemens'  dynamo-electrical  machines.— Fig.  846  represents 
the^  essential  features  of  one  of  the  small-sized  vertical  machines  made 
by  Messrs.  Siemens.  A  characteristic  is  the  cylindrical  or  drum  armature, 
which  may  be  regarded  as  an  extension  of  that  already  described  (914)- 
The  electromagnets  M  M  and  M'  M'  with  double  poles  feed  the  magnetism 
of  the  soft  iron  armatures  N  N,  which  are  bent  so  as  to  almost  completely 


-919]  Brush  Dynamo-electrical  Machine.  875 

encircle  the  inductor  ;  they  are  in  detached  pieces,  so  that  air  can  freely 
circulate  between  them,  and  thereby  the  temperature  be  kept  down. 

The  inductor  itself,  D,  consists  of  a  drum-shaped  frame  of  soft  iron 
wire  covered  with  a  layer  of  insulating  material,  and  fixed  to  an  axle 
which  rests  in  the  strong  upright  supports,  and  is  rotated  by  means  of  power 
transmitted  to  the  sheave  A.  The  wire  is  coiled  on  this  :  one  end  is  attached 
to  a  plate  which  forms  part  of  the  collector,  as  in  Gramme's  machine  ;  it 
passes  lengthwise  round  the  drum  in  several  turns,  and  the  other  end  is 
attached  to  a  similar  piece  on  the  collector,  which  is  diametrically  opposite 
the  first.  The  wire  is  continuous,  the  connection  of  the  individual  strands 
being  effected  by  means  of  the  collector.  On  the  collector  rest  two  pairs 
of  brushes,  b  b  and  b'  b' ;  they  are  connected  respectively  with  insulated 
binding  screws  ;  from  these  the  current  passes  through  the  wires  of  the 
electromagnet,  and  thence  to  the  terminals,  p  p,  where  it  may  be  utilised  in 
the  external  circuit. 

The  advantage  of  this  construction  is  that  from  the  length  of  the  inductor 
the  wires  are  moving  in  a  more  extended  field  ;  and  being  on  the  surface 
and  quite  close  to  the  armature  of  the  field  magnets,  are  more  under  their 
influence. 

A  small  machine  of  this  kind,  which  does  not  occupy  a  space  of  more 
than  three  cubic  feet,  and  rotating  with  a  velocity  of  1 5  turns  in  a  second, 
which  is  effected  by  i|  horse-power,  can  produce  a  light  of  1,400  candles. 
The  larger  sizes  produce  far  more  powerful  effects,  but  require  of  course 
greater  power  to  work  them. 

Machines  of  this  class  give  continuous  currents.  A  kind  is  constructed 
for  alternating  currents  ;  it  consists  of  a  combination  of  two  machines,  one 
of  which  is  on  the  dynamo  principle,  as  in  the  above  case,  while  the  other  is 
analogous  to  the  magneto-electrical  machine. 

919.  Brush  dynamo-electrical  machine. — The  armature  of  this 
machine  (fig.  847)  is  ring-shaped,  and  has  some  resemblance  to  Gramme's, 


Fig.  847. 

but  the  coiling  is  different.  The  section  of  the  ring  is  rectangular  (fig.  848) 
and  there  are  deep  rectangular  grooves  in  it,  in  which  are  the  coils  of  wire 
eight  in  number.  The  projecting  cheeks  thus  formed  between  the  coils  form 


876  Dynamical  Electricity.  [919- 

polar  appendices,  which  are  intended  to  act  laterally  on  the  coils.  These 
cheeks  are  traversed  by  deep  horizontal  grooves,  and  also  by  a  large  and  deep 
vertical  groove,  which  almost  divides  the  ring  into  two  parts.  By  this  means 
the  formation  of  local  currents  is  hindered,  and  a  greater  cooling  surface  is 
obtained. 

The  ring  rotates,  between  the  four  poles  of  two  very  powerful  electro- 
magnets, M  and  M/,  whose  soft  iron  armatures  are 
prolonged  in  pole  plates,  N  and  S,  double  poles  being 
adjacent. 

On  the  collector  are  four  rings  (fig.  849).  Each 
ring  consists  of  two  segments,  A  B,  separated  from 
each  other  at  one  end  by  an  air  space,  while  be- 
tween the  others  is  a  smaller  segment,  C,  called  the 
'  insulator.'  During  the  rotation  one  pair  of  coils 
is  in  the  neutral  position  in  which  no  electromotive 

orce  is  being  developed  in  it.  In  this  position  the  coils  only  represent  a 
resistance,  and  their  presence  in  the  circuit  is  a  pure  loss.  The  contacts  are 
so  arranged  that  the  moment  the  pair  is  in  this  position,  which  is  at  each 
quarter  of  a  rotation,  one  of  the  brushes  touches  the  insulator,  and  is  thus 
not  only  removed  from  the  circuit,  but,  not  being  closed,  no  current  can 
circulate  in  it. 

One  end  of  each  coil  is  connected  with  one  end  of  the  coil  exactly 
opposite  it,  the  other  ends  being  connected  with  one  of  the  four  commutator 
rings  where  they  are  connected  to  isolated  segments.  From 
these  segments  the  current  of  the  two  coils  is  taken  off  by 
brushes  arranged  horizontally  and  in  connection  with  curved 
spring  bands,  which  lead  it  to  the  binding  screws,  from 
which  it  passes  into  the  external  circuit. 

In  a  machine  of  this  kind  which  gives  16  arc  lights  the 
Fig.  849.  rmg  js  j^f  a  metre  m  diameter,  and  each  of  the  8  coils  con- 

tains 275  metres  of  cotton-covered  copper  wire  2  mm.  in  diameter,  and  weigh- 
ing 10  kg.  Each  pair  of  coils  has  a  resistance  of  i^  ohms,  and  the  electro- 
magnets have  a  resistance  of  6  ohms,  so  that  the  total  internal  resistance  is 
12  ohms. 

In  any  such  machines,  the  strength,  of  the  current  which  it  produces  is 
proportional  to  the  strength  of  the  magnetic  field,  and  with  a  given  armature 
to  the  speed  of  rotation,  or  to  the  number  of  lines  of  force  cut  in  a  given 
time  (826) ;  and  is  inversely  as  the  resistance  of  the  circuit.  The  strength 
of  the  magnetic  field  in  a  magneto  machine  depends  on  the  strength  of  the 
permanent  magnets  which  form  the  field,  and  when  these  are  electromagnets 
and  are  separately  excited,  on  the  strength  of  the  magnets  by  which  they  are 
excited.  With  dynamo  machines  the  strength  of  the  field  magnets  is  a  func- 
tion of  the  current  which  it  itself  produces  in  the  coils  of  the  electromagnet, 
and  the  strength  of  this  current  depends  on  the  resistance  of  the  circuit,  the 
external  part  of  which  is  liable  to  frequent  variations  from  accidental  causes. 
Hence  dynamo  machines  are  more  irregular  in  their  action  than  magneto 
machines,  which  are  therefore  to  be  preferred  where  steadiness  is  required. 
With  both  classes  of  machines  the  most  favourable  results  are  obtained 
with  the  larger  sizes. 


-920]          Applications  of  Dynamo-electrical  Machines.  877 

920.  Applications  of  magneto  and  dynamo-electrical  machines. — 

Magneto-electrical  machines  with  constant  currents  are  a  triumph  of  modern 
times  ;  from  their  discovery  together  with  that  of  the  dynamo  principle  (946) 
is  dated  the  introduction  of  electricity  for  industrial  purposes.  Great  improve- 
ments have  of  late  been  made  in  magneto-electrical  machines,  both  in  the 
economy  and  simplicity  of  their  construction,  and  also  in  their  power ;  for 
details  on  these  matters  we  must  refer  to  special  technical  works. 

The  energy  of  any  electrical  current  or  portion  of  an  electrical  current  is 
measured  by  the  product  of  the  electromotive  force,  E,  or  difference  of  poten- 
tials at  the  ends  of  the  portion  considered,  into  the  strength  of  the  current 
itself.  The  magnitude  represented  by  an  electromotive  force  of  a  volt  multi- 
plied by  a  current  strength  of  an  ampere  is  called  a  volt-ampere,  and  from  its 
great  practical  utility  has  got  a  special  name,  that  of  Watt  (964).  A  horse- 
power is  equal  to  746  watts,  or  a  watt  is  0-0132  of  a  horse-power.  Hence,  if 
we  know  the  number  of  watts  produced  in  any  circuit,  this  divided  by  746 
gives  at  once  the  equivalent  in  mechanical  power. 

A  magneto-electrical  machine  may  be  compared  to  a  pump  forcing  water 
through  a  pipe  against  friction  ;  the  electrical  current  corresponds  to  the 
volume  of  water  passing  in  a  second,  and  the  electromotive  force  corresponds 
to  the  difference  in  pressure  on  the  two  sides  of  the  pump.  Just  as  the 
power  of  a  pump  is  measured  by  the  product  of  the  pressure,  and  volume  of 
water  per  second,  so  the  product  of  the  electromotive  force  and  current  is 
power,  and  the  ratio  of  this  power  to  the  mechanical  power  expended  in 
•driving  the  magneto-electrical  machine  is  the  efficiency  of  the  magneto- 
electrical  machine.  The  peculiarity  of  the  dynamo -electrical  machine  is 
this,  that  the  electromotive  force,  or  the  element  corresponding  to  difference 
of  pressure  in  the  case  of  a  pump,  depends  directly  on  the  current  passing. 
It  does  not  increase  indefinitely  with  increase  of  current,  but  increases  to  a 
•certain  limit,  and  then  remains  constant. 

Hopkinson  made  a  series  of  experiments  with  a  machine  of  Siemens' 
construction,  where  special  arrangements  were  made  for  determining  the 
speed  at  which  the  machine  was  driven,  the  driving  power,  the  resistances 
in  the  circuit  and  the  difference  in  potential  between  the  two  ends  of  a  known 
resistance  in  the  circuit.  He  thus  found  that  to  drive  the  machine  in  open 
circuit  at  a  speed  of  720  rotations  required  an  expenditure  of  0-28  horse- 
power. Exclusive  of  friction,  the  efficiency  of  the  machine  was  found  to  be 
about  90  per  cent.,  so  that  in  this  respect  little  improvement  can  be  expected. 

If  the  relation  between  the  electromotive  force  measured  in  volts  (814), 
and  the  strength  of  the  current  measured  in  amperes  (814),  for  a  given  speed 
of  rotation  be  expressed  by  a  curve,  it  is  found  that  this  curve  has  the  form 
of  a  slanting  straight  line  starting  from  the  origin,  and  then  begins  to  bend 
away,  approaching  a  horizontal  line.  The  point  at  which  it  begins  to  bend 
away  is  when  the  electromotive  force  is  about  two-thirds  of  its  maximum, 
and  this  is  called  by  Hopkinson  the  critical  current',  it  has  this  physical 
meaning,  that  below  this  point  any  change  in  the  speed  of  rotation,  with  a 
steady  external  resistance,  or  any  change  in  the  external  resistance,  with  a 
-constant  speed  of  rotation,  produces  considerable  changes  in  the  current. 

The  principal  application  which  has  been  made  of  the  currents  produced 
by  dynamo  machines  is  to  the  production  of  the  electrical  light  (837).  In 


878  Dynamical  Electricity.  [920- 

this  respect  it  may  be  said  that  the  arrangements  for  producing  the  electricity 
are  more  perfect  than  those  for  producing  the  light ;  for  while  over  90  per 
cent,  of  the  mechanical  power  used  appears  in  the  form  of  current,  only  about 
half  of  that  which  is  transmitted  to  the  machine  appears  in  the  electrical 
arc. 

For  electrodes  of  a  definite  material,  kept  at  a  definite  distance  apart, 
and  under  the  ordinary  atmospheric  pressure,  the  difference  of  potential  is 
approximately  constant.  The  product  of  difference  of  potential  into  the 
current  passing,  is  the  work  developed  in  the  arc,  and  the  ratio  of  this,  to  the 
mechanical  power  expended  in  driving  the  machine,  is  the  efficiency  of  the 
electrical  arc. 

Comparing  together  the  relative  costs  of  producing  a  certain  degree  of 
illumination — «,  by  means  of  gas  ;  b,  by  the  electrical  arc  with  alternating 
currents  ;  <:,  by  one  with  continuous  currents,  the  machines  for  the  production 
of  the  last  two  being  worked  by  a  gas-engine — it  was  found  that  the  ratio 
was  as  116  :  62  :  15  ;  when  the  machine  was  heated  by  coal  instead  of  gas 
the  cost  was  as  116  :  50  :  10,  it  being  assumed  that  four  pounds  of  coal  pro- 
duced one  horse-power  per  hour.  The  actual  cost  of  lighting  the  British 
Museum  with  a  light  representing  18,800  candles  was  six  shillings  an  hour, 
of  which  the  carbons  cost  nearly  one-half.  The  cheapening  of  the  electrical 
light  is  in  great  measure  a  question  of  cheapening  the  carbons. 

Hopkinson  gives  the  following  illustration  of  the  luminous  effect  produced 
by  converting  energy  into  heat  in  a  closed  space.  One  hundred  and  twenty 
feet  of  what  is  called  1 5-candle  gas  (509)  produce  a  light  of  360  standard  candles 
for  an  hour.  The  heat  produced  in  this  combustion  is  equivalent  to  about  60 
millions  of  foot-pounds  (484).  If  this  gas  be  burned  in  a  gas-engine  (476)  about 
8  million  foot-pounds  of  work  will  be  done  outside  the  engine,  or  4  horse- 
power for  an  hour  (472).  This  power  is  sufficient  to  drive  an  A  Gramme 
machine  for  an  hour  ;  the  amount  of  energy  which  is  converted  into  current 
is  6,400,000  foot-pounds,  of  which  about  one-half,  or  3,200,000,  appear  in  the 
form  of  energy  in  the  electric  arc.  Viewed  horizontally  this  radiates  a  light 
of  2,000  candles,  and  two  or  three  times  as  much  when  viewed  from  below. 
Hence  about  3  million  foot-pounds  changed  into  heat  in  the  electric  arc  will 
affect  our  eyes  six  times  as  powerfully  as  60  millions  changed  into  heat  in  a 
gas  burner. 

Both  for  arc  and  incandescent  lamps  the  relative  efficiency  is  greater  the 
higher  the  illuminating  power.  Thus  with  a  Swan  lamp  of  16  candles  the 
work  required  for  each  candle-power  is  4*4  kgm.,  or  272  candles  for  a  horse- 
power, while  with  a  32-candle  lamp  the  number  of  candles  equivalent  to  a 
horse-power  is  415. 

Although  the  temperature  of  the  electric  arc  is  exceedingly  high  (838),  yet 
from  the  small  amount  of  radiating  surface  the  heating  effect  is  far  less  than 
that  produced  by  other  sources  of  equal  illumination.  Thus  Siemens  found 
that  an  electric  arc  light  of  4,000  candles  radiated  142-5  thermal  units  in  a 
minute,  while  to  produce  this  light  by  gas  would  require  200  Argand  burners, 
which  would  emit  15,000  units,  or  over  a  hundred  times  as  much.  So  too  it 
has  been  found  that  incandescent  lamps  produce  less  than  five  per  cent,  of 
the  heat  from  other  sources  of  equal  intensity. 

Siemens  made  a  series  of  experiments  on  the  influence  of  the  electrical 


-920#]        Applications  of  Dynamo-electrical  Machines.  879 

light  on  vegetation.  The  light  was  produced  by  a  dynamo-electrical  machine 
of  his  construction,  and  was  equal  in  illuminating  power  to  1,400  candles.  Of 
a  series  of  four  sets  of  quickly  growing  plants  in  pots,  such  as  mustard,  beans, 
&c.,  one  set  was  left  in  the  dark,  and  two  other  sets  were  exposed  to  the  action 
of  the  daylight  and  of  the  electric  light  separately  ;  while  the  fourth  was  ex- 
posed to  the  joint  action  of  the  two  lights.  The  first  set  sowed  withered  and 
died  ;  those  exposed  to  the  electric  light  grew  and  flourished,  but  not  so  vigo- 
rously as  those  exposed  to  daylight  alone  ;  there  was,  however,  a  marked  im- 
provement in  the  case  of  those  which  had  been  exposed  to  the  conjoint  action 
of  both  lights  :  they  showed  the  most  vigorous  growth.  Plants  did  not  seem 
to  require  a  period  of  repose,  but  made  increased  and  vigorous  progress  if 
subjected  at  daytime  to  sunlight,  and  by  night  to  the  electric  light. 

The  electric  light  is  beneficial  not  merely  to  such  plants  as  the  above, 
but  also  in  promoting  the  formation  of  aromatic  and  saccharine  substances 
on  which  the  ripening  of  fruits  depends  ;  this  was  well  seen  in  some  experi- 
ments in  which  early  strawberries  were  forced. 

Abney  found  that  the  luminosity  and  also  the  actinic  action  of  the  light 
produced  by  the  electric  arc  increased  more  rapidly  than  in  direct  ratio  to 
the  velocity  of  rotation,  and  the  horse-power  required  to  produce  it.  This 
increase  was  slowest  for  red  light,  more  rapid  with  blue,  and  most  rapid  of 
all  with  the  actinic  action.  With  a  speed  of  565  rotations,  and  an  expendi- 
ture of  9  horse-power,  the  actinic  action  was  equal  to  that  of  1 1,000  candles. 

Cohn  found  that  the  electrical  light  is  more  favourable  for  the  pure  per- 
ception of  colour  than  any  other  light  of  equal  luminosity. 

It  is  probable  that  the  temperature  which  can  be  produced  by  the  oxy- 
hydrogen  flame  is  limited  and  has  been  already  reached,  and  that  we  must 
look  to  the  electrical  arc  for  the  production  of  higher  temperatures  than 
those  at  which  carbonic  acid  and  water  are  decomposed.  Direct  experi- 
ments by  Siemens  with  the  electrical  arc  show  not  only  that  it  produces  a 
very  high  temperature  within  a  contracted  space,  but  also  that  it  will  con- 
veniently and  economically  produce  such  larger  effects  as  will  render  it 
useful  for  many  purposes  in  the  arts,  like  the  fusion  of  platinum  and  steel. 
He  constructed  an  arrangement  by  which  the  electric  arc  was  formed  within 
a  crucible  made  of  the  most  refractory  materials  ;  the  one  electrode  passed 
through  the  bottom  of  the  crucible  and  the  other  through  the  lid,  and  there 
was  an  arrangement  by  which  the  distance  of  the  electrodes  could  be  auto- 
matically regulated  ;  another  important  point  was  to  constitute  the  posi- 
tive pole  of  the  material  to  be  fused,  as  it  is  at  this  pole  that  the  heat 
is  principally  developed.  A  dynamo  machine  capable  of  producing  a  current 
of  36  amperes,  arid  which  produces  a  light  equal  to  6,000  candles,  fused  a 
kilogramme  of  steel  within  half  an  hour.  Siemens  calculated  that  the  heat 
in  his  furnace  represented  ^  of  the  horse-power  expended  in  working  the 
machine  ;  and  as  a  good  engine  only  utilises  about  \  of  the  combustible 
value  of  the  coal  employed  in  working  it,  it  follows  that  the  electrical 
furnace  utilises  5\  of  the  energy  residing  in  the  fuel  under  the  engine.  The 
electrical  furnace  is  theoretically  more  economical  than  the  ordinary  air 
furnaces. 

920*2.  Electrical  transmission  of  power. — When  a  magneto  or  dynamo 
machine  is  coupled  up  with  a  second  one,  on  working  the  first  the  second 


88o  Dynamical  Electricity. 

is  put  in  rotation,  and  in  a  direction  opposed  to  that  of  the  first.  Two  such 
machines  coupled  in  this  way  are  called  the  generator  and  the  motor.  This 
motor  may  be  geared  up  with  any  machine,  such  as  a  saw  wheel,  a  lathe,  or 
a  pump,  which  is  thereby  made  to  do  its  special  work.  On  this  depends 
the  possibility  of  transmitting  by  electricity  to  great  distances  power  from  a 
•common  centre,  and  of  thereby  utilising  natural  sources  of  power,  such  as 
waterfalls,  windmills,  and  the  like. 

The  efficiency  of  any  magneto  machine,  as  we  have  seen,  is  the  ratio-  of 
the  energy  w'  developed  in  the  machine  to  the  mechanical  power  «/,  expended 
in  producing  it.  Apart  from  friction,  more  than  90  per  cent,  of  the  power 
can  be  thus  converted  ;  if  such  a  machine  works  on  short  circuit  the  whole 
of  this  energy  would  appear  as  heat ;  when  external  work  is  done,  such  as  in 
producing  the  electric  light,  the  energy  is  shared  between  the  various  parts  of 
the  circuit,  and  the  amount  of  this  energy  in  any  part  can  be  easily  obtained 
if  we  know  the  fall  of  potential  between  the  part  in  question  and  the  current 
which  is  passing. 

When  a  motor  is  connected  with  a  generator  at  work,  the  former  is  set 
in  motion,  and  in  a  direction  opposed  to  that  of  the  generator  ;  it  thereby 
developes  an  electromotive  force  £,  opposed  to  that  of  the  generator  E. 

The  total  work  w  of  the  generator  in  unit  time  is  — ••  horse-power.     Part  of 

746 

this  work  appears  in  the  heating  of  the  conducting  wires,  and  the  rest  in  the 
form  of  the  energy  of  the  motor  iv',  which  is  h.p.,  where  e  is  the  differ- 
ence of  potentials  at  the  two  terminals  of  the  machine.  The  ratio  —  =  ?  • 

iv      E  ' 

that  is,  the  work  of  the  motor,  is  to  that  of  the  generator,  in  the  ratio  of  their 
electromotive  forces,  in  other  words,  to  the  differences  of  potentials  at  the  re- 
spective terminals.  In  practice  the  best  condition  of  working  is  to  arrange 
so  that  the  generator  has  twice  the  electromotive  force  of  the  motor,  the 
current  being,  of  course,  the  same  in  each. 

In  some  experiments  as  much  as  4^  horse-power  has  been  electrically 
transmitted  through  eight  miles  of  an  ordinary  galvanised  iron  telegraph  line 
4  mm.  in  diameter,  and  with  an  efficiency  of  over  30  per  cent,  of  the 
mechanical  power  employed. 

The  magneto-electrical  machine  has  been  applied  to  propelling  car- 
riages along  a  railway.  A  narrow-gauge  railway  was  laid  down,  and  upon 
this  a  train  of  three  or  four  carriages  was  laid,  and  on  the  first  of  these 
a  medium-sized  dynamo  machine,  so  fixed  and  connected  with  the  axle  of 
one  pair  of  wheels  as  to  give  motion  to  the  same.  The  two  rails,  being  laid 
upon  wooden  sleepers,  were  sufficiently  insulated  to  serve  for  electrical  con- 
ductors. Between  the  two  rails  a  bar  of  iron  was  fixed  on  wooden  supports, 
through  which  the  current  was  conveyed  to  the  train  by  brushes  fixed  to  the 
driving  carriage,  while  the  return  circuit  was  completed  through  the  rails. 
At  the  station  the  centre  bar  and  rails  were  electrically  connected  with 
the  poles  of  a  dynamo  machine  like  that  on  the  carriage,  and  which  was 
worked  from  a  fixed  steam-engine  on  the  ground.  The  magneto  machine 
exerted  5  horse-power,  and  it  travelled  with  a  velocity  of  15  to  20  miles 
^an  hour. 


-921]  Inductorium.     Ruhmkorff's  Coil.  88 1 

Another  application  is  to  what  is  called  telpherage,  by  which  is  meant 
a  means  of  propelling  light  carriages  or  buckets  along  a  single  metal  rope 
or  rod,  supported  on  posts  at  some  height  above  the  ground.  A  working 
line  has  been  already  constructed  and  used  with  success,  and  this  method  of 
electrical  haulage  will  probably  be  of  great  service  in  conveying  minerals  in 
mountainous  countries,  from  the  facility  with  which  it  can  be  constructed  on 
uneven  ground,  and  particularly  in  those  cases  in  which  water  supply  is 
available. 

V92I.  Inductorium.  RuhmkorfTs  coil. — These  are  arrangements  for 
producing  induced  currents,  in  which  a  current  is  induced  by  the  action  of 
an  electric  current,  whose  circuit  is  alternately  opened  and  closed  in  rapid 
succession.  These  instruments,  known  as  inductoriums,  or  induction  coils, 
present  considerable  variety  in  their  construction,  but  all  consist  essentially 
of  a  hollow  cylinder  in  which  is  a  bar  of  soft  iron,  or  bundle  of  iron  wires, 
with  two  helices  coiled  round  it,  one  connected  with  the  poles  of  a  battery, 
the  current  of  which  is  alternately  opened  and  closed  by  a  self-acting  arrange- 
ment, and  the  other  serving  for  the  development  of  the  induced  current.  By 
means  of  these  apparatus,  and  with  a  current  of  three  or  four  Grove's  cells, 
physical,  chemical,  and  physiological  effects  are  produced  equal  and  superior 
to  those  obtainable  with  electrical  machines  and  even  the  most  powerful 
Leyden  batteries. 

Of  all  the  forms  those  constructed  by  Ruhmkorff  are  the  most  powerful. 
Fig.  850  is  a  representation  of  one,  the  coil  of  which  is  about  14  inches  in 


Fig.  850. 

length.  The  primary  or  inducing  wire  is  ot  copper,  and  is  about  2  mm.  in 
diameter,  and  40  or  50  yards  in  length.  It  is  coiled  directly  on  a  cylinder  of 
cardboard,  which  forms  the  nucleus  of  the  apparatus,  and  is  enclosed  in  an  in- 
sulating cylinder  of  glass,  or  of  caoutchouc.  On  these  is  coiled  the  secondary 
or  induced  wire,  which  is  also  of  copper,  and  is  about  \  mm.  in  diameter. 
A  great  point  in  these  apparatus  is  the  insulation.  The  wires  are  not  merely 
insulated  by  being  in  the  first  case  covered  with  silk,  but  each  individual 
coil  is  separated  from  the  rest  by  a  layer  of  melted  shellac.  The  length  of 
the  secondary  wire  varies  greatly  ;  in  the  largest  size  hitherto  made,  that  of 
Mr.  Spottiswoode,  it  is  as  much  as  280  miles.  With  these  great  lengths  the 
wire  is  thinner,  about  |  mm.  The  thinner  and  longer  the  wire  the  higher 
the  potential  of  the  induced  electricity. 

3L 


882 


Dynamical  Electricity. 


[921- 


The  following  is  the  working  of  the  apparatus  : — The  current  arriving  by 
the  wire  P  at  a  binding  screw,  «,  passes  thence  in  the  commutator  C,  to  be 
afterwards  described  (fig.  853),  thence  by  the  binding  screw  b  it  enters  the 
primary  wire,  where  it  acts  inductively  on  the  secondary  wire  ;  having  tra- 
versed the  primary  wire,  it  emerges  by  the  wire  s  (fig.  851).  Following  the 
direction  of  the  arrows,  it  will  be  seen  that  the  current  ascends  in  the 
binding  screw  /,  reaches  an  oscillating  piece  of  iron,  0,  called  the  hammer, 
descends  by  the  anvil  h,  and  passes  into  a  copper  plate,  K,  which  takes  it 
to  the  commutator  C.  It  goes  from  there  to  the  binding  screw  c,  and 
finally  to  the  negative  pole  of  the  battery  by  the  wire  N. 

The  current  in  the  primary  wire  only  acts  inductively  on  the  secondary 
wire  (901),  when  it  opens  or  closes,  and  hence  must  be  constantly  in- 
terrupted. This  is  effected  by  means  of  the  oscillating  hammer  o  (fig.  851). 
In  the  centre  of  the  bobbin  is  a  bundle  of  soft  iron  wires,  forming  together  a 
cylinder  a  little  longer  than  the  bobbin,  and  thus  projecting  at  the  end  as 
seen  at  A.  When  the  current  passes  in  the  primary  wire  this  hammer,  o, 
is  attracted  ;  but  immediately,  there  being  no  contact  between  o  and  ^,  the 
current  is  broken,  the  magnetisation  ceases,  and  the  hammer  falls  ;  the 
current  again  passing,  the  same  series  of  phenomena  recommences,  so  that 
the  hammer  oscillates  with  great  rapidity. 

922.  Condenser. — In  proportion  as  the  current  passes  thus  intermittently 
in  the  primary  wire  of  the  bobbin,  an  induced  current,  alternately  direct 

and  inverse,  is  produced  at  each 
interruption  in  the  secondary  wire. 
But  as  this  is  perfectly  insulated, 
the  induced  current  requires  such  a 
strength  as  to  produce  very  power- 
ful effects.  Fizeau  increased  this 
strength  still  more  by  interposing 
a  condenser  in  the  primary  circuit. 
This  condenser  (fig.  852),  con- 
sists of  sheets  of  tinfoil  placed  over 
each  other  and  insulated  by  larger 
sheets  of  stout  paper,  v,  soaked  in 
paraffine  or  resin.  The  sheets  of 
tinfoil  project  at  the  end  of  the 
paper,  one  set  at  s  s'  s",  and  the  other  at  the  other  end,  at  e  e'  e",  so  that 
when  joined  by  a  binding  screw  the  odd  numbers  form  one  coating  of  a 
condenser,  and  the  even  numbers  the  other  coating.  In  large  condensers, 
the  surface  of  each  condenser  is  as  much  as  75  square  yards.  The  whole 
being  placed  in  a  box  at  the  base  of  the  apparatus,  one  of  the  coatings, 
the  positive,  is  connected  with  the  binding  screw  z,  which  receives  the 
current  on  emerging  from  the  bobbin  ;  and  the  other,  the  negative,  is  con- 
nected with  the  binding  screw  ;«,  which  communicates  by  the  plate  K  with 
the  commutator  C,  and  with  the  battery. 

To  understand  the  effect  of  the  condenser,  it  must  be  observed  that  at 
each  break  of  the  inducing  current  an  extra  current  is  produced  in  the  same 
direction,  which,  continuing  in  a  certain  manner,  prolongs  its  duration.  It 
is  this  extra  current  which  produces  the  spark  that  passes  at  each  break 


Fig.  851. 


-923J 


Effects  produced  by  Ruhmkorff's  Coil. 


883 


Fig.  852. 


between  the  hammer  and  the  anvil  ;  when  the  current  is  strong  this  spark 
rapidly  alters  the  surface  of  the  hammer  and  anvil,  though  they  are  of 
platinum.  By  interposing 
the  condenser  in  the  inducing 
circuit,  the  extra  current,  in- 
stead of  producing  so  strong 
a  spark,  passes  into  the 
condenser  —  the  positive 
electricity  in  the  coating 
connected  with  /,  and  the 
negative  in  that  connected 
with  m.  But  the  opposite  electricities  combining  quickly  by  the  thick  wire  of 
the  primary  coil,  by  the  battery,  and  the  circuit  C  K  m,  give  rise  to  a  current 
contrary  to  that  of  the  battery,  which  instantaneously  demagnetises  the 
bundle  of  soft  iron  :  the  induced  current  is  thus  shorter  and  more  intense. 
The  binding  screws  m  and  n  on  the  base  of  the  apparatus  are  for  receiving 
this  extra  current. 

The  commutator  or  key  serves  to  break  contact  or  send  the  current  in 
either  direction.  The  section  in  fig.  853  is  entirely  of  brass,  excepting  the 
core,  A,  which  is  of  ebonite  :  on  the  two  sides  are  two  brass  plates,  C  C'. 
Against  these  press  two  elastic  brass  springs,  joined  to  two  binding  screws, 
a  and  c,  with  which  are  also  connected  the  electrodes  of  the  battery.  The 
current  arriving  at  a  ascends  in  C,  thence  by  a 
screw,  _y,  it  attains  the  binding  screw  b  and  the 
bobbin  :  then  returning  by  the  plate  K,  which 
is  connected  with  the  hammer,  the  current  goes 
to  C'  by  the  screw  .r,  descends  to  r,  and  rejoins 
the  battery  by  the  wire  N.  If,  by  means  of  the 
milled  head,  the  key  is  turned  180  degrees,  it 
is  easy  to  see  that  exactly  the  opposite  takes 
place ;  the  current  reaches  the  hammer  by  the 
plate  K  and  emerges  at  b.  If,  lastly,  it  is  only 
turned  through  90  degrees,  the  elastic  plates 
rest  on  the  ebonite  A  instead  of  on  the  plate  Fig.  853. 

C  C',  and  the  current  is  broken. 

The  two  wires  from  the  bobbin  at  o  and  o'  (fig.  850)  are  the  two  ends  of 
the  secondary  wire.  They  are  connected  with  the  thicker  wires  P  P',  so 
that  the  current  can  be  sent  in  any  desired  direction.  With  large  coils  the 
hammer  cannot  be  used,  for  the  surfaces  become  so  much  heated  as  to  melt. 
But  Foucault  invented  a  mercury  contact-breaker  which  is  free  from  this 
inconvenience,  and  which  is  an  important  improvement. 

^"923.  Effects  produced  by  Ruhmkorff's  coil. — The  high  potential  of 
the  electricity  of  induction  coils  has  long  been  known,  and  many  luminous 
and  heating  effects  have  been  obtained  by  their  means.  But  it  is  only 
since  the  improvements  which  Ruhmkorff  introduced  into  his  coil,  that 
it  has  been  possible  to  utilise  all  the  potential  of  induced  currents,  and  to 
show  that  these  currents  possess  powerful  statical  as  well  as  dynamical 
properties. 

Induced  currents  are  produced  in  the  coil  at  each  opening  and  breaking 

3L2 


884  Dynamical  Electricity.  [923 

of  contact.  But  these  currents  are  not  equal  either  in  duration  or  in 
potential.  The  direct  current,  or  that  on  opening,  is  of  shorter  duration,  but 
higher  potential ;  that  of  closing  of  longer  duration,  but  lower  potential. 
Hence  if  the  two  ends  P  and  P'  of  the  fine  wire  (figs.  850  and  851)  are  con- 
nected, as  there  are  two  equal  and  contrary  quantities  of  electricity  in  the 
wire  the  two  currents  neutralise  each  other.  If  a  galvanometer  is  placed  in 
the  circuit,  only  a  very  feeble  deflection  is  produced  in  the  direction  of  the 
direct  current.  This  is  not  the  case  if  the  two  ends  P  and  P'  of  the  wire  are 
separated.  As  the  resistance  of  the  air  is  then  opposed  to  the  passage  of  the 
currents,  that  which  has  highest  potential — that  is,  the  direct  one — passes  in 
excess,  and  the  more  so  the  greater  the  distance  of  P  and  P'  up  to  a  certain 
limit  at  which  neither  passes.  There  are  then  at  P  and  P'  nothing  but 
potentials  which  are  alternately  contrary. 

The  physiological  effects  of  Ruhmkorff's  coil  are  very  powerful ;  in  fact, 
shocks  are  so  violent  that  many  experimenters  have  been  suddenly  pros- 
trated by  them.  A  rabbit  may  be  killed  with  two  of  Bun  sen's  elements,  and 
a  somewhat  larger  number  of  couples  would  kill  a  man. 

The  calorific  effects  are  also  easily  observed ;  it  is  simply  necessary  to 
interpose  a  very  fine  iron  wire  between  the  two  ends  P  and  P'  of  the  induced 
wire  ;  this  iron  wire  is  immediately  melted,  and  burns  with  a  bright  light. 
A  curious  phenomenon  may  here  be  observed,  namely,  that  when  each  ot 
the  wires  P  and  P'  terminates  in  a  very  fine  iron  wire,  and  these  two  are 
brought  near  each  other,  the  wire  corresponding  to  the  negative  pole  alone 
melts,  showing  that  its  temperature  is  higher. 

The  chemical  effects  are  very  varied  ;  thus,  according  to  the  shape  and 
distance  of  the  platinum  electrodes  immersed  in  water,  and  to  the  degree  of 
acidulation  of  the  water,  either  luminous  effects  may  be  produced  in  water 
without  decomposition,  or  the  water  may  be  decomposed  and  the  mixed 
gases  disengaged  at  the  two  poles,  or  the  decomposition  may  take  place,  and 
the  mixed  gases  separate  either  at  a  single  pole  or  at  both  poles. 

Gases  may  also  be  decomposed  or  combined  by  the  continued  action  of 
the  spark  from  the  coil.  If  the  current  of  a  Ruhmkorff's 
coil  be  passed  through  an  hermetically  sealed  tube  con- 
taining air,  as  shown  in  fig.  854,  nitrogen  and  oxygen 
combine  to  form  nitrous  acid. 

The  luminous  effects  of  Ruhmkorff's  coil  are  also 
very  remarkable,  and  vary  according  as  they  take  place 
in  air,  in  vapour,  or  in  very  rarefied  vapours.  In  air  the 
coil  produces  a  very  bright  loud  spark,  which,  with  the 
largest  sized  coil  hitherto  made,  that  of  Mr.  Spottiswoode, 
has  a  length  of  42  inches.  In  vacuo  the  effects  are  also 
remarkable.  The  experiment  is  made  by  connecting  the 
two  wires  of  the  coil  P  and  P'  with  the  two  rods  of  the 
electric  egg  (fig.  684)  used  for  producing  in  vacuo  the 
Fig  854  luminous  effects  of  the  electrical  machine.  Exhaustion 

having  been  produced  up  to  i  or  2  millimetres,  a  beauti- 
ful luminous  trail  is  produced  from  one  knob  to  the  other,  which  is  virtually 
constant,  and  has  the  same  intensity  as  that  obtained  with  a  powerful 
electrical  machine  when  the  plate  is  rapidly  turned.  This  experiment  is 


923]  Effects  produced  by  Ruhmkorff's  Coil.  885 

shown  in  rigs.  859  and  860.  Fig.  858  represents  a  remarkable  deviation  which 
light  undergoes  when  the  hand  is  presented  to  the  egg. 

The  positive  pole  of  the  current  shows  the  greatest  brilliancy ;  its  light 
is  of  a  fiery  red,  while  that  of  the  negative  pole  is  of  a  feeble  violet  colour; 
moreover,  the  latter  extends  along  all  the  length  of  the  negative  rod,  which 
is  not  the  case  with  the  positive  pole. 

The  coil  also  produces  mechanical  effects  so  powerful  that,  with  the  largest 
apparatus,  glass  plates  two  inches  thick  have  been  perforated.  This  result, 
however,  is  not  obtained  by  a  single  charge,  but  by  several  successive  charges. 

The  experiment  is  arranged  as  shown  in  fig.  855.  The  two  poles  of  the 
induced  current  correspond  to-  the  binding  screws  a  and  b ;  by  means  of  a 


Fig.  855. 

copper  wire,  the  pole  a  is  connected  with  the  lower  part  of  an  apparatus  for 
piercing  glass  like  that  already  described  (fig.  690) ;  the  other  pole  is  attached 
to  the  other  conductor  by  a  wire,  d.  The  latter  is  insulated  in  a  large 
glass  tube,  r,  filled  with  shellac,  which  is  run  in  while  in  a  state  of  fusion. 
Between  the  two  conductors  is  the  glass  to  be  perforated,  V.  When  this 
presents  too  great  a  resistance,  there  is  danger  lest  the  spark  pass  in  the  coil 
itself,  perforating  the  insulating  layers  which  separate  the  wires,  and  then 
the  coil  is  destroyed.  To  avoid  this,  two  wires,  e  and  <:,  connect  the  poles  of 
the  coil  with  two  metallic  rods  whose  distance  from  each  other  can  be  regu- 
lated. If  then  the  spark  cannot  penetrate  through  the  glass,  it  strikes  across, 
and  the  coil  is  not  injured. 

The  coil  can  also  be  used  to  charge  Leyden  jars.  With  a  large  coil 
giving  sparks  of  6  to  8  inches,  and  using  6  Bunsen's  elements  with  a  large 
surface,  Ruhmkorff  charged  large  batteries  of  6  jars  each,  having  about  3 
square  yards  of  coated  surface. 

The  experiment  with  a  single  Leyden  jar  (fig.  856)  is  made  as  follows : — 
The  coatings  of  the  latter  are  in  connection  with  the  poles  of  the  coil  by 
the  wires  d  and  z,  and  these  same  poles  are  also  connected,  by  means  of 
the  wires  e  and  c,  with  the  two  horizontal  rods  of  a  universal  discharger 
(fig.  667).  The  jar  is  then  being  constantly  charged  by  the  wires  i  and  d, 
sometimes  in  one  direction  and  sometimes  in  another,  and  as  constantly 
discharged  by  the  wires  e  and  c\  the  discharges  from  m  to  n  taking  place  as 


Dynamical  Electricity. 


[923- 


886 

sparks  two  or  three  inches  in  length,  very  luminous,  and  producing  a  deafen- 
ing sound  ;  they  can  scarcely  be  compared  with  the  sparks  of  the  electrical 
machine,  but  are  rather  true  lightning  flashes. 


Fig.  856. 

To  charge  a  battery,  the  form  of  the  experiment  is  somewhat  varied,  the 
outer  coating  being  connected  with  one  pole  of  the  coil  by  the  wire  d,  and 
the  inner  coating  with  the  other  by  the  rods  m  #,  and  the  wire  c  (fig.  857). 
The  rods  m  and  n  are  not,  however,  in  contact.  If  they  were — as  the  two 


Fig.  857. 

currents,  the  inverse  and  direct,  pass  equally — the  battery  would  not  be 
constantly  charged  and  discharged ;  while  from  the  distance  between  m  and 
n  the  direct  current,  that  of  breaking,  which  has  higher  potential,  passes 
alone,  and  it  is  this  which  charges  the  battery. 

924.  Stratification  of  the  electric  light. — Quet  observed,  in  studying 
the  electric  light  which  RuhmkorfFs  coil  gives  in  a  vacuum,  that  if  some  of 
the  vapour  of  turpentine,  wood  spirit,  alcohol,  or  bisulphide  of  carbon,  &c., 
be  introduced  into  the  vessel  before  exhaustion,  the  aspect  of  the  light  is 


Geisslers  Tubes. 


887 


-925] 

totally  modified.  It  appears  then  like  a  series  of  alternately  bright  and  dark: 
zones,  forming  a  pile  of  electric  light  between  the  two  poles  (fig.  859). 

In  this  experiment  it  follows,  from  the  discontinuity  of  the  current  of 
induction,  that  the  light  is  not  continuous,  but  consists  of  a  series  of  dis- 
charges which  are  nearer  each  other  in  proportion  as  the  hammer  o  (fig.  851) 
oscillates  more  rapidly.  The  zones  appear  to  possess  a  rapid  gyratory  and 
undulatory  motion.  Quet  considers  this  as  an  optical  illusion  ;  for  if  the 
hammer  is  slowly  moved  by  the  hand,  the  zones  appear  very  distinct  and 
fixed. 

The  light  of  the  positive  pole  is  most  frequently  red,  and  that  of  the 
negative  pole  violet.  The  tint  varies,  however,  with  the  vapour  or  gas  in  the 
-lobe. 


Fig.  860. 


Y92$.  Geissler's  tubes. — The  brilliancy  and  beauty  of  the  stratification 
of  the  electric  light  are  most  remarkable  when  the  discharge  of  the  Ruhm- 
korff  coil  takes  place  in  glass  tubes  containing  a  highly  rarefied  vapour  or 
gas.  These  phenomena,  which  were  originally  investigated  by  Gassiott,  are 
produced  by  means  of  sealed  glass  tubes  first  constructed  by  Geissler,  of 
Bonn,  and  generally  known  as  Geissler^s  tubes.  The  tubes  are  filled  with 
different  gases  or  vapours,  and  are  then  exhausted,  so  that  the  pressure  does 
not  exceed  half  a  millimetre.  At  the  ends  of  the  tubes  two-platinum  wires 
are  soldered  into  the  glass. 

When  the  two  platinum  wires  are  connected  with  the  ends  of  a  Rubm- 


888 


Dynamical  Electricity. 


[925- 


korff  coil  magnificent  lustrous  striae,  separated  by  dark  bands,  are  produced 
all  through  the  tube.  These  striae  vary  in  shape,  colour,  and  lustre  with  the 
degree  of  the  vacuum,  the  nature  of  the  gas  or  vapour,  and  the  dimensions 
of  the  tube.  The  phenomenon  has  occasionally  a  still  more  brilliant  aspect 
from  the  fluorescence  which  the  electric  discharge  excites  in  the  glass. 

Fig.  86 1  shows  the  striae  in  carbonic  acid  under  a  quarter  of  a  millimetre 
pressure ;  the  colour  is  greenish,  and  the  striae  have  not  the  same  form  as 
hydrogen.  In  nitrogen  the  light  is  orange-yellow. 

Pliicker  found  that  the  light  in  a  Geissler's  tube  did  not  depend  on  the 
substance  of  the  electrodes,  but  simply  on  the  nature  of  the  gas  or  vapour 
in  the  tube.  He  found  that  the  lights  furnished  by  hydrogen,  nitrogen, 


Fig.  86r. 

carbonic  oxide,  &c.,  give  different  spectra  when  they  are  decomposed  by 
a  prism.  The  discharge  of  the  coil  which  passes  through  a  highly  rarefied 
gas  would  not  pass  through  a  perfect  vacuum,  from  which  it  follows  that  the 
presence  of  a  ponderable  substance  is  absolutely  necessary  for  the  passage 
of  electricity. 

By  the  aid  of  a  powerful  magnet  Pliicker  tried  the  action  of  magnetism 
on  the  electric  discharge  in  a  Geissler's  tube,  as  Davy  had  done  with  the 
ordinary  voltaic  arc,  and  obtained  many  curious 
results,  one  of  which  may  be  mentioned.  He  found 
that  where  the  discharge  is  perpendicular  to  the  line 
of  the  poles,  it  is  separated  into  two  distinct  parts, 
which  can  be  referred  to  the  different  action  exerted 
by  the  electromagnet  on  the  two  extra  currents  pro- 
duced in  the  discharge. 

The  light  of  Geissler's  tubes  has  been  applied 
to  medical  purposes.  A  long  capillary  tube  is 
soldered  to  two  bulbs  provided  with  platinum  wires  ; 
this  tube  is  bent  in  the  middle,  so  that  the  two 
branches  touch,  and  their  extremities  are  twisted 
as  shown  at  a  (fig.  862).  This  tube  contains  a  highly 
rarefied  gas,  like  those  previously  described,  and 

when  the  discharge  passes  a  light  is  produced  at  a,  bright  enough  to  illu- 
minate any  cavity  of  the  body  into  which  the  tube  is  introduced. 


-926]  De  la  Rue  and  Milllers  Experiments.  889 

926.  Be  la  Rue  and  IVIuller's  experiments. — These  physicists  have 
made  a  very  extensive  and  elaborate  series  of  experiments  on  the  stratifica- 
tion of  the  electric  light  by  means  of  the  currents  produced  by  their  battery 
(812).  They  employed  for  some  of  these  experiments  as  many  as  14,400 
cells,  which  is  by  far  the  most  powerful  battery  ever  put  together.  It  is 
impossible  to  attempt  here  even  a  condensed  account  of  these  experiments  ; 
but  the  following,  which  are  some  of  the  results  obtained,  may  be  mentioned. 

The  discharge  in  a  vacuum  tube  is  essentially  of  the  same  nature  as  that 
which  takes  place  in  gases  under  the  ordinary  atmospheric  pressure.  A 
vacuum  tube  was  interposed  in  the  circuit  of  a  battery  of  2,400  cells,  to- 
gether with  a  very  long  resistance.  It  was  found  that  the  potentials  at  the 
two  ends  of  the  tube  are  virtually  the  same  :  now  according  to  Ohm's  law 
there  should  be  a  fall  of  potential  along  the  entire  circuit ;  it  is  accordingly 
concluded  that  the  discharge  is  not  a  current  in  the  ordinary  sense  of  the 
term,  but  is  disruptive,  the  electricity  being  carried  by  the  molecules  of  the 
gas.  At  no  degree  of  exhaustion  is  air  a  conductor. 

All  the  strata  start  from  the  positive  pole.  For  a  definite  pressure  an 
aureole  is  formed  at  the  positive  pole  ;  with  a  diminished  pressure  this  de- 
taches itself,  is  succeeded  by  others,  and  so  on. 

One  of  the  most  curious  results  is  the  definite  and  stationary  character  of 
the  striae  for  given  conditions  ;  they  are  remarkably  permanent,  and  seem 
almost  as  if  they  could  be  manipulated  ;  a  single  stratum  may  be  seen  fall- 
ing down  a  tube  like  a  feather  in  a  vacuum,  or  like  a  drop  of  water.  They 
are  not  produced  in  the  same  way  as  drops  falling,  but  all  and  each  of  the 
little  strata  are  so  many  Leyden  jars. 

The  length  of  the  arc  found  between  two  terminals  varies  with  the  square 
of  the  number  of  cells  ;  thus  while  1,000  cells  give  a  spark  of  0-005 1  inch 
under  ordinary  atmospheric  pressure,  11,000  cells  give  a  spark  of  0-62  inch. 

With  an  increase  of  exhaustion  the  potential  necessary  to  cause  a  current 
to  pass  diminishes  to  a  certain  pressure  which  represents  an  exhaustion  of 
least  resistance  ;  from  this  it  again  increases,  and  the  strata  thicken  and 
diminish  in  number  until  a  point  is  reached  at  which  no  discharge  takes 
place,  however  high  be  the  potential. 

A  change  in  the  current  often  produces  an  entire  change  in  the  colour  of 
the  stratification,  thus  in  hydrogen  the  change  is  from  blue  to  pink.  If  the 
discharge  is  irregular  and  the  strata  indistinct  an  alteration  in  the  strength 
of  the  current  makes  the  strata  distinct  and  steady.  Even  when  the  strata 
are  apparently  quite  steady  and  permanent,  a  pulsation  may  be  detected  in 
the  current  by  means  of  the  telephone. 

In  the  same  tube,  and  with  the  same  gas,  a  very  great  variety  of  phe- 
nomena can  be  produced  by  varying  the  pressure  and  the  current.  The 
peculiar  luminosity  and  form  of  stratification  in  their  various  forms  can  be 
reproduced  in  the  same  tube  or  in  others  having  similar  dimensions. 

The  colour  of  the  discharge  in  one  and  the  same  gas  greatly  depends  on 
the  degree  of  rarefaction.  The  least  resistance  to  the  discharge  in  hydrogen, 
and  when  its  brilliancy  is  greatest,  is  at  a  pressure  of  0-642  mm.  or  845  M 
(M  is  a  very  convenient  symbol  for  the  millionth  of  an  atmosphere).  When 
the  rarefaction  has  attained  0*002  mm.  or  3  M,  the  discharge  only  just  passes 
even  with  a  potential  of  11*330  volts  ;  while  with  an  exhaustion  of  O'oooo55 


890  Dynamical  Electricity.  [926- 

mm.,  the  nearest  approach  to  a  perfect  vacuum  ever  attained,  not  only  does 
this  fail  to  produce  a  discharge,  but  the  i  inch  spark  of  an  induction  coil 
does  not  pass. 

Air  offers  a  greater  resistance  than  hydrogen  ;  a  spark  which  passes  in 
hydrogen  across  a  distance  of  5-6  mm.  will  only  strike  across  a  distance  of 
3  mm.  in  air. 

In  air  at  a  pressure  of  62  mm.,  which  corresponds  to  an  atmospheric  height 
of  12-4  miles,  the  electric  discharge  has  the  carmine  tint  so  often  seen  in  the 
display  of  the  aurora  borealis  (991)  ;  at  a  pressure  of  1-5  mm.,  correponding 
to  a  height  of  30-96  miles,  it  is  salmon-coloured  ;  and  at  a  pressure  of  0-8  mm.,, 
representing  a  height  of  33-96  miles,  it  is  of  a  pale  white.  Under  a  pressure 
of  0-379  mm.  the  discharge  has  the  greatest  brilliancy.  This  represents  a 
height  of  37-67  miles,  and  would  be  visible  at  a  distance  of  585  miles  ;  it  is  pro- 
bably the  upper  limit  of  the  height,  though  on  the  other  hand  it  is  possible  that 
the  discharge  may  sometimes  take  place  at  a  height  of  a  few  thousand  feet. 

927.  Crookes's  experiments. — Dr.  Crookes  has  made  a  remarkable 
series  of  experiments  on  the  phenomena  produced  when  the  electrical  dis- 


Fig.  863. 

charge  is  produced  in  tubes  very  highly  exhausted,  that  is,  beyond  the  point 
at  which  the  best  effects  of  the  stratification  are  produced. 

When  the  electrical  discharge  is  passed  through  a  Geissler's  tube  in 
which  the  exhaustion  is  as  low  as  2  mm.,  the  negative  pole  is  surrounded 
by  a  narrow  layer,  and  then  by  a  relatively  dark  bluish  space,  the  rest  of 
the  tube  being  filled  by  layers  of  reddish-yellow  light,  separated  by  dark 
spaces  ;  as  the  rarefaction  proceeds,  the  bluish  light  extends,  and  under  cer- 
tain circumstances  fills  the  entire  tube.  Wherever  the  light  strikes  against 
the  glass  it  excites  the  brightest  fluorescence.  But  the  most  remarkable 


-927] 


Crookes' s  Experiments. 


Sgi 


feature  is  that  when  the  vacuum  is  almost  complete  the  nature  of  the  phe- 
nomenon changes.  The  light  now  proceeds  from  the  electrode  in  straight 
lines,  and  does  not  follow  any  bends  in  the  tubes.  This  rectilinear  propaga- 
tion is  well  illustrated  by  the  following  experiment  of  Crookes.  In  fig.  863,  A, 
the  negative  pole  of  the  induction  coil,  is  connected  with  the  electrode  a, 
which  is  made  of  aluminum,  and  forms  a  slightly  concave  mirror.  If  the 
exhaustion  is  not  more  than  2  mm.  pressure,  and  the  positive  pole  is  con- 
nected successively  with  the  electrodes  £,  c,  d,  the  discharge  takes  place  in 
curved  lines  as  shown  in  the  figure.  But  when  the  rarefaction  is  exceed- 
ingly great,  about  a  millionth  of  an  atmosphere,  the  appearance  is  that  pre- 
sented in  fig.  863,  B.  With  whatever  electrode  the  positive  pole  is  connected, 
the  rays  proceeding  in  straight  lines  cross  in  the  focus,  and,  striking  against 
the  opposite  side,  excite  there  the  most  brilliant  fluorescence. 

If  a  screen  of  mica  of  any  shape  be  interposed  in  the  path  of  the  rays  it 
stops  the  light  on  its  path,  and  a  shadow  is  formed  at  the  other  end  of  its  own 
shape,  surrounded  by  a  bright  fluorescence. 

The  discharge  can  also  produce  mechanical  effects.  A  Geissler's  tube  is 
constructed  with  a  pair  of  glass  rails  in  it,  on  which  rolls  the  axis  of  a  light 
wheel,  on  the  spokes  of  which  are  mica  vanes.  If  now  the  discharge  be 
directed  against  the  top  of  the  vanes,  the  wheel 
moves  along  towards  the  positive  pole. 

The  experiment  represented  in  fig.  864  shows  the 
very  great  heat  which  the  glow  light  can  produce. 
a  is  the  negative  electrode  in  the  form  of  a  concave 
mirror,  <£a  strip  of  platinum  foil.  With  a  sufficiently 
powerful  induction  coil  the  platinum  can  be  made 
white  hot  or  even  melted. 

Some  of  the  most  beautiful  of  these  experiments 
are  those  made  by  directingthe  discharge  on  various 
precious  stones.  In  these  circumstances  diamond 
emits  a  splendid  green  fluorescence,  ruby  a  brilliant 
red,  emerald  a  carmine,  and  so  forth. 

The  electrical  discharge  does  not  pass  through 
a  vacuum,  as  is  shown  by  the  following  experiment. 
A  small  tube  containing  caustic  potash  is  fused  to 
a  Geissler's  tube  connected  with  a  Sprengel  pump. 
By  continual  exhaustion  while  the  caustic  potash  is 
being  heated,  as  complete  a  vacuum  as  possible  is 
made  of  the  tube  sealed.  The  last  minute  trace  of  i  * lg'  864' 

aqueous  vapour  is  absorbed  by  the  caustic  potash  as  it  cools.  In  this  com- 
plete vacuum  the  discharge,  however  strong,  no  longer  passes  ;  the  vacuum 
acts  as  a  complete  non-conductor. 

If,  however,  the  caustic  potash  is  gently  heated,  a  trace  of  aqueous  vapour 
is  given  off,  and  a  green  fluorescent  light  flashes  along  the  tube  ;  as  the  heating 
is  continued  and  the  vapour  becomes  denser  we  get  the  stratification,  until 
ultimately  the  electricity  passes  along  the  tube  in  the  form  of  a  narrow 
purple  line.  If  the  tube  is  allowed  again  to  cool,  the  phenomena  reproduce 
themselves  in  the  reverse  order. 

The  phenomena  here  described  are  regarded  by  Crookes  as  due  to  an 


892 


Dynamical  Electricity* 


[927- 


w//rrt-gaseous  state,  which  he  calls  radiant  matter.  In  gas  under  the  ordinary 
pressure  the  average  free  path  of  a  molecule  of  air  is  o-oooo95  mm. ;  as  the 
gas  is  more  rarefied  the  length  of  the  path  increases,  so  that  with  the  high 
degrees  of  exhaustion  which  Crookes  employs  in  his  later  experiments— as 
much  as  the  one  twenty-millionth  of  an  atmosphere — the  length  of  the  mean 
path  is  so  much  increased  that  its  dimensions  are  comparable  with  those  of 
the  vessel,  and  along  with  this  increase  the  number  of  intramolecular  shocks 
diminishes  in  a  corresponding  ratio.  It  is  to  this  condition,  in  which  the 
molecules  move  forward  with  their  own  motion,  and,  striking  against  the  sides, 
give  rise  to  the  fluorescence,  that  Crookes  accounts  for  the  effects  produced. 
The  theoretical  views  to  which  Crookes  has  been  led  by  his  experiments 
have  met  with  a  considerable  degree  of  criticism,  and  it  must  be  added  that 
none  of  the  explanations  of  these  singularly  beautiful  experiments  have  met 
with  general  adoption. 

928.  Rotation  of  induced  currents  by  magnets. — De  la  Rive  devised 
an  experiment  which  shows  in  a  most  ingenious  manner  that  magnets  act  on 
the  light  in  Geissler's  tubes  in  accordance  with  the  laws  with  which  they 
act  on  any  other  movable  conductor. 

This  apparatus  consists  of  a  glass  globe  or  electrical  egg  (fig,  865),  pro- 
vided at  one  end 
with  two  stopcocks, 
one  of  which  can  be 
screwed  on  the  air- 
pump,  and  the  other, 
which  is  a  stopcock 
like  that  of  Gay 
Lussac  (383),  serves 
to  introduce  a  few 
drops  of  the  liquid 
into  the  globe.  At 
the  other  end  a 
tubulure  is  ce- 
mented, through 
which  passes  a  rod 
of  soft  iron  about  \ 
of  an  inch  in  dia- 
meter, the  top  of 
which  is  about  the 
centre  of  the  globe. 
Except  at  the  two 
ends,  this  rod  is  en- 
tirely covered  with 
a  very  thick  insulat- 
ing layer  of  shellac, 
then  with  a  glass 
tube  also  coated  with 
shellac,  and  finally 
with  another  glass 
This  insulating  layer  must  be 


Fig.  865. 
tube  uniformly  coated  with  a  layer  of  wax. 


-929]      Heat  Developed  by  Magnets  on  Bodies  in  Motion.        893 

at  least  f  of  an  inch  thick.  Inside  the  globe,  the  insulating  layer  is  sur- 
rounded at  x  with  a  copper  ring,  connected  with  a  binding  screw,  c,  by  means 
of  a  copper  wire. 

The  vessel  having  been  exhausted  as  completely  as  possible,  a  few  drops 
of  ether  or  of  turpentine  are  introduced  by  means  of  the  stopcock  a  ;  it  is 
again  exhausted,  so  that  the  vapour  remaining  is  highly  rarefied. 

A  thick  disc  of  soft  iron,  o,  provided  with  a  binding  screw,  is  then  placed 
on  one  of  the  branches  of  a  powerful  electromagnet,  and  the  end  m  of  the 
rod  mn  is  placed  on  this  disc,  while  at  the  same  time  one  of  the  ends  of  the 
secondary  wire  of  Ruhmkorffs  coil  is  connected  with  the  binding  screw,  £, 
and  the  other  with  the  knob  o.  Tf  then  the  coil  is  worked  without  setting  in 
action  the  electromagnet,  the  electricity  of  the  wire  s  passes  to  the  top,  ?z,  of 
the  soft  iron  rod,  and  that  of  the  second  wire  to  the  ring  .r,  and  a  more  or 
less  irregular  luminous  sheaf  appears  on  the  inside  of  the  globe  round  the 
rod,  as  in  the  experiment  of  the  electric  egg. 

But  if  a  voltaic  current  passes  into  the  electromagnet,  the  phenomenon 
is  different  ;  instead  of  starting  from  different  points  of  the  upper  surface 
n,  and  the  ring  x,  the  light  is  condensed  and  emits  a  single  arc,  from 
n  to  x.  Further — and  this  is  the  most  remarkable  part  of  the  experiment 
— this  arc  turns  slowly  round  the  magnetised  cylinder  mn^  sometimes  in 
one  direction,  and  sometimes  in  another,  according  to  the  direction  of  the 
induced  current,  or  the  direction  of  the  magnetisation.  As  soon  as  the  magne- 
tisation ceases,  the  luminous  phenomenon  reverts  to  its  original  appearance. 

This  experiment  is  remarkable  as  having  been  devised  d  priori  by  De  la 
Rive  to  explain,  by  the  influence  of  terrestrial  magnetism,  a  kind  of  rotatory 
motion,  from  east  to  west,  observed  in  the  aurora  borealis.  The  rotation  of 
the  luminous  arc  in  the  above  experiment  can  evidently  be  referred  to  the 
rotation  of  currents  by  magnets  (868). 

Geissler  has  constructed  a  very  useful  form  of  the  above  experiment,  in 
which  the  globe  is  exhausted  once  for  all.  Apart  from  the  purpose  for  which 
it  was  originally  devised,  it  is  a  very  convenient  arrangement  for  demon- 
strating the  action  of  magnets  on  movable  currents. 

929.  Heat  developed  by  the  induction  of  powerful  magnets  on  bodies 
in  motion. — We  have  already  seen  in  Arago's  experiments  (914)  that  a  rota- 
ting copper  disc  acts  at  a  distance  on  a  magnetic  needle,  communicating  to  it 
a  rotatory  motion.  We  shall  presently  see  that  a  cube  of  copper,  rotating 
with  great  velocity,  is  suddenly  stopped  by  the  influence  of  the  poles  of  two 
strong  magnets  (938).  It  is  clear  that,  in  order  to  prevent  the  rotation  of  the 
needle  or  of  the  copper,  a  certain  mechanical  force  must  be  consumed  in 
overcoming  the  resistance  which  arises  from  the  inductive  action  of  the  mag- 
net. Reasoning  upon  the  theory  of  the  transformation  of  mechanical  work 
into  heat  (497),  it  has  been  attempted  to  ascertain  what  quantity  of  heat 
is  developed  by  the  action  of  induced  currents  under  the  influence  of  power- 
ful magnets.  Joule,  with  a  view  of  determining  the  mechanical  equivalent 
of  heat,  coiled  a  quantity  of  copper  wire  round  a  cylinder  of  soft  iron,  and 
having  enclosed  the  whole  in  a  glass  tube  full  of  water,  he  imparted  to  the 
system  a  rapid  rotation  between  the  branches  of  an  electromagnet.  A 
thermometer  placed  in  the  liquid  served  to  measure  the  quantity  of  heat 
produced  by  the  induced  currents  in  the  soft  iron  and  the  wire  round  it. 


894  Dynamical  Electricity.  [929- 

It  was  thus  found  that  the  heat  developed  was  proportional  to  the  square  ot 
the  magnetism  evoked,  and  was  equivalent  to  the  work  used  in  the  rotation. 
Foucault  made  a  remarkable  experiment  by  means  of  the  apparatus 
represented  in  fig.  866.  It  consists  of  a  powerful  electromagnet  fixed 
horizontally  on  a  table.  Two  pieces  of  soft  iron,  A  and  B,  are  in  contact 
with  the  poles  of  the  magnet,  and  becoming  magnetised  by  induction, 
they  concentrate  their  magnetic  inductive  action  on  the  two  faces  of  a 
copper  disc,  D,  3  inches  in  diameter,  and  a  quarter  of  an  inch  thick  ; 


Fig.  866. 


this  disc  partly  projects  between  the  pieces  A  and  B,  and  can  be  moved  by 
means  of  a  handle  and  a  series  of  toothed  wheels  with  a  velocity  of  150  to 
200  turns  in  a  second. 

So  long  as  the  current  does  not  pass  through  the  wire  of  the  electro- 
magnet, very  little  resistance  is  experienced  in  turning  the  handle,  and 
when  once  it  has  begun  to  rotate  rapidly,  and  is  left  to  itself,  the  rotation 
continues  in  virtue  of  the  acquired  velocity.  But  if  the  current  passes,  the 
disc  and  other  pieces  stop  almost  instantaneously ;  and  if  the  handle  is 
turned  considerable  resistance  is  felt.  If,  in  spite  of  this,  the  rotation  be 
continued,  the  force  used  is  transformed  into  heat,  and  the  disc  becomes 
heated  to  a  remarkable  extent.  In  an  experiment  made  by  Foucault  the 
temperature  of  the  disc  rose  from  10°  to  61°,  the  current  being  formed  by 
three  of  Bunsen's  elements  ;  with  six  the  resistance  was  such  that  the  rotation 
could  not  long  be  continued.  The  currents  thus  produced  in  solid  conductors, 
and  which  are  converted  into  heat,  are  often  spoken  of  as  Foucault  currents. 
'  Such  currents  are  of  constant  occurrence  in  magneto-electrical  machines, 
and  weaken  their  force,  firstly,  by  owing  their  existence  to  some  part  of  the 
work  expended ;  secondly,  they  weaken  the  magnetism  of  the  armatures  by 
their  direction  ;  and,  lastly,  they  are  converted  into  heat,  which  increases 
the  internal  resistance  of  the  machine. 


-930] 


The  Telephone. 


895 


r  930.  The  Telephone. — To  the  number  of  instruments  depending  on  in- 
duction may  be  added  this  discovery,  which  is  equally  remarkable  for  the 
surprising  character  of  the  results  which  it  produces,  and  for  the  sim- 
plicity of  the  means  by  which  they  are  produced.  Fig.  867  represents  a 
perspective,  and  fig.  868  a  section,  of  the  latest  form  of  telephone  as  improved 
by  its  inventor,  Mr.  Graham  Bell. 

It  consists  essentially  of  a  steel  magnet  of  about  4  inches  in  length  by 
half  an  inch  in  diameter,  enclosed  in  a  wooden  case.  Round  one  end  of  this 
magnet  is  fitted  a  thin  flat  bobbin,  BB,  of  fine 
insulated  copper  wire.  For  a  magnet  of  this 
size  a  length  of  250  metres  of  No.  38  wire, 
offering  a  resistance  of  350  ohms,  is  well 
suited. 

The  ends  of  this  coil  pass  through  longi- 
tudinal holes,  LL,  in  the  case,  and  are  con- 
nected with  the  binding  screws  CC.  In  front 
of  the  magnet  and  at  a  distance  which  can 
be  regulated  by  a  screw,  S,  but  which  is  some- 
thing less  than  a  millimetre,  is  the  essential 
feature  of  the  instrument,  a  diaphragm,  D,  of 
soft  iron,  not  much  thicker  than  a  sheet  ot 
stout  letter-paper.  This  diaphragm  is  screwed 
down  by  the  mouthpiece  E,  which  is  similar 
to,  though  somewhat  larger  than,  that  of  a 
stethoscope. 

The  instruments  are  connected  by  wires, 
for  one  of  which  the  earth  may  be  substituted, 
as  in  ordinary  telegraphic  communication 
(886).  Each  instrument  can  be  used  either 
as  sender  or  receiver,  though  in  actual  prac- 
tice it  is  more  convenient  for  each  operator 
to  have  two  telephones,  one  of  which  is 
held  to  the  ear,  while  the  other  is  used  for 
speaking  into  ;  the  latter  being  larger  and 
more  powerful  than  the  receiver. 

The  action  of  the  instrument  depends  on  the  fact  that  whenever  the 
relative  positions  of  a  magnet  and  of  a  closed  coil  of  wire  are  altered  there 
is  produced  within  the  coil  a  current  or  currents  of  electricity.  This  may 
be  illustrated  by  reference  to  fig.  818.  When  the  magnet  is  suddenly 
brought  into  the  coil,  a  current  is  produced  in  the  coil  in  a  particular 
direction.  There  is  no  current  so  long  as  the  coil  and  the  magnet  are 
stationary.  When,  however,  the  magnet  is  suddenly  withdrawn,  a  current  is 
produced  in  the  opposite  direction.  Similar  effects  are  produced  if,  while  the 
magnet  is  in  the  coil,  its  magnetism  is  by  any  means  increased  or  diminished. 

Now  in   the   telephone  the  magnet  and  the  coil,  when   once   properly 

adjusted,  remain  fixed.      But  the  magnet  M  magnetises  by  induction  the 

soft   iron  membrane  D  in  front  of  it,  that   is,  converts  it  into  a  magnet. 

When,  by  the  mouthpiece  being  spoken  into,  this  iron  membrane  vibrates 

i  backwards  and  forwards,  these  vibrations  give  rise  to  an  alteration  in  the 


Fig.  867. 


896 


Dynamical  Electricity. 


[930 


magnetism  of  the  permanent  magnet,  the  effect  of  which  is  that  currents 
are  produced  in  alternate  directions  in  the  coil  surrounding  the  pole. 
Moreover,  the  alteration  in  the  relative  positions  of  the  magnetised  dia- 
phragm, thus  magnetised  by  induction,  and  of  the  coil,  gives  rise  to  currents 
in  the  same  direction  as  the  above.  These  alternating  currents,  being 
transmitted  through  the  circuit  to  the  distant  coil,  alternately  attract, 

and  cease  to  attract, 
the  corresponding 
diaphragm.  They 
thereby  put  this  in 
vibration,  and  when 
the  mouthpiece  of 
this  telephone  is 
held  to  the  ear, 
these  vibrations  are 
perceived  as  sound 
corresponding  to 
that  which  is  trans- 
Fl*- 868'  mitted.  Hence, 

whatever  sound  produces  the  vibration  ot  the  diaphragm  of  the  sending 
instrument  is  repeated  by  that  of  the  receiver. 

The  reproduction  of  the  sound  in  the  receiving  instrument  is  perfect  as 
far  as  articulation  is  concerned,  but  it  is  considerably  enfeebled,  as  might  be 
expected.  The  sound  has  something  of  a  metallic  character,  appearing  as 
if  heard  through  a  long  length  of  tubing,  while  it  faithfully  reproduces  the 
characteristics  of  the  person  speaking.  It  does  not  result  from  a  series  of 
sharp  and  distinct  makes  and  breaks,  but  in  each  of  the  momentary  currents 
there  is  a  continuous  rise  and  fall,  corresponding  in  every  gradation  and 
inflection  to  the  motion  of  the  air  agitated  by  the  speaker. 

Various  attempts  have  been  made  to  improve  the  loudness  of  the  sounds 
produced  in  the  telephone,  by  varying  the  form  of  the  various  parts,  and 
using  more  powerful  magnets  of  horseshoe  and  circular  forms  ;  but  experi- 
ment shows  that  increased  loudness  is  always  produced  at  the  expense  of 
distinctness  of  articulation. 

The  amplitude  of  the  vibration  of  the  disc  is  extremely  small.  According 
to  Bosscha  a  unit  current  produced  a  displacement  of  0-034  of  a  mm.,  and  as 
currents  of  j~  of  this  are  perceptible,  it  follows  that  the  amount  of  displace- 
ment must  be  about  the  ^oth  of  the  wave-length  of  yellow  light  (637). 

The  current  in  a  telephone  is  estimated  by  De  la  Rue  as  not  exceeding 
that  which  would  be  produced  by  one  DanielFs  cell  in  a  circuit  of  copper 
wire  4  mm.  in  diameter  of  a  length  sufficient  to  go  290  times  round  the  earth. 
This  current  would  have  to  pass  19  years  through  a  voltameter,  to  produce 
i  c.c.  of  detonating  gas.  This  is  about  1,000  million  times  less  than  the 
currents  in  ordinary  use.  Such  currents  are,  however,  sufficient  to  cause 
the  contraction  of  a  frog's  leg  (797). 

Siemens  estimates  that  not  more  than  ^Q~  of  the  mass  of  sound  which 
the  sender  receives  is  produced.  That  it  is  possible  to  perceive  this,  is  due 
to  the  great  sensitiveness  and  range  of  the  ear,  which  can  endure  the  sound 
of  a  cannon  at  a  distance  of  5  yards,  and  still  perceives  it  at  a  distance 


930]  The  Telephone.  897 

10,000  times  as  great.  This  represents  a  ratio  of  intensities  of  one  to  one 
hundred  millions. 

From  some  experiments  on  the  transmission  of  the  sound  of  a  high- 
pitched  tuning-fork  (251)  Rontgen  concludes  that  no  less  than  24,000  currents 
are  transmitted  in  one  second. 

This  extreme  delicacy  of  the  telephone  is  its  drawback  to  speaking 
through  ordinary  telegraph  circuits.  The  currents  in  adjacent  wires,  the 
vibration  of  the  posts  and  of  the  insulators,  or  the  passage  of  a  cart  over 
the  streets,  acts  by  induction  on  the  telephone  circuit,  and  overpowers  its 
indications.  When  a  telephone  circuit  was  placed  at  a  distance  of  20  metres 
from  a  well-insulated  line,  through  which  signals  were  sent  by  means  of  a 
battery  of  a  few  elements,  sounds  were  distinctly  heard  in  the  telephone. 
Speaking  under  such  circumstances  is  like  speaking  in  a  storm.  The 
powerful  currents  used  for  systems  of  electric  lighting  produce  such  a  roar 
in  an  adjacent  telephone  circuit  that  it  is  impossible  to  speak  through  the 
telephone.  The  only  effective  way  of  diminishing  the  inductive  action  of 
adjacent  systems  is  to  have  two  wires  in  close  proximity  to  each  other. 
They  are  thus  at  the  same  distance  from  the  inducing  circuit,  and  as  one  of 
the  wires  is  used  for  going  and  the  other  for  returning,  the  similar  influences 
must  be  in  opposite  directions,  and  therefore  neutralise  each  other. 

If  a  telephone  is  inserted  in  the  circuit  of  a  Morse's  instrument,  the 
sound  of  the  working  is  heard,  and  the  messages  can  be  read  ;  this  is  the 
case  also  of  the  telephone  in  the  branch  circuit  of  a  Morse.  If  the  tele- 
phone is  joined  up  with  the  primary,  and  another  with  the  secondary  wire 
of  an  induction  coil,  communication  is  almost  as  good  as  if  the  two  apparatus 
were  directly  united. 

Telephones  have  been  constructed  in  which  the  thin  iron  plate  is  re- 
placed by  a  thicker  one,  or  by  an  unmagnetic  one  ;  or  if  the  telephone  is 
held  close  to  the  ear,  the  plate  can  be  dispensed  with  altogether.  In  the 
latter  two  cases  the  sounds  are  only  perceived  when  the  spiral  surrounding 
the  magnet  can  vibrate  with  it. 

A  telephone  may  be  constructed  with  a  rod  of  soft  iron  instead  of  a 
magnet ;  when  the  rod  is  held  in  the  line  of  dip,  and  the  mouthpiece  is  sung 
into,  the  sounds  are  reproduced. 

From  its  extreme  sensitiveness,  being  perhaps  the  most  delicate  galvano- 
scope  we  possess,  the  telephone  has  become  of  great  service  in  scientific 
research.  It  may  be  used  instead  of  a  galvanometer  in  a  Wheatstone's 
bridge.  If  inserted  in  either  of  the  circuits  of  an  induction  coil,  the 
number  of  breaks  can  be  determined  from  the  height  of  the  tone  which  is 
produced.  When  inserted  in  the  current  of  a  Holtz's  machine,  the  disc  of 
which  is  rotating  with  a  uniform  velocity,  the  height  of  the  note  varies  with 
the  resistance  of  the  circuit,  and  with  the  capacity  of  the  condensers.  It 
can  be  shown  also  that  the  circumstances  most  favourable  for  the  production 
of  a  most  distinct  stratification  in  a  Geissler's  tube  correspond  to  a  definite 
pitch  in  the  telephone. 

The  telephone  has  been  used  to  test  hardness  of  hearing.  If  the  mag- 
netism of  a  telephone  be  excited  by  galvanic  currents  which  are  made  inter- 
mittent by  a  vibrating  tuning-fork,  and  if  a  telephone  is  inserted  in  a  branch 
circuit  (961),  then  by  varying  the  strength  of  the  principal  current,  by  the 

3M 


898  Dynamical  Electricity.  [930- 

insertion  of  resistances,  the  strength  of  the  sounds  in  the  telephone  may 
be  varied  at  will. 

When  a  telephone  is  held  to  the  ear  during  a  thunderstorm,  every  lightning 
flash  in  the  sky  is  simultaneously  heard  to  be  accompanied  by  a  sharp  crack. 
Dolbear  has  constructed  a  telephone  in  which  the  electrostatic  action  of 
currents  is  used.  It  consists  of  two  circular  flat  discs  of  metal  rigidly  fixed 
to  each  other  in  an  insulated  case  of  ebonite.  One  of  the  discs  is  in  metallic 
connection  with  the  line  wire,  in  which  is  a  battery  and  an  induction  coil ; 
in  this  way,  while  one  disc  is  electrified  positively,  the  other  is  negatively 
electrified  by  induction,  and  if  the  current  be  varied  by  speaking  through  a 
transmitter  in  the  circuit  their  varying  effects  are  faithfully  reproduced,  and 
reappear  as  sound  vibrations  on  the  receiver. 

X/^931.  The  microphone. — When  the  wires  of  an  electrical  circuit,  in  which 
is  interposed  a  telephone,  are  broken,  and  rest  loosely  on  each  other,  sounds 

produced  near  the  point  of  contact 
are  reproduced  and  magnified  in 
the  telephone.  The  microphone,  in- 
vented by  Prof.  Hughes,  depends  on 
this  fact  ;  its  arrangement  may  be 
greatly  varied  ;  one  of  the  simplest 
and  most  convenient  forms  is  that 
represented  in  fig.  869.  A  piece 
of  thin  wood  is  fitted  vertically  on 
a  base  of  the  same  material ;  two 
small  rods  of  gas  carbon,  C  C,  about 
|  of  an  inch  thick,  are  fixed  hori- 
zontally  in  the  upright ;  by  means  of 
binding  screws,  they  are  in  metallic 
connection  with  the  wires  of  a  cir- 
cuit in  which  is  a  small  battery  and 
a  telephone  ;  and  in  each  of  them 

is  a  cavity.  A  third  piece,  D,  of  the  same  material,  and  about  one  inch  long, 
is  pointed  at  each  end,  one  of  which  rests  in  the  lower  cavity,  while  the  other 
pivots  loosely  in  the  upper  one.  When  a  watch  is  placed  on  the  base  B,  its 
ticking  is  heard  in  the  telephone  with  surprising  loudness  ;  the  walking  of 
a  fly  on  the  base  suggests  the  stamping  of  a  horse  ;  the  scratching  of  a 
quill,  the  rustling  of  silk,  the  beating  of  the  pulse,  are  perceived  in  the 
telephone  at  a  distance  of  a  hundred  miles  from  the  source  of  sound  ;  while 
a  drop  of  water  falling  on  the  base  has  a  loud  crashing  sound.  To  obtain 
the  best  results  with  a  particular  instrument,  the  position  of  the  carbon  must 
be  carefully  adjusted  by  trial ;  and  indeed  the  form  of  the  instrument  itself 
must  be  variously  modified  for  the  special  object  in  view  :  in  some  cases 
great  sensitiveness  is  required  :  in  others  great  range.  In  order  to  eliminate 
as  far  as  possible  the  effect  of  accidental  vibrations  due  to  the  supports,  the 
base  should  rest  on  pieces  of  vulcanised  tubing,  or  on  wadding. 

It  is  known  that  the  compression  of  a  semiconductor,  such  as  carbon, , 
diminishes  its  resistance,  while  a  diminution  in  the  compression  in- 
creases the  resistance.  The  action  of  the  microphone  is  to  be  ascribed 
to  this  ;  in  consequence  of  the  minute  alterations  in  the  pressure  and  in  the 


-932] 


Hughes 's  Induction  Balance. 


899 


degree  of  contact  at  the  break,  the  electrical  resistance  in  the  circuit  varies 
in  accordance  with  the  sound  waves,  and  consequently  the  strength  of  the 
currents  varies  too.  The  result  of  this  is,  that  what  we  may  call  undulating 
currents  of  electricity  are  produced,  whose  amplitude,  height,  and  form  are 
in  exact  correspondence  with  the  sound  waves.  The  effect  of  the  micro- 
phone is  to  draw  supplies  of  energy  from  the  battery,  which  then  appear  in 
the  telephone. 

932.  Hughes's  induction  balance. — The  principle  of  this  apparatus  may 
be  thus  stated  : — Suppose  we  have  two  exactly  equal  primary  induction  coils, 
A  and  A',  and  near  them  two  secondary  coils,  B  and  B',  also  exactly  equal, 
and  connected  up  with  a  galvanometer,  so  that  the  coils  act  upon  it  in 
opposite  directions.  If  now  the  current  of  a  battery  be  sent'  through  the 
primary  coils,  joined  in  series,  the  inductive  effects  on  each  of  the  secondary 
coils  will  be  the  same,  and,  as  their  action  on  the  galvanometer  is  opposed, 
no  deflection  of  the  needle  will  be  produced.  If,  however,  a  piece  of  iron 

be  introduced  into  the  t _N 

core  of  one  of  the  secon- 
dary  coils,  the  equality 
in  the  induction  effects 
will  be  destroyed,  and 
the  needle  of  the  gal- 
vanometer at  once  de- 
flected. 

This  principle  was 
first  applied  by  Bab- 
bage,  Herschell,  and  in 
a  special  apparatus  by 
Dove  ;  but  the  micro- 
phone and  the  tele- 
phone have  led  the 
inventor  of  the  former 
to  the  invention  of  an 
apparatus  which  has 
opened  out  new  possi- 
bilities, and  has  placed 
in  the  hands  of  the 
physicist  an  elegant 
and  powerful  engine  of 
research,  which  in  cer- 
tain departments  of  in- 
vestigation promises  to 
be  of  great  service. 

The  form  of  instru- 


Fig.  870. 


ment  as  devised  by  Professor  Hughes  is  represented  in  fig.  870,  where  the 
essential  parts  are  drawn  to  scale,  though  the  relative  distances  of  the  parts 
are  not  so  ;  a  and  a'  are  the  two  primary  coils,  each  of  which  consists  of  100 
metres  of  No.  32  silk-covered  copper  wire  (0-009  m  diameter)  wound  on  a  flat 
boxwood  spool  10  inches  in  depth ;  b  and  £'are  two  secondary  coils,  all  four  coils 
being,  in  intention  at  least,  exactly  alike.  The  two  primary  coils  are  joined 

3  M  2 


poo  Dynamical  Electricity.  [932- 

in  series  with  a  battery  of  three  or  four  small  Darnell's  cells  in  which  circuit 
a  microphone,  ;;z,  is  also  inserted  ;  the  ticking  of  a  small  clock  on  the  table 
acts  as  make  and  break. 

The  secondary  coils  are  joined  up  with  a  telephone  in  such  a  manner 
that  their  action  upon  it  is  opposed. 

Now,  whatever  care  be  taken  in  winding  the  wire  on* the  coils,  it  is  not 
possible  to  get  at  the  outset  an  exact  balance.  Hence,  while  one  of  the 
secondary  coils,  b,  is  at  a  fixed  distance  from  <z,  the  corresponding  one,  b\  is 
not  so  ;  its  distance  from  a'  can  be  slightly  modified  by  means  of  a  micro- 
metric  screw,  and  thus,  connection  with  the  battery  circuit  having  been  made, 
a  balance  is  obtained  by  slightly  varying  the  adjustment,  and  the  accomplish- 
ment  of  this  is  known  by  there  being  silence  in  the  telephone.  But  if  now 
any  metal  whatever  be  introduced  in  one  of  the  secondary  coils,  a  sound 
is  at  once  heard. 

This  arrangement  is  so  far  a  simple  differential  one,  and  furnishes  as  yet 
no  means  of  measuring  the  forces  brought  into  play,  and  for  this  purpose 
Hughes  uses  what  is  called  a  sonometer  or  audiometer.  This  consists  of 
three  similar  coils,  <r,  d,  and  ^,  placed  vertically  on  a  horizontal  graduated  rule 
along  which  d  can  be  moved.  By  means  of  a  switching  key  or  switch, 
the  primary  coils  c  and  e  can  be  put  in  communication  with  the  battery  and 
microphone  circuit  quite  independently  of  the  balance,  and  it  is  so  ar- 
ranged that  the  ends  of  the  coils  c  and  e  facing  each  other  are  of  the  same 
polarity  ;  the  third  coil,  d,  the  secondary  one,  is  connected  with  the  telephone 
circuit. 

If  these  primary  coils  c  and  ^were  quite  equal,  then,  when  connected  up 
with  the  battery  circuit,  no  sound  would  be  heard  in  the  telephone,  when  the 
secondary  d  is  exactly  midway  between  them.  But  as  the  coil  is  moved 
from  this  position  either  towards  c  or  e  a  sound  is  heard,  due  to  the  prepon- 
derance of  one  or  the  other.  In  practice  the  coils  are  so  arranged  that  a 
balance  is  obtained  when  the  secondary  circuit  is  near  one  of  the  coils,  c 
for  instance ;  this  represents  a  zero  of  sound,  and  as  the  coil  d  is  moved 
nearer  to  e  a  sound  of  gradually  increasing  intensity  is  heard  ;  distances 
measured  off  along  this  scale  represent  values  of  sound  on  an  arbitrary 
scale. 

Suppose  now  that  a  balance  has  been  obtained  in  the  induction  balance, 
and  that  the  coil  d  in  the  sonometer  is  at  zero ;  no  sound  is  then  heard 
in  the  telephone  when  the  current  is  switched  either  in  one  or  the  other 
circuit.  But  if  the  balance  is  disturbed  by  placing  a  piece  of  metal  in  the 
core  of  £,  a  definite  continuous  sound  is  heard.  The  current  is  then  switched 
into  the  sonometer,  and  the  secondary  coil  e  is  moved  until  the  ear  perceives 
the  same  sound  in  both  circuits.  The  distance  then  along  which  the  coil  d 
has  been  moved  is  thus  an  arbitrary  measure  of  the  effect  produced. 

Although  by  the  switch  the  transition  from  one  circuit  to  the  other 
can  be  effected  with  great  rapidity,  and  the  ear  can  appreciate  minute 
differences,  this  has  not  the  value  of  a  null  method.  Hughes  has  still 
further  improved  the  balance  by  the  following  device,  in  which  the  sono- 
meter is  dispensed  with  : — A  graduated  strip,  of  zinc  about  200  mm.  in  length 
by  25  mm.  wide,  and  tapering  from  a  thickness  of  4  mm.  at  one  end  to  a  fine 
edge  at  the  other,  is  made  use  of.  The  metal  to  be  tested  is  placed  in  a 


-933] 


Tasimeter. 


901 


plane  between  a  and  b  on  the  left  of  the  plate,  and  the  strip  is  moved  along 
the  top  of  bf  until  a  balance  is  obtained. 

The  instrument  is  of  surprising  delicacy  ;  a  milligramme  of  copper  or  a 
fine  iron  wire  introduced  into  one  of  the  coils  which  has  been  balanced  can 
be  loudly  heard,  and  appreciated  by  direct  measurement.  If  two  shillings 
fresh  from  the  Mint  be  balanced,  rubbing  one  of  them  or  breathing  on  it 
at  once  disturbs^the  balance.  A  false  coin  balanced  against  a  genuine  one 
is  at  once  detected.  The  instrument  furnishes  a  means  of  testing  the  deli- 
cacy of  hearing  ;  such  a  piece  of  wire  as  the  above,  or  a  fine  spiral  of  copper, 
furnishes  a  kind  of  test  object  for  this  purpose. 

933.  Tasimeter. — This  instrument,  invented  by  Edison,  consists  essen- 
tially of  an  arrangement  by  which  a  disc  of  carbon  forming  part  of  a  voltaic 
circuit  is  exposed  to  varying  pressure.  It  depends  on  the  fact  that  the  re- 
sistance of  carbon  varies  very  greatly  with  the  pressure  to  which  it  is  ex- 
posed. It  consists  of  an  iron  base,  on  which  are  two  rigid  supports  (fig. 
871),  one  of  which,  «,  is  connected  with  the  galvanometer,^,  by  means  of 
a  wire.  An  ebonite  disc,  d,  is  screwed  into  a,  and  in  a  circular  cavity  in 
this  ebonite  is  a  small  carbon  disc,  not  shown  in  the  figure,  in  the  outer 


Fig.  871. 

surface  of  which  is  a  strip  of  platinum  in  metallic  connection  with  one  pole 
of  an  element,  /.  The  disc  of  carbon  is  closed  in  the  cavity  by  a  metal 
plug,  c,  in  which  is  a  cavity.  There  is  a  similar  plug,  £,  with  a  correspond- 
ing cavity  at  the  end  of  a  screw,  £,  which  works  in  the  upright  support  ;  in 
the  two  cavities  is  placed  the  strip  of  substance, /,  with  which  the  experiment 
is  made. 

A  gentle  pressure  being  applied  by  the  screw,  the  needle  is  deflected 
through  a  few  degrees,  and  its  position,  when  it  comes  to  rest,  is  noted. 
The  slightest  subsequent  contraction  or  expansion  is  indicated  by  a  deflec- 
tion of  the  needle  of  the  galvanometer. 

The  sensitiveness  of  the  instrument  is  very  great  :  a  thin  strip  of  ebonite 
is  expanded  by  the  heat  of  the  hand  held  near  it,  so  as  to  affect  a  not  very 
delicate  galvanometer.  A  strip  of  gelatine,  inserted  instead  of  the  ebonite, 
is  expanded  by  the  moisture  of  a  damp  strip  of  paper  held  two  or  three 
inches  away. 

The  apparatus   seems  well   adapted  for  the  qualitative  observation  of 


go2  Dynamical  Electricity.  [933- 

minute  changes  in  length  ;  it  has  been  used,  for  instance,  to  show  the  very 
small  elongation  of  an  iron  rod  when  it  is  magnetised  (880).  Great  care  is 
required  in  the  preparation  of  the  carbon  disc  ;  the  best  kind  seems  to  be 
made  from  lampblack  prepared  at  a  low  temperature,  and  then  powerfully 
compressed  into  a  button. 

934.  Edison's  loud-speaking:  telephone. — Although  depending  on  a 
different  principle,  we  may  give  a  description  here  of  this  instrument. 

An  adjustable  metal  spring  passes  on  the  surface  of  a  small  cylinder, 
made  of  chalk,  moistened  with  solutions  of  caustic  potash  and  acetate  of 
mercury ;  both  the  spring  and  the  cylinder  form  part  of  a  circuit  in  which 
is  a  battery  and  a  Reis's  transmitter  (884).  The  spring  is  connected  in  a 
suitable  manner  with  a  mica  disc,  which  is  the  vibrating  part  of  a  mouth- 
piece like  that  of  an  ordinary  telephone.  The  cylinder  can  be  turned  at  a 
uniform  rate,  either  by  hand  or  by  an  automatic  clockwork  arrangement. 

Now  while  the  spring  is  pressing  on  the  cylinder,  if  the  latter  be  rotated 
in  a  direction  away  from  the  mouthpiece,  in  consequence  of  the  friction 
between  the  spring  and  the  surface  of  the  cylinder,  a  certain  pull  will  be 
exerted  on  the  disc,  which  will  tend  to  drag  it  outwards.  If  the  direction  of 
rotation  were  the  opposite,  the  disc  would  be  pushed  inwards.  Now  the 
amount  of  pull  or  push  will  depend  on  the  friction  between  the  point  and 
the  surface.  If  a  momentary  current  be  passed,  there  will  be  a  momentary 
decomposition  at  the  surface  of  the  cylinder,  its  friction  will  be  altered  in 
consequence  of  this  momentary  decomposition,  the  effect  of  which  is  that 
the  disc  moves  inwards,  and  a  series  of  such  intermissions  of  the  current 
produces  a  corresponding  series  of  pulsations  of  the  disc,  which  if  sufficiently 
rapid  produce  a  sound.  The  friction  of  the  surfaces  in  contact  is  in  fact 
modified  by  means  of  electrical  decomposition,  a  lubricator  is  liberated  in 
correspondence  with  the  sound  waves,  and  thus  the  sound  which  they  repre- 
sent is  reproduced.  The  reproduction  is  so  loud  as  to  be  heard  throughout 
a  room,  the  sounding  instrument  being  at  a  distance.  Although  ordinary 
speech  and  music  can  thus  be  transmitted,  yet  the  sounds  have  a  harsh 
metallic  character  which  is  not  pleasing,  but  at  the  same  time  the  individual 
character  of  the  voice  is  preserved. 


-935] 


Optical  Effects  of  Powerful  Magnets. 


903 


CHAPTER  VII. 

OPTICAL   EFFECTS   OF   POWERFUL   MAGNETS.      DIAMAGNETISM. 

935.  Optical  effects  of  powerful  magnets. — Faraday  observed,  in  1845, 
that  a  powerful  electromagnet  exercises  an  action  on  many  substances,  such 
that  if  a  polarised  ray  traverses  them  in  the  direction  of  the  line  of  the  mag- 
netic poles,  the  plane  of  polarisation  is  deviated  either  to  the  rightuor  to  the 
left  according  to  the  direction  of  the  magnetisation. 

Fig.  872  represents  Faraday's  apparatus,  as  constructed  by  Ruhmkorff. 
It  consists  of  two  very  powerful  electromagnets,  M  and  N,  fixed  on  two  iron 


Fig.  872. 

supports,  O  O',  which  can  be  moved  on  a  support,  K.  The  current  from  a 
battery  of  10  or  n  Bunsen's  elements  passes  by  the  wire  A  to  the  commu- 
tator, H,  the  coil  M,  and  then  to  the  coil  N,  by  the  wire  g,  descends  in  the 
wire  z,  passes  again  to  the  commutator,  and  emerges  at  B.  The  two 
cylinders  of  soft  iron,  which  are  in  the  axis  of  the  coils,  are  perforated  by 
cylindrical  holes,  to  allow  the  luminous  rays  to  pass.  At  b  and  a  there  are 
two  Nicol's  prisms,  b  serving  as  polariser  and  a  as  analyser.  By  means  of 
a  limb  this  latter  is  turned  round  the  centre  of  a  graduated  circle,  P. 

The  two  prisms  being  then  placed  so  that  their  principal  sections  are 
perpendicular  to  each  other,  the  prism  a  completely  extinguishes  the  light 
transmitted  through  the  prism  b.  If  at  c,  on  the  axis  of  the  two  coils,  a  plate 
be  placed  with  parallel  faces,  either  of  ordinary  or  flint  glass,  light  is  still 


904  Dynamical  Electricity.  [935- 

extinguished  so  long  as  the  current  does  not  pass  ;  but  when  the  communi- 
cations are  established,  the  light  reappears.  It  is  now  coloured,  and  if  the 
analyser  be  turned  from  left  or  right,  according  to  the  direction  of  the  current, 
the  light  passes  through  the  different  tints  of  the  spectrum,  as  is  the  case  with 
plates  of  quartz  cut  perpendicularly  to  the  axis  (674).  Becquerel  showed 
that  a  large  number  of  substances  can  also  rotate  the  plane  of  polarisation 
under  the  influence  of  powerful  magnets.  Faraday  assumed  that  in  these 
experiments  the  rotation  of  the  plane  of  polarisation  was  due  to  an  action  of 
the  magnets  on  the  luminous  rays,  while  Biot  and  Becquerel  ascribed  the 
phenomena  to  a  molecular  action  of  the  magnet  on  the  transparent  bodies 
submitted  to  its  influence. 

936.  Photophone. — Mr.  Graham  Bell,  the  inventor  of  the  telephone, 
has  invented  an  apparatus  by  which  articulate  speech  can  be  transmitted  to 
a  considerable  distance  by  the  simple  agency  of  a  ray  of  light. 

The  essential  features  of  the  apparatus  are  represented  in  fig.  873,  in 
which  m  is  the  transmitter.  This  consists  of  a  wooden  box  closed  by  a  thin 
plate  of  microscope  glass  silvered  in  front,  which  acts  as  mirror;  in  the 
back  of  the  box  is  an  aperture  provided  with  a  flexible  tube  and  mouthpiece. 


Fig.  873. 

A  powerful  beam  of  solar  or  of  the  electrical  light  falls  against  a  large 
mirror,  ^,  and  is  reflected  by  it  on  a  lens,  b,  by  which  the  rays  are  concentrated 
on  the  mirror,  m,  of  the  transmitter.  An  alum  cell,  a,  is  sometimes  interposed, 
to  cut  off  the  influence  of  the  heating  rays. 

From  the  mirror  m  the  reflected  rays  pass  through  a  lens,  z,  by  which  they 
are  rendered  parallel,  and  fall  on  a  parabolic  mirror,  /,  at  the  distant  station. 
Here  they  are  concentrated  on  what  may  be  called  a  selenium  rheostate,  j, 
which  is  interposed  in  a  circuit  consisting  of  a  few  Leclanche'  cells  and  a 
telephone,  /. 

The  action  depends  on  the  alterations  in  the  resistance  of  selenium 
produced  by  the  action  of  light.  The  construction  of  the  rheostate  is  as 
follows  : — A  number  of  discs  of  thin  sheet  brass  are  taken,  separated  from 
each  other  by  thin  discs  of  mica  of  somewhat  smaller  diameter,  and,  the 
whole  having  been  tightly  screwed  together,  the  interstitial  spaces  are  filled 


-937J  Kerr's  Electro- optical  Experiments.  905 

witti  melted  selenium.  All  the  odd  numbers  of  brass  discs  are  in  metallic 
connection  with  each  other  and  with  one  pole  of  the  circuit,  and  all  the  even 
ones  are  also  in  metallic  connection  with  each  other,  and  with  the  other 
pole.  In  this  way  two  conditions  are  realised  ;  namely,  that  the  surface  of 
selenium  exposed  to  the  action  of  light  is  as  large,  and  its  resistance  as  small, 
as  possible. 

This  being  premised,  when  light  falls  on  the  plane  mirror  at  rest,  its  rays 
are  reflected  parallel  against  the  parabolic  mirror  by  which  they  are  con- 
centrated on  the  cell,  the  cylindrical  shape  being  well  adapted  for  this. 
But  if,  by  being  spoken  against,  the  transmitting  mirror  m  is  put  in  vibration, 
it  bulges  in  and  out — that  is,  becomes  convex  and  concave — and  the  rays  no 
longer  fall  parallel  on  the  parabolic  mirror  ;  they  diverge  or  converge — in 
other  words,  the  whole  of  the  light  is  no  longer  concentrated  on  the  selenium 
cell  ;  its  intensity  changes  at  every  instant,  and  these  variations  in  the  action 
of  the  light  produce  corresponding  variations  in  the  resistance  of  the  sele- 
nium, which  again  produce  corresponding  variations  in  the  strength  of  the 
current,  and  these  are  revealed  by  the  articulate  sounds  of  the  telephone. 

Mr.  Bell  has  found  that  a  great  number  of  substances  are  thrown  into 
vibration  by  the  intermittent  action  of  light,  as  we  have  seen  (4460.).  Lord 
Rayleigh's  calculations  show  that  there  is  no  reason  for  discarding  the  ex- 
planation that  the  sounds  in  question  are  due  to  the  bending  of  the  plates  in 
consequence  of  unequal  heating. 

937.  XLerr's  electro-optical  experiments. — Dr.  Kerrhas  discovered  a  re- 
markable relationship  between  electricity  and  light.  He  finds  that  when  certain 
dielectrics  are  subjected  to  a  state  of  electrical  strain,  they  develop  doubly 
refringent  properties  (639).  The  general  arrangement  of  the  experiments  is 
as  follows  :  a  cell,  P  (fig.  874),  is  suitably  constructed  of  stout  glass  plates, 
in  which  is  placed  the  liquid  under  examination ;  its  dimensions  are  4 
inches  in  length  by  I  inch  in  width,  and  about  |th  of  an  inch  in  thickness. 
Two  copper  plates  placed  horizontally,  and  kept  at  a  distance  of  about  -^ 
of  an  inch,  can  be  connected  with  the  poles  of  a  Holtz's  machine  (fig.  650), 
or,  what  is  more  convenient,  with  the  opposite  coatings  of  a  Leyden  jar, 
which  in  turn  is  worked  by  such  a  machine.  B  is  the  mirror  of  a  heliostat, 
by  which  a  beam  of  light  may  be  sent  in  any  direction.  M  and  N  are  two 
NicoPs  prisms  (660) ;  C  is  a  compensator,  while  D  is  a  condensing  lens. 


L 

*   r~ 

7-7      aLXL 

----^-'-^r- 

i  —  ^- 

Fig.  874. 

Of  the  two  Nicol's  prisms,  M  serves  as  polariser,  and  N  as  analyser  (656) ; 
at  the  outset  they  are  arranged  so  that  their  principal  sections  are  at  right 
angles  to  each  other,  and  make  an  angle  of  45°  with  the  vertical.  Thus  the 
light  polarised  by  the  prism  M  is  extinguished  by  the  analyser  N,  so  that 
the  field  between  them  is  quite  dark,  and  remains  so  even  when  the  cell  is 


906  Dynamical  Electricity.  [937- 

filled  with  liquid  ;  the  cell  is  so  arranged  that  the  observer  looks  through  the 
slit  of  dielectric  which  is  between  the  conductors  in  the  cell. 

If  now  the  plates  are  placed  in  opposite  electrical  conditions,  the  field  at 
once  becomes  clear.  Of  all  dielectrics  hitherto  examined,  carbon  bisulphide 
is  that  which  best  exhibits  the  phenomenon.  A  fraction  of  a  turn  of  a  Holtz's 
machine  is  at  once  sufficient  to  produce  light  in  the  field,  which  disappears 
immediately  the  plates  are  discharged.  As  the  machine  is  worked  and  the 
potential  rises,  the  light  between  the  conductors  gradually  increases  in  bright- 
ness until  a  pure  and  brilliant  white  is  obtained  ;  with  increase  of  potential 
a  fine  progression  of  chromatic  effects  is  obtained  ;  the  luminous  band 
between  the  conductors  changes  first  from  white  to  a  straw-colour,  which 
deepens  gradually  to  a  rich  yellow  ;  it  then  passes  through  orange  to  a  deep 
brown,  next  to  a  pure  and  dense  red,  through  purple  and  violet  to  a  rich  and 
full  blue,  and  then  to  green.  All  the  colours  are  beautifully  dense  and  pure, 
and  as  fine  as  anything  seen  in  experiments  with  crystals  in  the  polariscope. 
The  phenomenon  generally  ceases  at  the  green  of  the  second  order  with  a 
discharge  of  electric  sparks.  The  action  of  bisulphide  of  carbon  under 
electrical  strain  is  similar  to  that  of  glass  stretched  in  a  direction  parallel  to 
the  lines  of  force  ;  it  is  an  action  of  the  same  kind  as  that  of  a  uniaxial  bi- 
refringent  crystal  (640) ;  in  this  respect  carbon  bisulphide  occupies  a  place 
among  dielectrics  similar  to  that  of  Iceland  spar  among  crystals. 

In  order  to  measure  the  effect  produced,  a  compensator,  C,  is  placed 
behind  the  cell  ;  the  plates  are  connected  with  a  Thomson's  electrometer 
in  such  a  manner  that  the  potential  can  be  directly  measured,  and  then 
compared  simultaneously  with  the  difference  of  the  path  of  the  extraordinary 
and  ordinary  ray  in  the  dielectric.  Kerr  arrived  thus  at  the  law  :  '  the  strength 
of  the  electro-optical  action  of  a  given  dielectric,  that  is,  the  difference  in  the 
path  of  the  ordinary  and  extraordinary  rays,  for  unit  thickness  of  the  di- 
electric, varies  directly  as  the  square  of  the  resultant  electrical  force.' 

938.  Diamagnetism. — Coulomb  observed,  in  1802,  that  magnets  act  upon 
all  bodies  in  a  more  or  less  marked  degree  ;  this  action  was  at  first  attributed 
to  the  presence  of  ferruginous  particles.  Brugmann  also  found  that  certain 
bodies — for  instance,  bars  of  bismuth — when  suspended  between  the  poles  of 
a  powerful  magnet,  do  not  set  axially  between  the  poles,  that  is,  in  the  line 
joining  the  poles,  but  equatorially,  or  at  right  angles  to  that  line.  This 
phenomenon  was  explained  by  the  assumption  that  the  bodies  were 
transversely  magnetic.  Faraday  made  the  important  discovery  in  1845 
that  all  solids  and  liquids  which  he  examined  are  either  attracted  or  repelled 
by  a  powerful  electromagnet.  The  bodies  which  are  attracted  are  called 
magnetic  or  paramagnetic  substances,  and  those  which  are  repelled  are 
diamagnetic  bodies.  Among  the  metals,  iron,  nickel,  cobalt,  manganese, 
platinum,  cerium,  osmium,  and  palladium  are  magnetic ;  while  bismuth, 
antimony,  zinc,  tin,  mercury,  lead,  silver,  copper,  gold,  and  arsenic  are 
diamagnetic,  bismuth  being  the  most  so  and  arsenic  the  least.  The  diamag- 
netic effects  can  only  be  produced  by  means  of  very  powerful  magnets,  and 
it  is  by  means  of  Faraday's  apparatus  that  they  have  been  discovered  and 
studied.  In  experimenting  on  the  diamagnetic  effects — solids,  liquids,  and 
gases— armatures  of  soft  iron,  S  and  Q  (figs.  875-877),  of  different  shapes 
are  screwed  on  the  magnets. 


_938]  Diamagnetism.  907 

i.  Diamagnetism  of  solids.  If  a  small  cube  of  copper,  suspended  by  a 
fine  silk  thread  between  the  poles  of  the  magnet  (fig.  876),  be  in  rapid  rota- 
tion between  the  poles  of  an  electromagnet,  it  stops  the  moment  the  current 
passes  through  the  bobbins.  If  the  movable  piece  have  the  form  of  a  small 


Fig.  875. 


Fig.  876. 


Fig.  877. 


rectangular  bar  it  sets  equalorially,  or  at  right  angles  to  the  axis  of  the  bob- 
bins, if  it  is  a  diamagnetic  substance,  such  as  bismuth,  antimony,  or  copper  ; 
but  axially^  or  in  the  direction  of  the  axis,  if  it  is  a  magnetic  substance,  such 
as  iron,  nickel,  or  cobalt.  Besides  the  substances  enumerated  above,  the 
following  are  diamagnetic  :  rock  crystal,  alum,  glass,  phosphorus,  iodine, 
sulphur,  sugar,  bread  ;  and  the  following  are  magnetic  :  many  kinds  of 
paper  and  sealing-wax,  fluorspar,  graphite,  charcoal,  &c. 

ii.  Diamagnetism  of  liquids.  To  experiment  with  liquids,  very  thin  glass 
tubes  filled  with  the  substance  are  suspended  between  the  poles  instead  of 
the  cube  m  in  the  figure  876.  If  the  liquids  are  magnetic,  such  as  solutions 
of  iron  or  cobalt,  the  tubes  set  axially ;  if  diamagnetic,  like  water,  blood, 
milk,  alcohol,  ether,  oil  of  turpentine,  and  most  saline  solutions,  the  tubes  set 
equatorially.  Very  remarkable  changes  take  place  in  the  direction  of  mag- 
netic and  diamagnetic  substances  when  they  are  suspended  in  liquids.  A 
magnetic  substance  is  indifferent  in  an  equally  strong  magnetic  liquid  ;  it  sets 
equatorially  in  a  stronger  magnetic  substance,  and  axially  in  a  substance 
which  is  less  strongly  magnetic ;  it  sets  axially  in  all  diamagnetic  liquids. 

A  diamagnetic  substance  surrounded  by  a  magnetic  or  diamagnetic  sub- 
stance sets  equatorially.  According  to  its  composition  glass  is  sometimes 
magnetic  and  sometimes  diamagnetic,  and  as  glass  tubes  are  used  for  con- 
taining the  liquids  in  these  investigations,  its  deportment  must  first  be  deter- 
mined, and  then  taken  into  account  in  the  experiment. 

The  action  of  powerful  magnets  on  liquids  may  also  be  observed  in  the 
following  experiment  devised  by  Pliicker.  A  solution  of  a  magnetic  liquid 
is  placed  on  a  watch-glass  between  the  two  poles,  S  and  Q,  of  a  powerful 
electromagnet.  When  the  current  passes,  the  solution  forms  the  enlarge- 
ment represented  in  fig.  877  ;  this  continues  as  long  as  the  current  passes, 
and  is  produced  to  different  extents  with  all  magnetic  liquids.  The  changes 
in  the  aspects  of  the  liquids  are,  however,  so  small  as  to  require  careful 
scrutiny  to  detect  their  existence.  A  method  of  magnifying  these  changes 
so  as  to  render  them  visible  to  larger  audiences  was  devised  by  Prof. 
Barrett.  A  source  of  light  is  placed  above  the  watch-glass  containing  a  drop 


908  Dynamical  Electricity.  [938 

of  the  solution  to  be  tried.  Below  the  watch-glass,  and  between  the  legs  of 
the  magnet,  is  placed  a  mirror  at  an  angle  of  45°.  By  this  means  the  beam 
of  light  passing  through  the  watch-glass  is  reflected  at  right  angles  on  to  a 
screen,  where  an  image  of  the  drop  is  focussed  by  the  lens.  If  now  a  drop  of 
diamagnetic  liquid,  such  as  water,  or,  better,  sulphuric  acid,  be  placed  on  the 
watch-glass,  as  soon  as  the  current  passes,  the  flattened  drop  retreats  from 
the  two  poles,  and  gathers  itself  up  into  a  little  heap,  as  at  A  (fig.  877).  So 
doing,  it  forms  a  double  convex  lens,  by  which  the  light  is  brought  to  a  short 
focus  below  the  drop,  an  effect  instantly  seen  on  the  screen.  When  the  current 
is  interrupted  the  drop  falls,  and  the  light  returns  to  its  former  appearance. 
A  magnetic  liquid,  such  as  a  solution  of  perchloride  of  iron,  has  exactly  the 
opposite  effect.  The  drop  attracted  to  the  two  poles  becomes  flattened,  and 
instead  of  a  plano-convex  shape,  at  which  it  rests,  it  becomes  nearly  concavo- 
convex,  as  at  B.  The  light  is  dispersed,  and  the  effect  manifest  on  the  screen. 
Instead  of  a  mirror  and  lens,  a  sheet  of  white  paper  may  be  placed  in  an  in- 
clined position  under  the  watch-glass,  and  the  effects  are  somewhat  varied? 
but  equally  well-pronounced. 

iii.  Diamagnetism  of  gases.  Bancalari  observed  that  the  flame  of  a  candle 
placed  between  the  two  poles  in  Faraday's  apparatus  was  strongly  repelled 
(fig.  875).  All  flames  present  the  same  phenomenon  to  different  extents, 
resinous  flames  or  smoke  being  most  powerfully  affected. 

The  magnetic  deportment  of  gases  may  be  exhibited  for  lecture  purposes 
by  inflating  soap  bubbles  with  them  between  the  poles  of  the  electromagnet, 
and  projecting  on  them  either  the  lime  or  the  electric  light. 

Faraday  experimented  on  the  magnetic  or  diamagnetic  nature  of  gases. 
He  allowed  gas  mixed  with  a  small  quantity  of  a  visible  gas  or  vapour,  so 
as  to  render  it  perceptible,  to  ascend  between  the  two  poles  of  a  magnet, 
and  observed  their  deflections  from  the  vertical  line  in  the  axial  or  equatorial 
direction  ;  in  this  way  he  found  that  oxygen  was  least,  nitrogen  more,  and 
hydrogen  most  diamagnetic.  With  iodine  vapour,  produced  by  placing  a 
little  iodine  on  a  hot  plate  between  the  two  poles,  the  repulsion  is  strongly 
marked.  Becquerel  found  that  oxygen  is  the  most  strongly  magnetic  of  all 
gases,  and  that  a  cubic  yard  of  this  gas  condensed  would  act  on  a  magnetic 
needle  like  5-5  grains  of  iron.  Faraday  found  that  oxygen,  although  magnetic 
under  ordinary  circumstances,  became  diamagnetic  when  the  temperature 
was  much  raised,  and  that  the  magnetism  or  diamagnetism  of  a  substance 
depends  on  the  medium  in  which  it  is  placed.  A  substance,  for  instance, 
which  is  magnetic  in  vacuo  may  be  diamagnetic  in  air. 

In  the  crystallised  bodies  which  do  not  belong  to  the  regular  system,  the 
directions  in  which  the  magnetism  or  diamagnetism  of  a  body  is  most  easily 
excited  are  generally  related  to  the  crystallographic  axis  of  the  substance. 
The  optic  axis  of  the  uniaxial  crystals  sets  either  axially  or  equatorially  when 
a  crystal  is  suspended  between  the  poles  of  an  electromagnet.  Faraday  has 
assumed  from  this  the  existence  of  a  magneto-crystalline  force,  but  it  appears 
probable  from  Knoblauch's  researches  that  the  action  arises  from  an  unequal 
density  in  different  directions,  inasmuch  as  unequal  pressure  in  different 
directions  produces  the  same  result. 

According  to  Pliicker,  for  a  given  unit  of  magnetising  force,  the  specific 
magnetisms  developed  in  equal  weights  of  the  undermentioned  substances 


938]  Diamagnetism.  909 

are  represented  by  the  following  numbers,  those  bodies  with  the  minus  signs 
prefixed  being  diamagnetic  : — 

Iron         .  .  .  1,000,000  Nickel  oxide  .  .  287 

Cobalt      .  .  .  1,009,000  Water.         .  .  .  -25 

Nickel      .  .  .  465,800  Bismuth    .    .  :  ,1-  .  -23-6 

Iron  oxide  .  .  759  Phosphorus  .  .  - 13-1 

iv.  Detonation  produced  by  the  rtipture  of  a  current  under  the  influence 
of  a  powerful  electromagnet.  The  following  experiment  by  Ruhmkorft  is  a 
remarkable  effect  of  Faraday's  apparatus.  When  the  two  ends  of  a  stout  wire 
in  which  the  current  of  the  electromagnet  passes  are  placed  between  the  two 
poles  S  and  Q  of  fig.  875 — that  is  to  say,  when  the  current  is  closed  between 
S  and  O — this  closing  takes  place  without  a  spark  and  without  noise,  or 
merely  a  feeble  noise  and  a  spark.  But  when  the  two  ends  are  separated, 
and  the  current  is  hence  broken,  a  violent  noise  is  heard,  almost  as  strong  as 
the  report  of  a  pistol.  This  appears  to  be  the  extra  current,  the  intensity  of 
which  is  greatly  increased  by  the  influence  of  two  poles. 

The  repulsion  produced  in  a  diamagnetic  body  under  the  influence  of  a 
powerful  magnet  is  due  to  the  fact  that  the  magnet  develops  in  the  end 
nearest  to  it  like  polarity,  and  in  the  end  furthest  away  unlike  polarity  ;  a 
phenomenon  the  exact  opposite  of  that  of  iron. 

The  following  experiment,  which  is  due  to  Weber,  is  considered  to  prove 
that  diamagnetism  is  a  polar  force.  A  coil  was  placed  near  the  end  of  an 
electromagnet,  its  axis  being  in  the  prolongation  of  the  axis  of  the  magnet, 
and  its  ends  being  connected  with  a  sensitive  galvanometer.  When  a  bar 
of  bismuth  was  suddenly  introduced  and  removed  from  the  coil,  induction 
currents  were  produced  in  the  circuit,  the  direction  of  which,  as  shown  by 
the  galvanometer,  was  the  exact  opposite  of  those  which  iron  would  have 
produced  under  the  same  circumstances. 


9io 


Dynamical  Electricity. 


[939- 


CHAPTER   VIII. 

THERMO-ELECTRIC  CURRENT. 


1  939.  Thermo-electricity. — In  1821,  Professor  Seebeck,  of  Berlin,  found 
that  by  heating  one  of  the  junctions  of  a  metallic  circuit,  consisting  of  two 
metals  soldered  together,  an  electric  current  was  produced.  This  pheno- 
menon may  be  shown  by  means  of  the  apparatus  represented  in  fig.  878, 

which  consists  of  a  plate 
of  copper,  mn,  the  ends 
of  which  are  bent  and 
soldered  to  a  plate  of  bis- 
muth, op.  Inside  the  cir- 
cuit is  a  magnetic  needle, 
a,  moving  on  a  pivot. 
When  the  apparatus  is 
placed  in  the  magnetic 
meridian,  and  one  of  the 
solderings  gently  heated, 
as  shown  in  the  figure, 
the  needle  is  deflected  in 
Fig.  878.  a  manner  which  indicates 

the  passage  of  a  current 

from  n  to  m,  that  is,  from  the  heated  to  the  cool  junction  in  the  copper.  If, 
instead  of  heating  the  junction  n,  it  is  cooled  by  ice,  or  by  placing  upon  it 
cotton  wool  moistened  with  ether,  the  other  junction  remaining  at  the  ordi- 
nary temperature,  a  current  is  produced,  but  in  the  opposite  direction,  that 
is  to  say,  from  m  to  n  ;  in  both  cases  the  current  is  in  general  stronger  in 
proportion  as  the  difference  in  temperature  of  the  solderings  is  greater. 

Seebeck  gave  the  name  thermo-electric  to  this  current,  and  to  the  couple 
which  produces  it,  to  distinguish  it  from  the  hydro-electric  or  ordinary  voltaic 
current  and  couple. 

940.  Thermo-electric  series. — If  small  bars  of  two  different  metals  are 
soldered  together  at  one  end  while  the  free  ends  are  connected  with  the 
wires  of  a  galvanometer,  and  if  now  the  point  of  junction  of  the  two  metals 
be  heated,  a  current  is  produced,  the  direction  of  which  is  indicated  by  the 
deflection  of  the  needle  of  the  galvanometer.  Moreover,  the  strength  of  the 
current,  calculated  from  the  deflection  of  the  galvanometer,  is  proportional 
to  the  electromotive  force  of  the  thermo-element.  By  experimenting  in  this 
way  with  different  metals,  they  may  be  formed  in  a  list  such  that  each  metal 
gives  rise  to  positive  electricity  when  associated  with  one  of  the  following, 
and  negative  electricity  with  one  of  those  that  precede  :— that  is,  that,  in 
heating  the  soldering,  the  positive  current  goes  from  the  positive  to  the  nega- 


-940]  Thermo-electric  Series.  911 

tive  metal  across  the  soldering,  just  as  if  the  soldering  represented  the  liquid 
in  a  hydro-electrical  element ;  hence  out  of  the  element— in  the  connecting 
wire  and  the  galvanometer,  for  instance — the  current  goes  from  the  negative 
to  the  positive  metal. 

Thus  a  couple,  bismuth-antimony,  heated  at  the  junction  would  corre- 
spond to  a  couple,  zinc-copper,  immersed  in  sulphuric  acid.  The  following 
is  a  list  drawn  up  from  Matthiessen's  researches,  which  also  gives  compara- 
tive numerical  values  for  the  electromotive  force  : — 

Bismuth       .         .         .  +25  Gas  coke    .         .'.._.      -o-i 

Cobalt          ...  9  Zinc    .....  0-2 

Potassium    .        .        .  S'S  Cadmium   .        .        ;;  0-3 

Nickel.         ...  5  Strontium  .         .J        .  '  2*0 

Sodium         ...  3  Arsenic       .         .  3-8 

Lead    .         .         .         .  1-03  Iron    .              'J  .'-       .  5-2 

Tin       ....  i  Red  Phosphorus         .  9*6 

Copper.         ...  i  Antimony   ...  9-8 

Silver    .      ><*"?*";'•';•     ro  Tellurium  .         .         .  179-9 

Platinum       .    .  Vr,    .  07  Selenium     .         .         .      -290-0 

Such  a  list  represents  what  is  called  a  thermo-electric  series,  and  the 
meaning  of  the  numbers  in  this  series  is  that,  taking  the  electromotive 
force  of  the  copper-silver  couple  as  unity,  the  electromotive  force  of  any  pair 
of  metals  is  expressed  by  the  difference  of  the  numbers  where  the  signs  are 
the  same  and  by  the  sum  where  the  signs  are  different.  Thus  the  electro- 
motive force  of  a  bismuth-nickel  couple  would  be  25  —  5  =  20  ;  of  a  cobalt- 
iron  9-(  — 5-2)  =  14-2,  and  of  an  iron-antimony- 5-2  — 9-8  = —4-6.  Where 
the  positive  sign  is  affixed,  the  current  is  from  the  other  metal  to  silver  across 
the  soldering  ;  and  where  the  negative,  from  silver  to  that  metal. 

It  will  be  observed  how  great  is  the  electromotive  force  of  the  highly  crys- 
talline metals.  Alloys  are  not  always  intermediate  to  the  metals  of  which 
they  are  composed,  and,  therefore,  the  position  of  the  metals  is  greatly 
affected  by  slight  admixtures.  The  thermo-electric  behaviour  of  substances 
is  greatly  affected  by  hardness,  direction  of  crystallisation,  and  so  forth,  and 
to  this  is  no  doubt  due  many  of  the  discrepancies  in  the  lists  given  by  different 
observers. 

Of  all  the  bodies  mentioned  in  the  above  series,  bismuth  and  selenium 
produce  the  greatest  electromotive  force  ;  but  from  the  expense  of  this 
latter  element,  and  on  account  of  its  low  conducting  power  and  the  difficulty 
of  making  good  joints,  antimony  is  generally  substituted.  The  antimony  is 
the  negative  metal  but  the  positive  pole,  and  the  bismuth  the  positive  metal 
but  the  negative  pole,  and  the  current  goes  from  bismuth  to  antimony  across 
the  junction. 

If  copper  wires  connected  with  the  ends  of  a  galvanometer  are  soldered 
together  to  the  ends  of  an  antimony  rod,  and  if  one  of  the  junctions  is  heated 
to  50°,  the  other  being  maintained  at  o°,  a  certain  deflection  is  observed  in 
the  galvanometer.  If,  similarly,  a  compound  bar,  consisting  of  antimony  and 
tin  soldered  together,  be  connected  with  the  ends  of  the  galvanometer,  and  if 
the  junction  copper-tin  as  well  as  the  junction  tin-antimony  be  heated  to  50°, 
while  the  junction  antimony-copper  is  kept  at  o°,  the  deflection  is  the  same 


912  Dynamical  Electricity.  [940- 

as  in  the  previous  case.  Hence  the  electromotive  force  produced  by  heating 
the  two  junctions,  copper-tin  and  tin-antimony,  is  equal  to  the  electromotive 
force  produced  by  heating  the  copper-antimony  ;  and,  generally,  if  a  metal,  <£, 
is  associated  with  a  metal,  a,  which  is  above  it  in  the  list,  and  in  like  manner 
if  b  is  associated  with  c,  which  is  below  it  in  the  list,  then  the  electromotive 
force  produced  by  heating  the  combination  ac  is  equal  to  the  sum  of  the 
electromotive  forces  produced  by  heating  ab  and  be  separately. 

If  the  two  junctions  of  a  given  couple  be  heated  to  the  temperatures  t 
and  8,  and  then  to  6  and  /',  respectively,  the  electromotive  force  produced  by 
heating  the  junctions  to  the  temperatures,  t  and  /',  is  equal  to  the  sum  of  the 
electromotive  forces  produced  in  the  other  two  cases  ;  that  is,  that  for  small 
intervals  the  electromotive  force  is  directly  proportional  to  the  temperature. 

With  greater  ranges  this  no  longer  holds  ;  as  the  temperature  increases 
the  differences  of  potential  gradually  diminish,  and  at  a  certain  temperature 
of  the  hot  junction  no  current  is  produced  ;  this  temperature  is  called  the 
neutral  temperature.  In  the  case  of  a  silver-iron  couple  this  is  when  one 
junction  is  at  o°,  the  other  is  at  223° ;  in  the  case  of  copper-iron,  it  is  when 
the  hot  junction  is  at  276°. 

When  the  couple  is  heated  beyond  the  neutral  temperature,  the  pheno- 
menon of  inversion  now  takes  place — that  is,  the  direction  of  the  current 
changes.  Thus,  with  iron-copper,  whereas  below  276°  copper  is  positive  to 
iron,  above  that  temperature  iron  is  positive  to  copper. 

There  is  another  general  case  in  which  no  current  is  produced  by  heating 
the  two  junctions,  and  that  is  whenever  the  arithmetical  mean  of  the  tempe- 
ratures of  the  junction  is  equal  to  this  neutral  temperature.  Thus,  for  silver 
and  iron  this  temperature  is  228*5°,  an(^  no  current'  is  produced  when  the 
temperature,  /,  of  the  one  is  186,  145,  and  118,  the  corresponding  one  of  the 
other  being  260,  302,  and  328.  If  the  mean  temperature  in  one  case  is  above 
and  in  another  below,  the  current  has  different  directions  in  the  two  cases  ; 
thence  the  electromotive  force  cannot  always  be  increased  by  raising  the 
temperature  of  one  or  lowering  the  temperature  of  another. 

As  compared  with  ordinary  hydro-electric  currents,  the  electromotive 
force  of  thermo  currents  is  very  small  ;  thus  the  electromotive  force  of  a 
bismuth-copper  element  with  a  difference  of  100°  C.  in  the  temperatures  of 
their  junctions  is  according  to  Wheatstone  i,  and  according  to  Neumann 
2!  g  that  of  a  Daniell's  element :  the  electromotive  force  of  an  iron-argentan 
couple  with  10°  to  15°  difference  of  temperature  at  their  junctions  is  ^^o  that 
of  a  Daniell's,  according  to"  Kohlrausch. 

941.  Causes  of  thermo-electric  currents. — Thermo-electric  currents 
are  probably  to  be  attributed  to  an  electromotive  force  produced  by  the  con- 
tact of  heterogeneous  substances,  a  force  which  varies  with  the  temperature. 
Becquerel  ascribed  them  to  the  unequal  propagation  of  heat  in  the  different 
parts  of  the  circuit.  He  found  that  when  all  the  parts  of  a  circuit  are  homo- 
geneous, no  current  is  produced  on  heating,  because  the  heat  is  equally 
propagated  in  all  directions.  This  is  the  case  if  the  wires  of  the  galvano- 
meter are  connected  by  a  second  copper  wire.  But  if  the  uniformity  of  this 
is  destroyed  by  coiling  it  in  a  spiral,  or  by  knotting  it,  the  needle  indicates 
by  its  deflection  a  current  going  from  the  heated  part  to  that  in  which  the 
homogeneity  has  been  destroyed.  If  the  ends  of  the  galvanometer  wires  be 


-942] 


Thermo-electric  Battery. 


913 


coiled  in  a  spiral,  and  one  end  heated  and  touched  with  the  other,  the 
current  goes  from  the  heated  to  the  cooled  end. 

When  two  plates  of  the  same  metal,  but  at  different  temperatures,  are 
placed  in  a  fused  salt  such  as  borax,  which  conducts  electricity  but 
exerts  no  chemical  action,  a  current  passes  from  the  hotter  metal  through 
the  fused  salt  to  the  colder  one.  Hot  and 
cold  water  in  contact  produce  a  current 
which  goes  from  the  warm  water  to  the 
cold. 

Svanberg  has  found  that  the  thermo- 
electromotive  force  is  influenced  by  the 
crystallisation  ;  for  instance,  if  the  cleavage 
of  bismuth  is  parallel  to  the  face  of  contact, 
it  is  greater  than  if  both  are  at  right  angles, 
and  that  the  reverse  is  the  case  with  anti- 
mony. Thermo-electric  elements  may  be 
constructed  of  either  two  pieces  of  bismuth 
or  two  pieces  of  antimony,  if  in  the  one 
the  principal  cleavage  is  parallel  to  the 
place  of  contact,  and  in  the  other  is  at  right 
angles.  Hence  the  position  of  metals  in  thermo-electric  series  is  influenced 
by  their  crystalline  structure. 

Many  crystallised  minerals  have  great  electromotive  force  when  heated 
with  metals  or  with  each  other.  Thus  the  combination  copper  pyrites — 
copper  when  heated  in  a  spirit  lamp  has  an  electromotive  force  of  0-12,  and 
copper  pyrites — iron  pyrites  of  o-i8  of  a  volt. 

942.  Thermo-electric  battery. — From  what  has  been  said  it  will  be 
understood  that  a  thermo-electric  couple  consists  of  two  metals  soldered 
together,  the  two  ends  of  which  can  be  joined  by  a  conductor.  Fig.  879 


Fig.  879. 


Fig.  880. 

represents  a  bismuth-copper  couple  ;  fig.  880  represents  a  series  of  couples 
used  by  Pouillet.  The  former  consists  of  a  bar  of  bismuth  bent  twice  at 
right  angles,  at  the  ends  of  which  are  soldered  two  copper  strips,  £,  d,  which 
terminate  in  two  binding  screws  fixed  on  some  insulating  material. 

When  several  of  these  couples  are  joined  so  that  the  second  copper  of 

3N 


9 1 4  Dynam ical  Electricity.  [9  42- 

the  first  is  soldered  to  the  bismuth  of  the  second,  then  the  second  copper  of 
this  to  the  bismuth  of  the  third,  and  so  on,  this  arrangement  constitutes  a 
thermo-electric  battery,  which  is  worked  by  keeping  the  odd  solderings,  for 
'instance,  in  ice,  and  the  even  ones  in  water,  which  is  heated  to  100°. 

943.  Nobili's  thermo-electric  pile. — Nobili  devised  a  form  of  thermo- 
electric battery,  or  pile,  as  it  is  usually  termed,  in  which  there  are  a  large 
number  of  elements  in  a  very  small  space.  For  this  purpose  he  joined  the 
couples  of  bismuth  and  antimony  in  such  a  manner  that,  after  having  formed 
a  series  of  five  couples,  as  represented  in  fig.  882,  the  bismuth  from  b  was 
soldered  to  the  antimony  of  a  second  series  arranged  similarly  ;  the  last 
bismuth  of  this  to  the  antimony  of  a  third,  and  so  on  for  four  vertical 
series,  containing  together  20  couples,  commencing  by  antimony,  finishing 
by  bismuth. 

Thus  arranged,  the  couples  are  insulated  from  one  another  by  means 
of  small  paper  bands  covered  with  varnish,  and  are  then  enclosed  in  a 
copper  frame,  P  (fig.  88 1)  so  that  only  the  solderings  appear  at  the  two 
ends  of  the  pile.  Two  small  copper  binding  screws,  m  and  «,  insulated 

in  an  ivory  ring,  communicate  in  the 
interior,  one  with  the  first  antimony, 
representing  the  positive  pole,  and 
the  other  with  the  last  bismuth,  repre- 
senting the  negative  pole.  These 
binding  screws  communicate  with  the 
extremities  of  a  galvanometer  wire 
when  the  thermo-electric  current  is  to 
be  observed. 

944.  Becquerel's  thermo-electric 
battery. — Becquerel  has  found  that 
artificial  sulphuret  of  copper  heated  from  200°  to  300°  is  powerfully  positive, 
and^that  a  couple  of  this  substance  and  copper  has  an  electromotive  force 
nearly  ten  times  as  great  as  that  of  the  bismuth  and  copper  couple  in  fig.  879. 


Fig.  883. 

Native  sulphuret,  on  the  contrary,  is  powerfully  negative.  As  the  artificial 
sulphuret. only  melts  at  about  1,035°,  it  may  be  used  at  very  high  tempera- 
tures. The  metal  joined  with  it  is  German  silver  (90  of  copper  and  10  of 


-945] 


C lament? s  Thermo-electric  Battery, 


915 


nickel).  Fig.  883  represents  the  arrangement  of  a  battery  of  50  couples 
arranged  in  two  series  of  25.  Fig.  885  gives  on  a  larger  scale  the  view  of  a 
single  couple,  and  fig.  884  that  of  6  couples  in  two  series  of  3.  The  sulphurct 
is  cut  in  the  form  of  rectangular  prisms,  10  centimetres  in  length,  by  18  mm. 
in  breadth,  and  12  mm.  thick.  In  front  is  a  plate  of  German  silver,  m,  intended 
to  protect  the  sulphuret  from  roasting  when  it  is  placed  in  a  gas  flame. 
Below  there  is  a  plate  of  German  silver  MM,  which  is  bent  several  times  so 


Fig.  884. 


as  to  be  joined  to  the  sulphuret  of  the  next,  and  so  on.  The  couples,  thus 
arranged  in  two  series  of  25,  are  fixed  to  a  wooden  frame  supported  by  two 
brass  columns,  A,  B,  on  which  it  can  be  more  or  less  raised.  Below  the  couples 
is  a  brass  trough,  through  which  water  is  constantly  flowing,  arriving  by 
the  tube  b  and  emerging  by  the  stopcock  r.  The  plates  of  German  silver 
are  thus  kept  at  a  constant  temperature.  On  each  side  of  the  trough  are  two 
long  burners  on  the  Argand  principle,  fed  by  gas  from  a  caoutchouc  tube,  a. 
The  frame.  being  sufficiently  lowered,  the  ends  are  kept  at  a  temperature  of 
200°  or  300°.  For  utilising  the  current,  two  binding  screws  are  placed  on 
the  left  of  the  frame,  one  communicating  with  the  first  sulphuret,  that  is,  the 
positive  pole,  and  the  other  with  the  last  German  silver,  or  the  negative  pole. 
At  the  other  end  of  the  frame  are  two  binding  screws,  which  facilitate  the 
arrangement  of  the  couples  in  different  ways. 

945.  ciamond's  thermo-electric  battery.  —  Of  the  attempts  which  have 
been  made  to  apply  thermo-electric  currents  to  directly  practical  purposes 
perhaps  the  most  successful  has  been  Ciamond's,  which  has  been  used 
both  for  telegraphic  purposes  and  also  for  electroplating.  Its  characteristic 
features  are  the  construction  and  arrangement  of  the  elements,  and  the 
manner  in  which  the  heating  is  effected. 

The  negative  element  consists  of  an  alloy  of  two  parts  of  antimony  and 
•one  of  zinc,  forming  a  flat  spindle-shaped  bar  from  2  to  3  inches  in  length,  by 
|  in.  in  thickness  (fig.  887).  The  positive  metal  is  a  thin  strip  or  lug  of  tin- 
plate,  stamped  as  represented  at  a  a'  in  fig.  886  ;  this  is  then  bent  in  as  shown 
at  c,  and  being  held  in  a  mould,  the  alloy,  which  melts  as  260°  C.,  is  poured 
in.  The  individual  elements  have  then  the  appearance  represented  in  fig. 
887,  and  to  connect  them  together  the  tin  lugs  are  bent  into  shape,  and  joined 
in  a  circle  of  elements  (fig.  888),  being  kept  in  their  position  by  a  paste  of 
asbestos  and  soluble  glass  ;  flat  rings  of  this  composition  are  also  made, 
-and  are  placed  between  each  series  of  rings  piled  over  each  other  ;  the  con- 

3  N  2 


916 


Dynamical  Electricity. 


[945- 


nection  between  the  individual  elements  and  between  the  sets  of  rings  is 
made  by  soldering  together  the  projecting  ends  of  the  tin  lugs.     Thin  plates 
of  mica  are  placed  between  the  alloy  and  the  tin  plate,  excepting  at  the 
place  of  soldering.     Looked  at  from  the  inside 
the  faces  of  the  battery  present  the  appearance 
of  a  perfect  cylinder. 

The  heating  is  effected  by  means  of  coal 
gas,  admitted  through  an  earthenware  tube, 
AB,  fig.  889,  perforated  by  numerous  small 
holes  ;  this  is  surrounded  by  a  somewhat  larger 
iron  tube,  C  D,  reaching  nearly  to  the  top  of  the 
cylinder,  which  is  closed  by  a  lid,  E  F.  Air 
enters  at  the  bottom  of  this  tube,  and  the  heated  gases,  passing  up  the  tube, 
curl  over  the  top,  descend  on  the  outside,  and  escape  by  a  chimney,  G  H.  This 


Fig.  886. 


Fig.  889. 

arrangement  economises  gas  and  prevents  danger  from  overheating,  as  the 
gas-jets  do  not  impinge  directly  on  the  element.  The  supply  of  gas  is 
regulated  by  an  automatic  arrangement,  so  that  the  temperature  is  not 
higher  than  about  200°. 

A  battery  of  60  such  elements  has  an  electro-motive  force  of  three  volts, 
and  an  internal  resistance  of  i|  ohms.  The  amount  of  the  gas  consumed 
per  hour  for  this  size  is  three  cubic  feet,  and  such  a  battery  costs  four 
pounds. 

946.  iwelloni's  therm  ©multiplier. — We  have  already  noticed  the  use 
which  Melloni  made  of  Nobili's  pile,  in  conjunction  with  the  galvano- 
meter, for  measuring  the  most  feeble  alterations  of  temperature.  The 
arrangement  he  used  for  his  experiment  is  represented  in  fig.  890. 

On  a  wooden  base,  provided  with  levelling  screws,  a  graduated  copper 
rule,  about  a  metre  long,  is  fixed  edgeways.  On  this  rule  the  various  parts 
composing  the  apparatus  are  placed,  and  their  distance  can  be  fixed  by 


-947J  Me  Horn's  Thennomultiplier.  917 

means  of  binding  screws,  a  is  a  support  for  a  Locatelli's  lamp,  or  other  source 
of  heat ;  F  and  E  are  screens  ;  C  is  a  support  for  the  bodies  under  experi- 
ment, and  in  is  a  thermo-electrical  battery.  Near  the  apparatus  is  a  gal- 
vanometer, D  ;  this  has  only  a  comparatively  few  turns  of  a  tolerably  thick 
(i  mm.)  copper  wire  ;  for  the  electromotive  force  of  the  thermo-currents  is 


Fig.  890. 

small,  ?and  as  the  internal  resistance  is  small  too,  for  it  only  consists  of  metal, 
it  is  clear  that  no  great  resistance  can  be  introduced  into  the  circuit  if  the 
current  is  not  to  be  completely  stopped.  Such  galvanometers  are  called 
ther mo  multipliers.  The  delicacy  of  this  apparatus  is  so  great  that  the  heat 
of  the  hand  is  enough,  at  a  distance  of  a  yard  from  the  pile,  to  deflect  the 
needle  of  the  galvanometer. 

In  using  it  for  measuring  temperature,  the  relation  of  the  deflection  of  the 
needle,  and  therefore  of  the  strength  of  the  current,  to  the  difference  of  the 
temperatures  of  the  two  ends  must  be  determined.  That  known,  the  tem- 
peratures of  the  ends  not  exposed  to  the  source  of  heat  being  known,  the 
observed  deflection  gives  the  temperature  of  the  other,  and  therewith  the 
intensity  of  the  source  of  heat. 

947.  Properties  and  uses  of  thermo-electric  currents. — Thermo-elec- 
tric currents  are  of  extremely  low  potential,  but  of  great  constancy :  for  their 
opposite  junctions,  by  means  of  melting  ice  and  boiling  water,  can  easily  be 
kept  at  o°  and  100°  C.  On  this  account,  Ohm  used  them  in  the  experimental 
establishment  of  his  law.  They  can  produce  all  the  actions  of  the  ordinary 
battery  in  kind,  though  in  less  degree.  By  means  of  a  thermo-electrical  pile 
consisting  of  769  elements  of  iron  and  German  silver,  the  ends  of  which 
differed  in  temperature  by  about  10°  to  15°,  Kohlrausch  proved  the  presence 
of  free  positive  and  negative  electricity  at  the  two  ends  of  the  open  pile 
respectively.  He  found  that  the  potential  of  the  free  electricity  was  nearly 
proportional  to  the  number  of  elements,  and  also  that  the  electromotive  force 
of  a  single  element  under  the  above  circumstances  was  about  ^^  that  of  a 
single  DanielPs  element.  On  account  of  their  low  potential,  thermo-electric 
piles  produce'only  feeble  chemical  actions.  Botto,  however,  with  1 20  platinum 
and  iron  wires,  has  decomposed  water. 


i8 


Dynamical  Electricity. 


[948- 


948.  Thermo-electric  diagram. — Thermo-electric  relations  may  be  very 
conveniently  illustrated  by  means  of  what  is  called  the  thermo-electric  dia- 
gram. In  fig.  891  the  abscissae  represent  the  temperatures  of  the  junctions 
on  the  centigrade  scale.  If,  now,  the  thermo-electric  deportment  of  any 
metal  with  another,  taken  as  standard,  be  determined  for  any  given  tempe- 
rature, the  corresponding  differences  of  potential  are  represented  by  an 
ordinate  according  to  a  definite  scale.  In  the  diagram  the  ordinates  repre- 
sent microvolts  (964),  and  lead  is  taken  as  standard.  A  line  which  connects 
the  ordinates  thus  determined  is  called  a  thermo-electric  line  ;  the  lines  are 
here  represented  as  straight,  though  some,  such  as  iron  and  nickel,  present 
distinct  sinuosities  and  may  thus  cross  the  straight  line  belonging  to  another 
metal  more  than  once,  indicating  therefore  more  than  one  neutral  temperature. 

It  will  be  seen  that,  if  we  know  the  differences  of  potential  of  any  two 
metals  in  respect  of  lead,  the  thermo-electrical  lines  give  us  the  differences 
of  potential  of  these  two  metals  directly.  If,  for  example,  for  the  metals 
copper  and  iron  the  junctions  are  heated  to  o°  and  100°  respectively,  the 
mean  temperature  is  50°,  and  the  difference  of  the  two  ordinates  y  y',  gives 
the  thermo-electric  force  of  the  combination  for  this  mean  temperature,  the 
metal  at  the  top,  copper,  being  electropositive  ;  the  area  x  o-  1 5  xf  represents 


Pis?.  891. 

the  total  thermo-electric  force  in  the  circuit.  If  the  temperatures  of  the  two 
junctions  were  300°  and  500°,  the  mean  temperature  will  now  be  400°,  and 
the  difference,  y  y',  would  represent  the  thermo-electric  force,  which  in  this 
case  would  be  from  iron  to  copper  ;  that  is,  iron  is  now  electropositive 
to  copper. 

The  point  n  where  two  lines  cross  one  another,  and  where,  therefore,  there 
is  no  electromotive  force,  represents  the  neutral  temperature,  or  temperature 
of  inversion  (940)  ;  for  copper-iron  this  is  at  276°,  for  iron-cadmium  it  is  at  140°. 


-949] 


Becquerers  Electric  Pyrometer. 


919 


949.  Becquerel's  electric  pyrometer. — This  apparatus  is  an  improved 
form  of  one  originally  devised  by  Pouillet.  It  consists  (fig.  892)  of  two  wires, 
one  of  platinum  and  the  other  of  palladium,  both  two  metres  in  length  and 
a  square  millimetre  in  section.  They  are  not  soldered  at  the  ends,  but  firmly 
tied  for  a  distance  of  a  centimetre  with  fine  platinum  wire.  The  palladium 
wire  is  enclosed  in  a  thin  porcelain  tube  ;  the  platinum  wire  is  on  the  outside, 
and  the  whole  is  enclosed  in  a  larger  porcelain  tube,  P.  At  the  end  of  this 
is  the  junction,  which  is  adjusted  in  the  place  the  temperature  of  which  is  to 
be  investigated.  At  the  other  end  project  the  platinum  and  palladium  wires 


Fig.  892. 

m  and  n,  which  are  soldered  to  two  copper  wires  that  lead  the  current  to  a 
magnetometer,  G.  These  wires  at  the  junction  are  placed  in  a  glass  tube 
immersed  in  ice,  so  that,  being  both  at  the  same  temperature,  they  give  rise 
to  no  current. 

The  magnetometer,  which  was  devised  by  Weber,  is  in  effect  a  large 
galvanometer.  It  consists  of  a  magnetised  bar,  a  b,  placed  in  the  centre  of 
a  copper  frame,  which  deadens  the  oscillations  (904)  and  rests  on  a  stirrup, 
H,  which  in  turn  is  suspended  to  a  long  and  very  fine  platinum  wire.  On 
the  stirrup  is  fixed  a  mirror,  M,  which  moves  with  the  magnet,  and  gives 


920  Dynamical  Electricity.  [949- 

by  reflection  the  image  of  divisions  traced  on  a  horizontal  scale,  E,  at  a 
distance.  These  divisions  are  observed  by  a  telescope.  With  this  view, 
before  the  current  passes  the  image  of  the  zero  of  the  scale  is  made  to  coin- 
cide with  the  micrometer  wire  of  the  telescope  :  then  the  slightest  deflection 
of  the  mirror  gives  the  image  of  another  division,  and  therefore  the  angular 
deflection  of  the  bar  (522).  This  angle  is  always  small,  and  should  not 
exceed  3  or  4  degrees  :  this  is  effected  by  placing,  if  necessary,  a  rheostat  or 
any  resistance  coil  in  the  circuit.  The  angular  deflection  being  known,  the 
intensity  of  the  current  and  the  temperature  of  the  junction  are  deduced 
from  pyrometric  tables.  These  are  constructed  by  interpolation  when  the 
strengths  are  known  which  correspond  to  two  temperatures  near  those  to  be 
observed.  The  indications  of  the  pyrometer  extend  to  the  fusing  point  of 
palladium. 

950.  Peltier's  experiment. — When  on  a  bar  of  bismuth,  B  B',  cut  half- 
way through  at  its  centre  (fig.  893),  is  soldered  a  bar  of  antimony  with  a 
similar  cut,  and  when  the  ends  A  and  B  are  connected  with  a  galvanometer, 
the  needle  of  the  galvanometer  is  deflected  in  one  direction  when  the  junction 
is  heated,  and  in  the  other  when  it  is  cooled. 

Peltier  found  by  means  of  this  apparatus,  which  is  known  as  Peltiers 
cross,  that  when  the  end  A'  was  connected  with  one  pole,  and  B'  with  the 
other  pole  of  a  voltaic  element,  so  that  a  current  passed  from  A'  through  the 
junction  to  B',  the  needle  was  deflected  in  such  a  direction  as  to  show  that 
the  junction  was  heated  when  the  positive  current  passed  from  A'  to  B', 
while  it  was  cooled  when  the  current  passed  in  the  opposite  direction. 
This  is  called  the  Peltier  effect.  In  order  to  show  the  cooling  effect,  this 
experiment  may  be  made  by  hermetically  fixing  in  two  tubulures  in  an  air 
thermometer  a  compound  bar  consisting  of  bismuth 
and  antimony  soldered  together,  in  such  a  manner 
that  the  ends  project  on  each  side.  The  projecting 
parts  are  provided  with  binding  screws,  so  as  to  allow 
a  current  to  be  passed  through.  When  the  positive 
current  passes  from  the  antimony  to  the  bismuth,  the 
air  in  the  bulb  is  heated,  it  expands,  and  the  liquid  in 
the  stem  sinks  ;  but  if  it  passes  in  the  opposite  direc- 
tion the  air  is  cooled,  it  contracts,  and  the  liquid  rises  in  the  stem.  The 
current  must  not  be  too  strong  ;  that  of  a  single  Bunsen's  cell  is  usually 
sufficient  ;  it  is  best  regulated  by  a  rheostat  (949). 

By  making  a  small  hole  at  the  junction  of  a  bismuth  and  antimony  bar,  in 
which  was  placed  a  drop  of  water  and  a  small  thermometer,  the  whole  being 
cooled  to  zero,  Lenz  found  that  when  a  current  was  passed  from  bismuth 
to  antimony  the  water  was  frozen  and  the  thermometer  sank  to  35°C. 

The  Peltier  effect  is  independent  of  the  heating  produced  when  a  current 
traverses  any  conductor,  and  which  may  be  called  the  frictional  heating  or 
Joule  effect.  The  heat  due  to  this  cause  is  proportional  to  the  square  of  the 
current,  to  the  resistance,  and  to  the  time,  /,  and  is  independent  of  the  direction 
of  the  current  (830)  ;  while  the  Peltier  effect  is  proportional  to  the  strength  of 
the  current  and  to  the  time,  and  is  reversible  with  its  direction.  This  suggests 
a  method  of  determining  the  effect  in  question.  If  this  be  called  Jj,  the  heat 
due  to  it  will  be  JiC/,  and  that  due  to  the  frictional  heating  will  be  C2R/. 


-950] 


Peltier's  Experiment. 


92  r 


Hence  if  the  current  be  passed  so  that  in  one  case  the  Peltier  effect  coincides 
with  the  Joule  effect,  while  in  the  other  it  is  opposed  to  that  effect,  we  shall 
have  for  the  total  heat  H  and  H'  in  the  two  cases  ;  H  =  C2R/+  $C/,  and 
H'  =  C2R/-  /aC/,  from  which 


H-H 


That  the  Peltier  effect  is  independent  of  the  Joule  heating  has  been  in- 
vestigated by  Edlund,  by  a  method  the  principle  of  which  is  represented  in 
fig.  894.  M  and  N  are  two  bulbs,  B 

and  are  connected  by  a  narrow  glass 
tube,  in  which  is  a  drop  of  liquid 
serving  as  index.  The  rods  of  metal 
A  and  B  are  fixed  airtight  in  the  bulbs, 
and  are  soldered  at  m  and  ?/,  while  M 
the  free  ends  can  be  connected 
with  a  battery.  If  the  pieces  m 
and  n  inside  the  glass  vessels 
offer  the  same  resistance,  and  these 
vessels  are  of  the  same  size,  when  the 
current  passes  the  Joule  effect  is  the  + 

same  in  each  case,  and  consequently 

the  index  is  equally  pressed  in  opposite  directions  and  therefore  does  not  move. 
But  the  Peltier  effect  is  opposite  in  the  two  vessels,  and  produces  a  displace- 
ment of  the  index,  from  which  the  change  of  temperature  can  be  deduced. 

These  experiments  form  an  interesting  illustration  of  the  principle,  that 
whenever  the  effects  of  heat  are  reversed  heat  is  produced  ;  and  whenever 
the  effects  ordinarily  produced  by  heat  are  otherwise  produced,  cold  is  the 
result  ;  for  cooling  takes  place  when  the  current  is  in  the  same  direction 
as  the  thermo-current  produced  at  the  junctions,  and  heating  when  the 
current  is  in  the  opposite  direction. 


922 


Dynamical  Electricity. 


[951- 


CHAPTER    IX. 

DETERMINATION  OF  ELECTRICAL  CONSTANTS. 


951.  Rheostat. — A  Rheostat  is  an  instrument  by  which  the  resistance 
of  any  given  circuit  can  be  increased  or  diminished  without  opening  the 

circuit.  The  original  form  invented 
by  Wheatstone  consists  of  two  parallel 
cylinders,  one,  A,  of  brass,  the  other, 
B,  of  wood  (fig.  895).  In  the  latter 
there  is  a  spiral  groove,  which  termi- 
nates at  a  in  a  brass  ring,  to  which  is 
fixed  the  end  of  a  fine  brass  wire.  This 
wire,  which  is  about  40  yards  long,  is 
partially  coiled  on  the  groove  ;  it  passes 
to  the  cylinder  A,  and,  after  a  great 
number  of  turns  on  this  cylinder,  is 
fixed  at  the  extremity  e.  Two  binding 
screws,  n  and  o,  connected  with  the 
battery,  communicate  by  two  steel 
plates  ;  one  with  the  cylinder  A,  the 
other  with  the  ring  a. 

When   a    current   enters    at   o,   it 


Fig.  895. 


simply  traverses  that  portion  of  the  wire  rolled  on  the  cylinder  B,  where  the 
windings  are  insulated  by  the  grooves  ;  passing  thence  to  the  cylinder  A, 
which  is  of  metal,  and  in  contact  with  the  wire,  the  current  passes  directly 
to  ;;z,  and  thence  to  //.  Hence,  if  the  length  of  the  current  is  to  be  in- 
creased, the  handle  */must  be  turned  from  right  to  left.  If,  on  the  contrary, 
it  is  to  be  diminished,  the  handle  is  to  be  fixed  on  the  axis  <r,  and  turning 
then  from  left  to  right,  the  wire  is  coiled  on  the  cylinder  A.  The  length  of 
the  circuit  is  indicated  in  feet  and  inches,  by  two  needles,  at  the  end  of 
the  apparatus  not  seen  in  the  figure,  which  are  moved  by  the  cylinders  A 
and  B. 

952.  Determination  of  the  resistance  of  a  conductor.  Reduced 
length. — If  in  the  circuit  of  a  constant  element  a  tangent  galvanometer  be 
interposed,  a  certain  deflection  of  the  needle  will  be  produced.  If,  then,  dif- 
ferent lengths  of  copper  wire  of  the  same  diameter  be  successively  interposed, 
corresponding  deflections  will  in  each  case  be  produced.  Let  us  suppose 
that  in  a  particular  case  the  tangent  of  the  angle  of  deflection  (823)  observed 
with  the  element  and  tangent  galvanometer  alone  was  i  '88,  and  that  when 
5,  40,  70,  and  100  yards  of  copper  wire  were  successively  placed  in  the 
circuit,  the  tangents  of  the  corresponding  deflections  were  0-849,  0-172, 


-953]  Resistance  Coils.  923 

0-105,  anc*  0-074.  Now,  in  this  experiment,  the  total  resistance  consists  of  two 
components— the  resistance  offered  by  the  element  and  the  tangent  gal- 
vanometer, and  the  resistance  offered  by  the  wire  in  each  case.  The  former 
resistance  may  be  supposed  to  be  equal  to  the  resistance  of  x  yards  of  copper 
wire  of  the  same  diameter  as  that  used,  and  then  we  have  the  following 
relations  : — 

Length  of  wire.  Tangent  of  angle  of  deflection. 

x          yards     .        -.         .      :  .         .         .  :      .         .     i'88 
x+5        „        .        .        .        .        ....    0-849 

^•  +  40      „        :-     >;V       V 0-172 

X+IQ      „       '•.  '  .        .        .  .        .    0-105 

x+ 100    „  0-074 

If  the  intensities  of  the  currents  are  inversely  as  the  resistances — that  is, 
as  the  lengths  of  the  circuits — the  proportion  must  prevail, 

x  :  x  +  5  =  0-849  :  J  '8%6  > 

from  which  ^-  =  4-11.  Combining,  in  like  manner,  the  other  observations,  we 
get  a  series  of  numbers,  the  mean  of  which  is  4-08.  That  is,  the  resistance 
offered  by  the  element  and  galvanometer  is  equal  to  the  resistance  of  4-08 
yards  of  such  copper  wire,  and  this  is  said  to  be  the  reduced  length  of  the 
element  and  galvanometer  in  terms  of  the  copper  wire. 

It  is  of  great  scientific  and  practical  importance  to  have  a  unit  or  standard 
of  comparison  of  resistance,  and  numerous  such  have  been  proposed.  Jacobi 
proposed  the  resistance  of  a  metre  of  a  special  copper  wire  a  millimetre  in 
diameter.  Copper  is,  however,  ill  adapted  for  the  purpose,  as  it  is  difficult 
to  obtain  pure.  Matthiessen  proposed  an  alloy  o  gold  and  silver,  contain- 
ing two  parts  of  gold  and  one  of  silver  ;  its  conducting  power  is  very  little 
affected  by  impurities  in  the  metals,  by  annealing,  or  by  moderate  changes 
of  temperature. 

Siemens'  unit  is  a  metre  of  pure  mercury,  having  a  section  of  a  square 
millimetre.     Its  actual  material  reproduction  for  ordinary  use  is  a  German 
silver  wire  3-8  metres  in  length  and  0*9  mm.  in  diameter.     It  is  0-9534  of 
an  ohm  (963).      A 
mile  of  No.  16  pure 
copper  wire  repre- 
sents  a    resistance 
of  13-67  ohms. 

953.  Resistance 
coils. — The  actual 
material  production 
of  a  standard  resist- 
ance is  ordinarily  a 
given  length  of  wire 
of  a  certain  defi- 
nite material,  and  is 
known  as  a  resist- 
ance coil.  An  alloy 
of  silver  with  about  |  of  platinum  is  best,  as  it  is  very  permanent,  and  its  re- 
sistance varies  little  with  increase  of  temperature.  Such  resistance  coils  are 


Fig.  896. 


924 


Dynamical  Electricity. 


[953- 


T' 


usually  employed  in  what  are  called  resistance  boxes  (fig.  896).  Fig.  897 
represents  the  way  in  which  resistance  coils  are  affixed  inside  the  box.  On 
the  top  of  the  box,  whfch  is  of  slate  or  ebonite,  are  a  number  of  solid  pris- 
matic pieces  of  brass  fixed  a  little 
distance  apart ;  at  their  ends  are 
conical  perforations  in  which  fit  brass 
plugs.  Inside  the  box  are  fitted  to 
these  brass  pieces  the  various  lengths 
of  wires  which  represent  very  accu- 
rately the  resistances  ;  they  are 
covered  with  insulated  wire,  and  are 
wound  double,  so  as  to  neutralise  any 
extraneous  inductive  action.  If  the 
terminals  of  a  circuit  are  connected 
with  T  T',  fig.  897,  and  all  the  plugs  are  inserted,  the  resistance  box  offers  no 
appreciable  resistance,  for  the  current  passes  by  the  plugs  and  the  massive 
metal  ;  but  by  taking  out  any  of  the  plugs  the  current  has  to  pass  through  the 
wire  coil  between  the  two  brass  pieces,  and  thus  its  resistance  is  introduced. 
In  figure  896  this  represents  the  use  of  a  resistance  of  74  ohms. 

The  coils  are  in  multiples  and  submultiples  of  ohms,  and  are  so  arranged 
that  their  combination  may  be  as  greatly  varied  with  as  few  resistances  as 
possible.  Thus  a  set  of  eleven  coils  of  o-i,  02,  0-2,  0-5,  2,  2,  5,  10,  10,  20,  and 
50  enables  us  to  introduce  any  resistance  from  o-i  to  100  into  the  circuit. 

Resistance  boxes  have  almost  entirely  superseded  the  rheostat  and 
similar  instruments.  They  are  more  accurate,  and  not  nearly  so  likely  to 
suffer  from  use. 

954.  Absolute  measure  of  electrical  resistance. — When  the  resistance 
of  any  conductor  has  been  measured  and  expressed  by  reference  to  any  of 
the  standards  of  resistance  mentioned  in  the  preceding  paragraph,  the  num- 
ber denoting  the  result  of  the  measurement  still  does  not  tell  us  what  the 
resistance  of  the  conductor  in  question  really  is  ;  it  only  tells  us  what  mul- 
tiple it  is  of  the  resistance  of  the  particular  conductor  with  which  the  com- 
parison has  been  made.  It  gives  us  merely  a  relative  and  not  an  absolute 
measure.  Just  in  the  same  way,  if  we  are  told  that  the  pressure  of  the  steam 
in  a  boiler  is  equal  to  (say)  8  atmospheres  (157),  this  statement  does  not  in 
itself  enable  us  to  form  any  estimate  of  what  the  actual  pressure  of  the  steam 
is  ;  it  only  tells  us  that,  whatever  the  pressure  of  an  atmosphere  may  be, 
that  of  the  steam  is  8  times  as  great.  In  order  that  we  may  be  able  to  cal- 
culate what  effects  the  pressure  of  the  steam  is  capable  of  producing,  we 
require  to  have  it  stated  in  absolute  measure — that  is,  not  how  much  greater 
or  less  it  is  than  some  other  pressure — but  what  actual  force  is  exerted  by  it 
on  each  unit  of  surface.  So,  for  very  many  purposes  we  require  absolute 
measures  of  electrical  resistance,  instead  of  mere  comparisons  of  the  resist- 
ance of  one  conductor  with  that  of  another. 

To  see  how  it  is  possible  to  get  an  absolute  measure  of  resistance,  we 
must  go  back  to  the  fundamental  meaning  expressed  by  the  term.  If,  by 
any  means  whatever,  a  definite  electromotive  force  or  difference  of  potential  is 
maintained  between  any  two  given  cross-sections  of  a  conductor,  a  constant 
electric  current  flows  from  one  cross-section  to  the  other,  and,  for  the  same 


-954]  Absolute  Measure  of  Electrical  Resistance.  925 

conductor,  the  ratio  of  the  electromotive  force  to  the  strength  of  the  resulting 
current  is  constant.  That  is,  if  El5  E2,  E3,  .  .  .  be  various  values  succes- 
sively given  to  the  electromotive  force,  and  C1}  C2,  G3,  .  .  .  be  the  corre- 
sponding strengths  of  the  current,  then 

Ei  =  E2     ES  = .  .  .  •.=  R  (a  constant). 
Cx      C.2      C3 

This  constant  ratio  of  electromotive  force  to  strength  of  current  is  charac- 
teristic of  the  individual  conductor  employed,  and  is  called  its  electrical 
resistance.  And,  when  the  resistance  of  a  conductor  is  stated  as  the  value 
of  the  ratio  in  question,  the  statement  gives  us  the  absolute  measure  of  the 
resistance  :  that  is,  it  gives  us  definite  information  about  the  electrical  pro- 
perties of  that  particular  conductor  without  implying  a  comparison  of  it  with 
any  other  conductor. 

Hence  it  appears  that  the  absolute  resistance  of  a  given  conductor  is 
determined  if  we  can  ascertain  the  ratio  of  any  electromotive  force  to  the 
strength  of  the  current  which  it  is  capable  of  producing  in  the  conductor  in 
question.  It  is  not,  however,  needful  to  make  an  independent  measurement 
of  this  ratio  in  the  case  of  every  conductor  whose  resistance  we  require  to 
know ;  it  is  sufficient  to  determine  it  once  for  all  for  some  one  conductor,  and 
then,  taking  this  conductor  as  a  standard,  td  compare  the  resistance  of  other 
conductors  with  that  of  this  one,  by  means  of  Wheatstone's  Bridge  (948), 
or  any  other  convenient  method. 

The  methods  available  for  determining  the  ratio  between  electromotive 
force  and  resistance,  required  for  an  absolute  measurement  of  resistance, 
depend  on  the  electromagnetic  phenomena  presented  by  electric  conductors 
and  currents  ;  it  will  be  sufficient  here  to  indicate  the  general  principles 
upon  which  such  methods  can  be  founded.  From  what  has  been  said  it  will 
be  seen  that  any  method  for  this  purpose  involves  a  measurement  of  electro- 
motive force  and  a  measurement  of  the  strength  of  a  current.  It  will  be 
convenient  to  treat  these  two  parts  of  the  process  separately. 

A.  Absolute  measurement  of  electromotive  force. — When  any  electric 
conductor  is  moved  in  a  magnetic  field  (707),  that  is  to  say,  in  any  region 
where  there  is  magnetic  force,  an  electromotive  force  is  in  general  developed 
in  the  conductor  during  its  motion.  The  magnitude  of  this  electromotive 
force  depends  upon  the  strength  of  the  magnetic  field,  on  the  length  and 
form  of  the  conductor,  and  on  the  velocity  and  direction  of  its  motion.  The 
simplest  case  is  presented  by  a  straight  conductor,  with  its  length  perpen- 
dicular to  the  direction  of  the  force  in  a  uniform  magnetic  field,  and  moving 
at  right  angles  to  its  length  and  to  the  direction  of  the  force.  If  T  be  the 
strength  of  the  field,  /  the  length  of  the  conductor,  and  v  the  velocity,  the 
electromotive  force  E  is 

E  -  kllv, 

where  k  is  a  constant,  depending  on  the  unit  adopted  for  the  measurement 
of  electromotive  force.  If  we  define  the  unit  of  electromotive  force  as  that 
which  is  developed  in  a  conductor  of  unit  length  moving  (m.  the  way  specified 
above)  with  unit  velocity  in  a  magnetic  field  of  unit  intensity,  the  constant  k 
becomes  =  I,  and  the  value  of  E  is 

E  =  Tiv. 


926  Dynamical  Electricity.  [954 

If  the  length  and  the  direction  of  motion  of  the  conductor  are  not  at  right 
angles  to  the  direction  of  magnetic  force,  we  must  project  both  on  a  plane 
perpendicular  to  the  direction  of  the  force ;  thus,  if  the  conductor  is  inclined 
at  an  angle  a,  and  moves  in  a  direction  making  an  angle  /3,  both  being 
measured  from  the  direction  of  magnetic  force,  the  electromotive  force 
becomes 

E  -  T/  sin  a.  v  sin  /3. 

If  the  conductor  is  bent  in  any  way,  so  that  a  has  different  values  for  different 
parts,  and  if  the  direction  or  velocity  of  its  motion  varies  from  one  part  to 
another,  we  may  conceive  of  it  as  divided  into  a  great  number  of  equal  parts, 
each  so  small  that  no  sensible  variation  of  a,  /3,  or  v  can  occur  within  it,  we 
may  calculate  the  electromotive  force  due  to  each  of  these  small  parts  taken 
separately  by  the  last  formula,  and  then,  adding  all  the  results  together,  we 
obtain  the  electromotive  force  developed  in  the  whole  conductor.  A  little 
consideration  will  show  that  the  following  statement  is  equivalent  to  that  just 
given  :  namely,  the  electromotive  force  generated  in  a  conductor  moving 
in  any  manner  in  a  magnetic  field  is  proportional  at  each  instant  to  the 
rate  of  variation  of  the  area  swept  over  by  its  projection  on  a  plane  perpen- 
dicular to  the  direction  of  the  magnetic  force  ;  and  the  average  electromotive 
force  acting  in  the  conductor  during  any  interval  of  time  is  proportional 
directly  to  the  total  area  swept  over  by  its  projection  during  the  interval, 
and  inversely  to  the  length  of  the  interval. 

In  order  to  apply  practically  the  principles  that  have  been  pointed  out, 
it  is  most  convenient  to  take  advantage  of  the  magnetic  field  due  to  the 
magnetism  of  the  earth.  Throughout  any  moderate  space  at  a  distance 
from  magnets  or  masses  of  iron,  the  magnetic  force  due  to  the  earth  is 
uniform  in  intensity  and  direction.  Suppose,  then,  a  circular  conducting 
ring,  placed  so  that  its  plane  is  perpendicular  to  the  direction  of  the  earth's 
magnetic  force — that  is,  to  the  direction  of  the  dipping  needle — to  be  turned 
through  half  a*  revolution  about  one  of  its  diameters;  we  may  regard  its  pro- 
jection on  a  plane  perpendicular  to  the  direction  of  the  earth's  force  to  be 
made  up  of  the  projections  of  the  two  semicircles  into  which  it  is  divided  by 
the  axis  of  rotation.  During  the  half-turn  made  by  the  ring,  the  projection 
of  each  semicircle  sweeps  through  an  area  equal  to  that  of  the  whole  ring ; 
but  one  projection  passes  over  this  area  in  one  direction,  and  the  other  in 
the  opposite  direction.  Consequently,  equal  electromotive  forces  are  gene- 
rated in  the  two  halves  of  the  ring,  in  opposite  directions  as  regarded  from 
outside,  but  both  in  the  same  direction  if  considered  as  tending  to  produce  a 
current  round  the  ring  :  the  total  electromotive  force  is  therefore  the  sum  of 
the  forces  in  the  two  halves,  and  if  r  be  the  radius  of  the  ring  and  therefore 
Trr2  its  area,  and  n  the  number  of  revolutions  per  second,  so  that  the  time 

occupied  by  each  half-revolution  is  — ,  the  average  electromotive  force  act- 
ing in  the  ring  as  it  rotates  uniformly  about  a  diameter  is 
2T  .  Tj-r'-f-—  =4T7rr2«, 

where  T  stands  for  the  whole  intensity  of  the  earth's  magnetic  force.  If, 
instead  of  a  single  ring,  we  have  a  circular  coil  of  wire  of  u  convolutions, 


954]  Absolute  Measure  of  Electrical  Resistance.  927 

and  if  the  axis  of  rotation  makes  any  angle  a  with  the  line  of  dip,  the  elec- 
tromotive force  due  to  the  rotation  of  the  coil  is 

E  =  4TTrr~nu  sin  a. 

Consequently,  the  rotation  of  a  coil  of  wire  under  the  circumstances  named 
furnishes  the  means  of  obtaining  an  electromotive  force,  the  absolute  value 
of  which  is  given  by  the  intensity  of  the  magnetic  field,  the  dimensions  and 
speed  of  the  coil,  and  the  position  of  its  axes  of  rotation.  If  we  can  deter- 
mine the  strength  of  current  which  this  electromotive  force  is  capable  of 
producing  in  a  given  conductor,  the  absolute  resistance  of  the  conductor  is 
at  once  known. 

B.  Absolute  measurement  of  the  strength  of  currents.  —  The  method  of 
measuring  the  strength  of  electric  currents  is  founded  on  the  fact  that  a 
force  is  exerted  between  a  conductor  carrying  a  current  and  any  magnetic 
pole  in  its  neighbourhood.  In  general,  both  the  distance  and  the  direction, 
as  seen  from  a  given  magnetic  pole,  vary  from  point  to  point  of  the  con- 
ductor, so  that  it  is  generally  impossible  to  give  any  simple  statement  of 
the  law  according  to  which  a  given  current  acts  upon  a  magnetic  pole  in  a 
given  position.  But,  if  we  consider  only  a  very  small  length  of  a  current, 
neither  the  distance  of  its  various  points  from  a  given  magnetic  pole,  nor 
their  directions,  can  vary  to  a  sensible  extent  ;  and  when  these  two  condi- 
tions are  constant,  the  law  of  the  force  between  the  current  and  the  pole 
may  be  stated  as  follows  :  As  to  direction  the  force  is  perpendicular  to  a 
plane  containing  the  current  and  the  pole,  and  acts  upon  a  north  pole,  to- 
wards the  left  hand  of  an  observer  looking  at  the  pole  from  the  line  of  the 
current,  and  so  placed  that  the  nominal  direction  of  the  current  is  from  his 
feet  to  his  head,  or,  upon  a  south  pole,  towards  the  right  hand  of  an  obser- 
ver similarly  placed  ;  as  to  magnitude,  the  force  is  proportional  directly  to 
the  length  (/)  and  to  the  strength  (C)  of  the  current,  to  the  strength  of  the 
magnetic  pole  (m),  and  to  the  sine  of  the  angle  (B)  made  by  the  direction  of 
the  current  with  a  straight  line  drawn  from  it  to  the  pole,  and  inversely  to 
the  square  of  the  distance  (r'}  from  the  current  to  the  pole.  Hence,  if  the 
force  be  denoted  by/j  we  have 


, 

where  k  is  a  constant,  depending  on  the  units  in  which  the  numerical  values 
of  the  various  quantities  are  expressed.  If  we  define  the  unit  strength  of 
current  as  the  strength  of  a  current  of  which  unit  length  placed  at  unit  dis- 
tance from  a  magnetic  pole  of  unit  strength,  and  making  everywhere  a  right 
angle  with  a  line  drawn  from  it  to  the  pole,  exerts  unit  force  on  the  pole,  k 
becomes  unity,  and  we  have 


6 

The  most  convenient  way  of  founding  upon  these  principles  a  practical 
measurement  of  the  strength  of  a  current  is  to  cause  the  current  to  go  one 
or  more  times  round  a  vertical  circle  of  known  radius  placed  in  the  plane 
of  the  magnetic  meridian,  with  a  very  short  magnet  suspended  at  the  centre. 
This  is  the  arrangement  of  the  tangent  galvanometer  already  described 


928  Dynamical  Electricity.  [954- 

(823).  If  H  is  the  intensity  of  the  horizontal  component  of  the  earth's  mag- 
netic force,  the  force  which  must  be  exerted  upon  each  pole  of  a  magnet 
whose  poles  are  of  the  strength  +  m  and  —  ;«,  in  a  direction  perpendicular 
to  the  magnetic  meridian,  in  order  to  deflect  the  magnet  through  an  angle 
y  is 

f=  Hm  tan  y. 

Putting  this  value  off  into  the  expression  given  above  for  the  strength  of 
a  current,  we  have 

^  _  H;/z  tan  y  r72 
ml  sin  6 

But  in  the  case  supposed,  that  of  a  tangent-galvanometer  with  the  current 
going  u'  times  round  the  circle,  we  have  /  =  z/27r#,  if  a  is  the  radius  of  the 
circle  ;  moreover,  the  distance  r'  of  each  part  of  the  current  from  the  magnet 
is  constant  and  equal  to  the  radius,  or  r'  =  a,  and  the  angle  6  is  also  constant, 
being  everywhere  a  right  angle,  so  that  sin  6  =  i  ;  consequently  we  get  for 
the  strength  of  the  current  in  absolute  measure, 


~  , 

C  =  —  tan  y  =  .  -  tan  y. 

mu  2-rra  2iru' 

We  have  thus  shown  how  both  electromotive  force  and  strength  of  cur- 
rent can  be  measured  in  absolute  units,  and  if  these  two  measurements  be 
combined,  the  ratio  of  the  numerical  value  of  the  electromotive  force,  acting 
in  a  conductor,  to  that  of  the  strength  of  the  resulting  current,  is  the  measure 
of  the  resistance  of  the  conductor  in  question.  Using  the  notation  employed 
above,  this  leads  to  the  following  expression  for  the  absolute  measure  of  re- 
sistance, 

R  __  E  _  4  Tirr^un  sin  a  .  2iru' 
_„_       _______ 

Various  practical  methods  of  measurement  founded  upon  this  principle  have 
been  devised,  and  when  any  of  them  is  employed  the  value  of  the  resistance 
under  investigation  is  obtained  by  putting  in  this  formula  the  values  of  elec- 
tromotive force  and  strength  of  current  that  result  from  the  particular 
arrangement  adopted. 

It  may  be  observed  with  regard  to  the  above  expression,  that  the  factors 
TT,  #,  uf,  sin  a  and  tan  /3,  are  all  of  them  simple  numbers,  that  T  and  H  are 
quantities  of  the  same  kind,  so  that  their  ratio  is  also  a  pure  number.  The 
only  factors  which  involve  reference  to  physical  units  are  therefore  r2,  r'  and 
«,  and  the  two  former  being  both  distances,  the  ratio  ri-^-rf  is  the  first  power 
of  a  distance,  while  n,  the  number  of  revolutions  per  unit  of  time,  is  the  re- 
ciprocal of  the  time  occupied  by  a  single  revolution.  Hence  the  expression 
for  the  absolute  resistance  of  a  conductor  is  in  all  cases  reducible  to 

adistancex  a  numerical  factor; 
a  time 

that  is  to  say,  electrical  resistance  may  be  expressed  in  terms  of  the  units  of 
length  (or  distance)  and  time  in  the  same  manner  as  a  velocity,  and  the 
natural  unit  of  resistance,  like  the  natural  unit  of  velocity,  would  be  repre- 
sented by  a  unit  of  length  per  unit  of  time.  Adopting  the  C.G.S.  system,  the  ab- 
solute unit  of  resistance  becomes  one  centimetre  per  second  '  ;  such  a  resistance, 


-955J  Wheatstone's  Bridge.  929 

however,  is  so  small  that  resistances  commonly  occurring  in  practice  would 
have  to  be  represented  by  inconveniently  great  multiples  of  it.  As  a 
practical  standard  of  resistance,  it  is,  therefore,  more  usual  to  employ  the 
ohm  (963),  which  is  a  resistance  of  one  thousand  million  centimetres  per 
second,  or 

io9  centimetres 
i  second 

955.  Wiieatstone's  bridge. — The  various  methods  of  determining  the 
electrical  conductivity  of  a  body  consist  essentially  in  ascertaining  the  ratio 
between  the  resistance  of  a  certain  length  of  the  conductor  in  question, 
having  a  given  section,  to  that  of  a  known  length  of  a  known  section  of  some 
substance  taken  as  standard.  The  most  convenient  method  of  ascertaining 
experimentally  the  ratio  between  the  resistance  of  two  conductors  is  by  a 
method  known  as  that  of  Wheatstone's  bridge,  the  general  principle  of  which 
may  be  thus  stated  :  — 

The  conductors,  which  may  be  denoted  by  AB  and  BC,  are  connected  end 
to  end,  as  shown  in  fig.  898,  and  one  end  of  each  is  also  connected  with  a 
battery,  say  the  end  A  of  AB  with  the  positive  pole,  and  the  end  C  of  BC 
with  the  negative  pole  ;  the  ends  that  are  in  connection  with  the  battery  are 
likewise  connected  together  by  another  conductor,  AB'C.  A  current  will 
thus  pass  from  A  to  C  by  each  of  the  two  paths  ABC  and  AB'C,  and  there 


Fig. 


will  be  a  gradual  fall  of  potential  in  passing  from  A  to  C  along  either  path, 
so  that  for  every  point  in  the  conductors  AB  and  BC  there  is  a  point  in  the 
wire  AB'C  which  has  the  same  potential.  If  one  end  of  a  galvanometer 
wire  BGB'  be  connected  with  the  point  of  junction  B,  the  point  of  AB'C 
which  has  the  same  potential  as  the  point  B  can  be  found  by  applying  the 
other  end  of  the  galvanometer  wire  to  AB'C,  and  shifting  the  point  of  con- 
tact towards  A  or  C  until  the  galvanometer  shows  no  deflection.  Let  B'  be 
the  point  so  found  ;  the  fact  that  when  it  is  connected  with  B  by  the  bridge 
BGB'  no  current  passes  from  one  to  the  other  proves  that  the  potential 
at  B/  is  the  same  as  the  potential  at  B.  From  this  it  follows  that  if  r  and  r'' 
are  the  resistances  of  AB  and  BC  respectively,  and  s  and  s'  the  resistances 
of  AB'  and  B'C, 

r  '.  rf  =  s  :  s'. 

If  the  conductor  AB'C  is  a  wire  of  uniform  material  and  diameter,  the 
ratio  of  the  resistances  s  and  s'  will  be  the  ratio  of  the  lengths  of  the  corre- 
sponding portions  of  wire,  and  can  therefore  be  at  once  really  ascertained. 

To  prove  this,  let  MN,  NO,  MN'  and  N'O'  (fig.  899)  be  taken  in  the 
same  straight  line,  proportional  respectively  to  the  several  resistances 
r,  r',  s,  s' ;  and  let  MP  be  drawn  at  right  angles  to  O 'MO  of  a  length 

30 


930 


Dynamical  Electricity. 


[955- 


proportional  to  the  difference  of  potential  between  the  points  A  and  C.  Then 
if  the  straight  lines  PO  and  PO'  be  drawn,  the  potential  at  N  (the  point  of 
junction  of  the  conductors  whose  resistances  r  and  r'  are  to  be  compared — 


i.e.  the  point  corresponding  to  B  in  the  previous  figure)  will  be  given  by  the 
length  of  the  line  NQ,  drawn  from  N  at  right  angles  to  NO  ;  and  the  point 
N'  (corresponding  to  B'  in  the  previous  figure),  where  the  potential  is  the 
same  as  at  N,  will  be  found  by  drawing  QQ'  parallel  to  OO',  and  letting  fall 
from  Q'  the  perpendicular  O'N'  upon  O'M.  The  geometry  of  the  figure 
gives  obviously, 


_ 

MP 


-- 

s  +  s'      MP 


and  therefore  since  NO  =  N1Q1 


A  convenient  form  of  Wheatstone's  bridge,  and  one  well  adapted  for 
purposes  of  instruction,  is  that  represented  in  fig.  900.  It  consists  of  a  long 
mahogany  board,  on  which  is  fixed  a  thick  copper  band,  which  practically 
offers  no  resistance.  To  the  ends  of  this  band  is  fixed  a  straight  platinum 


c 


Fig.  900. 

wire,  near  which  is  a  scale  divided  into  100  parts.  At  c  and  d  are  breaks 
in  the  copper  band,  provided  with  binding  screws,  in  which  are  introduced 
the  resistances  to  be  compared,  o  and  x.  The  wires,  from  an  element 
which  gives  only  a  weak  current,  so  as  not  to  introduce  heating  effects,  are 
connected  with  the  binding  screws  b  and  b'.  Another  wire  connects  the 
binding  screw  g  and  one  end  of  a  sensitive  galvanometer,  the  other  end 
of  which  is  connected  with  a  sliding  spring  contact-key  g\  which  is  so 
constructed  that  when  the  knob  is  depressed  a  knife-edge  makes  contact 
with  any  part  of  the  wire.  The  resistances  to  be  compared  having  been 


-957]    Determination  of  Internal  Resistance  of  an  Element.     931 

introduced  at  c  and  */,  the  position  on  the  platinum  wire  is  found  by  trial, 
at  which,  when  the  key  is  depressed,  the  needle  of  the  galvanometer  is  not 
deflected.  When  this  is  found  for  instance  at  34,  the  resistance  of  O  :  the 
resistance  of  x  =  34  :  66. 

The  principle  of  Wheatstone's  bridge  is  of  constant  use  in  the  measure- 
ments required  in  telegraphy,  and  many  other  applications  of  electricity. 
In  practice  the  variations  of  the  resistance  are  effected  by  means  of  resist- 
ance coils  (953)  suitably  arranged. 

The  resistance  of  a  galvanometer  may  be  determined  by  making  it  one 
of  the  four  conductors  of  a  Wheatstone's  bridge  arrangement,  replacing  it 
in  the  bridge  by  an  ordinary  contact-key.  The  resistances  of  the  other  con- 
ductors are  then  varied  until,  on  making  contact,  the  deflection  of  the  galva- 
nometer is  constant. 

956.  Equivalent  conductors. — The  resistance  of  a  conductor  depends, 
as  we  have  seen  (825),  on  its  length,  section,  and  conductivity.  Two  con- 
ductors C  and  (7,  whose  length,  conductivity,  and  section,  are  respectively 
X,X',  *,*',  CO,G/,  would  offer  the  same  resistance,  and  might  be  substituted  for 
each  other  in  any  voltaic  circuit,  without  altering  its  strength,  provided  that 

—  =  — -  ;  and  such  conductors  are  said  to  be  equivalent  to  each  other.     An 

KdO          K  Q) 

example  will  best  illustrate  the  application  of  this  principle. 

It  is  required  to  know  what  length  of  a  cylindrical  copper  wire  4  mm. 
in  diameter  would  be  equivalent  to  12  metres  of  copper  wire  I  mm.  in 
diameter. 

Let  X=  12  the  length  of  the  copper  wire  i  mm.  in  diameter,  and  X'  the 
length  of  the  other  wire  ;  then  since  in  this  case  the  material  is  the  same,  the 

X      X' 
conductivity  is  also  the  same,  and  the  equation  becomes  —  =  — .       Now   the 

00        00 

sections  of  the  wires  are  directly  as  .the  squares  of  the  diameters,  and  hence 

12       Xx 

we  have— ^  =  -5,  or  X'=  12  x  16=  192.     That  is,  192  metres  of  copper  wire  4 

mm.  in  thickness  would  only  offer  the  same  resistance  as  12  metres  of  copper 
wire  i  mm.  in  thickness. 

How  thick  must  an  iron  wire  be  which  for  the  same  length  shall  offer  the 
same  resistance  as  a  copper  wire  2-5  mm.  in  diameter? 

Here,  the  length  being  the  same,  the  expression  becomes  KOO  =  K'O/,  or  since 
trie  sections  are  as  the  squares  of  the  diameter,  ^3  =  Kfd'z.  The  conductivity 
of  copper  is  unity,  and  that  of  iron  0-138.  Hence  we  have  2'52  =  <aT2  x  0-138 
or  d/<z  =  6'2$  -^-0-138  =  45-3  mm.  or  ^'  =  67  mm.  That  is,  any  length  of  a 
copper  wire  2-5  mm.  in  diameter  might  be  replaced  by  iron  wire  of  the  same 
length,  provided  its  diameter  were  67  mm. 

957*  Determination  of  the  internal  resistance  of  an  element. — The 
following  is  the  method  of  determining  the  internal  resistance  of  an  element. 
A  circuit  is  formed  consisting  of  one  element,  a  rheostat,  and  a  galvanometer, 
and  the  strength  C  is  noted  on  the  galvanometer.  A  second  element  is  then 
joined  with  the  first,  so  as  to  form  one  of  double  the  size,  and  therefore  half 
the  resistance,  and  then  by  adding  a  length,  /,  of  the  rheostat  wire,  the 
strength  is  brought  to  what  it  originally  was.  Then  if  E  is  the  electromotive 
force,  and  'R  the  Resistance  of  the  element,  r  the  resistance  of  the  galvano- 

302 


932  Dynamical  Electricity.  [957- 

meter  and  the  other  parts  of  the  circuit  ;  the  current  strength  C  in  the  one 

-p>  "p 

case  is  C  =  -  and  in  the  other  =  —  -  and  since  the  strength  in  both 
R  +  r,  ±R  +  r  +  /, 

cases  is  the  same,  R  =  2/. 

Another  method  is  that  due  to  Mance.  The  element  whose  internal 
resistance  is  to  be  determined  is  placed  in  one  of  the  arms  of  a  Wheatstone 
bridge,  as  at  fig.  900,  a  resistance  box  being  placed  in  the  other.  The  gal- 
vanometer is  connected  with  the  ends  of  the  wire,  and  a  simple  contact-key  is 
interposed  in  the  ordinary  position  of  the  galvanometer,  and  by  trial  its  posi- 
tion is  found  for  the  sliding  contact  such  that  when  the  key  is  depressed  no 
alteration  is  produced  in  the  deflection  of  the  galvanometer.  When  this 
is  found  the  ordinary  conditions  of  the  bridge  hold,  that  is,  that  the  cross 
products  of  the  resistances  are  equal. 

958.  Electrical  conductivity.  —  We  can  regard  conductors  in  two 
aspects,  and  consider  them  as  endowed  with  a  greater  or  less  facility  for 
allowing  electricity  to  traverse  them,  a  property  which  is  termed  conductivity, 
or  we  may  consider  conductors  interposed  in  a  circuit  as  offering  an  obstacle 
to  the  passage  of  electricity  —  that  is,  a  resistance  which  it  must  overcome. 
A  good  conductor  offers  a  feeble  resistance,  and  a  bad  conductor  a  great 
resistance.  Conductivity  and  resistance  are  the  inverse  of  each  other. 

The  conductivity  of  metals  has  been  investigated  by  many  physicists  by 
methods  analogous  in  general  to  that  described  in  the  preceding  paragraph, 
and  very  different  results  have  been  obtained.  This  arises  mainly  from  the 
various  degrees  of  purity  of  the  specimens  investigated,  but  their  molecular 
condition  has  also  great  influence.  Matthiessen  found  the  difference  in  con- 
ductivity between  hard-drawn  and  annealed  silver  wire  to  amount  to  8*5, 
for  copper  2-2,  and  for  gold  1-9  per  cent.  The  following  are  results  of  a 
series  of  careful  experiments  by  Matthiessen  on  the  electrical  conductivity 
of  metals  at  o°  C.  compared  with  silver  as  a  standard  :  —  • 

Silver  .  .  .  100-0  Platinum  .  .  .18-0 
Copper  ....  99-9  Iron  ....  16-8 
Gold  ....  8o-o  Tin  .  .  .  .13*1 
Sodium  ....  37-4  Lead  .  .  .  .8-3 
Aluminum  .  .  .  34-0  German  silver  .  .  77 
Zinc  ....  29-0  Antimony  .  .  .4-6 
Cadmium  .  .  .  237  Mercury  .  .  .  1-6 
Brass  ....  22-0  Bismuth  .  .  .1*2 
Potassium  .  .  .  20-8  Graphite  .  .  .  0-07 
Silver  and  copper  have  the  smallest  resistance  for  a  given  volume^  while 
aluminum  has  the  smallest  for  a  given  weight. 

The  conductivity  of  metals  is  diminished  by  an  increase  in  temperature. 
The  law  of  this  diminution  is  expressed  by  the  formula 


where  K(  and  KO  are  the  conductivities  at  /  and  o°  respectively,  and  a  and  b 
are  constants,  which  are  probably  the  same  for  all  pure  metals.  For  ten 
metals  investigated  by  Matthiessen  he  found  that  the  conductivity  is 
expressed  by  the  formula 

K(  —  K°  (  i  -  0-C037647/  +  0-000008  3  4/2).    ' 


-958]  Electrical  Conductivity.  933 

It  seems  that  this  value  is  about  0*00368  for  each  degree  C.  This  co- 
efficient agrees  in  a  surprising  manner  with  the  coefficient  of  expansion  of 
gases,  which  is  £$. 

Liquids  are  far  worse  conductors  than  metals.  The  conductivity  of 
a  solution  of  one  part  of  chloride  of  sodium  in  100  parts  of  water  is 
3000*0006  tnat  °f  c°PPer-  In  general,  acids  have  the  highest  and  solutions  of 
alkalies  and  neutral  salts  the  lowest  conductivity.  Yet,  in  solutions,  the 
conductivity  does  not  increase  in  direct  proportion  to  the  quantity  of  salt 
dissolved.  If  two  badly  conducting  liquids  be  mixed  the  conductivity  of  the 
mixture  is  greater  than  that  of  either  of  the  constituents. 

The  following  is  a  list  of  the  conductivity  of  a  few  liquids  as  compared 
with  that  of  pure  silver  :  — 

Pure  silver      .         .         .         .         .  ,,...,     ,  100,000,000,000 

Nitrate  of  copper,  saturated  solution       .        ..  .  "..-.  8990 

Sulphate  of  copper            ditto         .         .        »  .  ..  5420 

Chloride  of  sodium            ditto        ,  ..    ...  ^  "...  ,  .  31520 

Sulphate  of  zinc                 ditto        .         .,      \*.  •  •«.  577° 

Sulphuric  acid,  no  sp.  gr.      .         .         .*"'.•  .  .  99070 

„  i-24sp.gr.   .  .;,.  132750 

„     „  1-40  sp.  gr.   .  .  90750 

Nitric  acid,  commercial  .....  .  .  88680 

Distilled  water        .         .         .         .        .         .      ;  „  ,  7 

The  last  number  was  that  found  by  Kohlrausch  for  distilled  water,  which 
had  been  specially  purified.  Accordingly,  a  disc  of  water  a  millimetre  in 
thickness  offers  the  same  resistance  as  a  column  o  silver  of  the  same  diameter, 
but  of  a  length  equal  to  that  of  the  moon's  orbit.  The  least  trace  of  im- 
purity in  water  markedly  raises  its  conductivity  :  thus  standing  in  the  air  for 
5  hours  doubles  it  ;  the  addition  of  a  millionth  part  of  sulphuric  acid  —  that  is, 
a  drop  in  about  17  gallons  —  increases  the  conductivity  tenfold. 

Liquids  and  fused  conductors  increase  in  conductivity  by  an  increase  of 
temperature  (845).  This  increase  is  expressed  by  the  formula 


and  the  values  of  a  are  considerable.     Thus  for   a  saturated  solution  of 
sulphate  of  copper  it  is  0-0286. 

The  influence  of  light  upon  electrical  conductivity  in  the  case  of  selenium 
has  been  already  alluded  to  (930),  and  is  directly  proved  by  the  following 
experiment.  A  thin  strip  of  this  metalloid,  about  38  mm.  in  length  by  13 
in  breadth,  was  provided  at  the  ends  with  conducting  wires  and  placed  in  a 
box  with  a  draw-lid.  The  selenium,  having  been  carefully  balanced  in  a 
Wheatstone's  bridge,  was  exposed  to  diffused  light  by  withdrawing  the  lid, 
when  the  resistance  at  once  fell  in  the  ratio  of  1  1  to  9.  On  exposure  to  the 
various  spectral  colours,  after  having  been  in  the  dark  it  was  found  to  be  most 
affected  by  the  red  ;  but  the  maximum  action  was  just  outside  the  red,  where 
the  resistance  fell  in  the  ratio  of  3  to  2.  Momentary  exposure  to  the  light  of 
a  gas  lamp  or  even  to  that  of  a  candle  caused  a  diminution  of  resistance. 
Exposure  to  full  sunlight  diminished  the  resistance  to  one  half. 


934  Dynamical  Electricity.  [958- 

The  effect  produced  on  exposure  to  light  is  immediate,  while  recurrence 
to  the  normal  state  takes  place  more  slowly.  A  vessel  of  hot  water  placed 
near  the  strip  produced  no  effect,  and  hence  the  phenomenon  cannot  be 
due  to  heat,  but  there  appear  to  be  certain  rays  which  have  the  power  of 
producing  a  molecular  change  in  the  selenium  by  which  its  conductivity  is 
increased. 

959.  Determination  of  electromotive  force. — Wheatstone's  method. 
In  the  circuit  of  the  element  whose  electromotive  force  is  to  be  determined 
a  tangent  galvanometer  and  a  rheostat  are  inserted,  the  latter  being  so 
arranged  that  the  strength,  C,  of  the  current  is  a  definite  amount  ;  for 
example,  the  galvanometer  indicates  45°.  By  increasing  the  amount  of  the 
rheostat  wire  by  the  length,  /,  a  diminished  strength,  c  (for  instance,  40°),  is 
obtained. 

A  second  standard  element  is  then  substituted  for  that  under  trial,  and 
by  arranging  the  rheostat,  the  strength  of  the  current  is  first  made  equal  to 
C,  and  then,  by  addition  of  /,  length  of  the  rheostat,  is  made  =  c. 

Then  if  E  and  Ex  are  the  two  electromotive  forces,  R  and  Rx  their  resist- 
ances when  they  have  the  intensity  I,  and  /  and  /t  the  lengths  added,  we 
have 

Trial  Element.  Standard  Element. 

c-E 

~R 


from  which  we  have 

-.'.  '*-*•<••..;:     ,'. 

Hence  the  electromotive  forces  of  the  elements  compared  are  directly  as  the 
lengths  of  the  wire  interposed. 

Another  method  is  that  of  Wiedemann.  The  two  elements  are  con- 
nected in  the  same  circuit  with  a  tangent  galvanometer,  or  other  apparatus 
for  measuring  strength,  first,  in  such  a  manner  that  their  currents  go 
in  the  same  direction,  and  secondly,  that  they  are  opposed.  Then  if  the 
electromotive  forces  are  E  and  E',  their  resistances  are  R  and  R',  the  other 
resistances  in  the  circuits  r,  while  Cs  is  the  intensity  when  the  elements  are 
in  the  same  direction,  and  Cd  the  intensity  when  they  go  in  opposite  direc- 
tions, then 

C  =     E  +  E/      and  c  =       E-E7 

whence  -TV    E  (Cg  —  Cd) 

J—i     — • 

The  difference  of  potentials  or  EMF  between  any  two  points  of  a 
circuit  conveying  a  current,  such  as  that  of  a  magneto  machine,  may  be 
determined  by  charging  a  condenser  from  the  terminals  at  the  points  in 
question,  and  discharging  it  through  a  galvanometer  with  a  high  resistance, 
and  then  repeating  the  operation  with  a  standard  cell,  such  as  that  of  Latimer 
Clarke,  the  EMF  of  which  is  1-433  volts  (964).  If  </ is  the  deflection  of  the 
galvanometer  when  the  standard  cell  is  used,  and  D  the  deflection  after  the 


-961]  Divided  or  Branch  Currents.  935 

discharge  of  the  current,  and  if  a  shunt  be  used  so  that  only  —  of  the  current 

passes  through  the  galvanometer,  then  EMF  =^,-x  i*433- 

960.  Siemens'  electrical  resistance  thermometer. — Supposing  in  a 
Wheatstone's  bridge  arrangement,  after  the  ratio  r  \  rl=s  :  st  has  been  esta- 
blished, the  temperature  of  one  of  the  coils,  r,  for  instance,  be  increased,  the 
above  ratio  will  no  longer  prevail,  for  the  resistance  of  r  will  have  been 
altered  by  the  temperature,  and  the  ratio  of  s  and  s±  must  be  altered  so  as  to 
produce  equivalence.  On  this  idea  Siemens  has  based  a  mode  of  observing 
the  temperature  of  places  which  are  difficult  of  direct  access.  He  places  a 
coil  of  known  resistance  in  the  particular  locality  whose  temperature  is  to  be 
observed  :  it  is  connected  by  means  of  long  good  conducting  wires  with  the 
place  of  observation,  where  it  forms  part  of  a  Wheatstone's  bridge  arrange  - 
inent.  The  resistance  of  the  coil  is  known  in  terms  of  the  rheostat,  and  by 
preliminary  trials  it  has  been  ascertained  how  much  additional  wire  must  be 
introduced  to  balance  a  given  increase  in  the  temperature  of  the  resistance 
coil.  This  being  known,  and  the  apparatus  adjusted  at  the  ordinary  tempera- 
ture, when  the  temperature  of  the  resistance  coil  varies,  this  variation  in  either 
direction  is  at  once  known  by  observing  the  quantity  which  must  be  brought 
in  or  out  of  the  rheostat  to  produce  equivalence. 

This  apparatus  has  been  of  essential  service  in  watching  the  tempera- 
ture of  large  coils  of  telegraph  wire,  which,  stowed  away  in  the  hold  of  vessels, 
are  very  liable  to  become  heated.  It  might  also  be  used  for  the  continuous 
and  convenient  observation  of  underground  and  submarine  temperatures. 
If  a  coil  of  platinum  wire  were  substituted  for  the.  copper,  the  apparatus  could 
be  used  for  watching  the  temperature  of  the  interior  of  a  furnace.  It  has 
been  found  that  the  magnetism  of  ships  (715)  excited  so  perturbing  an 
influence  on  the  needle  of  the  galvanometer  as  to  make  its  indications 
untrustworthy.  Hence  for  use  in  such  cases  Siemens  replaces  the  galvano- 
meter, as  an  indicator,  by  a  voltameter  specially  constructed  for  the  purpose. 
The  same  principle  has  been  applied  by  Professor  Langley  to  the  inven- 
tion of  an  instrument  called  the  Bolometer,  for  measuring  radiant  heat.  In 
the  two  arms  of  a  Wheatstone's  bridge  are  introduced  resistances  which 
have  very  small  mass,  each  consisting  of  a  band  of  iron  half  a  millimetre  in 
breadth,  and  0-004  mms.  in  thickness  folded  on  itself  14  times  so  as  to  form 
a  rectangle  07  cm.  in  length  by  i  -2  cm.  in  breadth.  The  sensitiveness  is 
far  greater  than  that  of  the  most  sensitive  thermopile,  and  makes  it  possible 
to  measure  a  difference  of  temperature  of  the  JQ^QO  °f  a  degree  between  the 
two  resistances.  It  has  been  used  by  the  inventor  to  measure  the  distribu- 
tion of  heat  in  the  solar  spectrum. 

961.  Divided  or  branch  currents. — In  fig.  901  the  current  from  Bunsen's 
element  traverses  the  wire  rqpnm.  Let  us  take  the  case  in  which  any  two 
points  of  this  circuit,  n  and  qy  are  joined  by  a  second  wire,  nxq.  The  current 
will  then  divide  at  the  point  q  into  two  others,  one  of  which  goes  in  the 
direction  qpnm,  while  another  takes  the  direction  qznm.  The  two  points  q 
and  n  from  which  the  second  conductor  starts  and  ends  are  called  the  points 
of  derivation >  the  wire  qpm  and  the  wire  qxn  are  derived  wires.  The  currents 
which  traverse  these  wires  are  called  the  derived  vr  partial  currents  \  the 
current  which  traversed  the  circuit  rqpnm  before  it  branches  is  the  primitive 


936  Dynamical  Electricity.  [961  - 

current',  and  the  name  principal current  is  given  to  the  whole  of  the  current 
which  traverses  the  circuit  when  the  derived  wire  has  been  added.  The 

principal  cur- 
rent is  stronger 
than  the  primi- 
tive one,  because 
the  interposition 
of  the  wire  qxn 
lessens  the  total 
^  JP  resistance  of  the 
circuit. 

If    the    two 

derived  wires  are  of  the  same  length  and  the  same  section,  their  action 
would  be  the  same  as  if  they  were  juxtaposed,  and  they  might  be  replaced  by 
a  single  wire  of  the  same  length  but  of  twice  the  section,  and  therefore  with 
half  the  resistance.  Hence  the  current  would  divide  into  two  equal  parts 
along  the  two  conductors. 

When  the  two  wires  are  of  the  same  length  but  of  different  sections,  the 
current  would  divide  unequally,  and  the  quantity  which  traversed  each  wire 
would  be  proportional  to  its  section,  just  as  when  a  river  divides  into  two 
branches,  the  quantity  of  water  which  passes  in  each  branch  is  proportional 
to  its  dimensions.  Hence  the  resistance  of  the  two  conductors  joined  would 
be  the  same  as  that  of  a  single  wire  of  the  same  length,  the  section  of  which 
would  be  the  sum  of  the  two  sections. 

If  the  two  conductors  qpn  and  qxn  are  different,  both  in  kind,  length, 
and  section,  they  could  always  be  replaced  by  two  wires  of  the  same  kind 
and  length,  with  such  sections  that  their  resistances  would  be  equal  to  the 
two  conductors  ;  in  short,  they  might  be  replaced  by  equivalent  conductors. 
These  two  wires  would  produce  in  the  circuit  the  same  effect  as  a  single 
wire,  which  had  this  common  length,  and  whose  section  would  be  the  sum 
of  the  sections  thus  calculated.  The  current  divides  at  the  junction  into  two 
parts  proportional  to  these  sections,  or  inversely  as  the  resistances  of  the  two 
wires.  Suppose,  for  instance,  qpn  is  an  iron  wire  5  metres  in  length  and 
3  mm.  square  in  section,  and  qxn  a  copper  wire. 

The  first  might  be  replaced  by  a  copper  wire  a  metre  in  length,  whose 
section  would  be  f  x  \  (taking  the  conductivity  of  copper  at  7  times  that  of 
iron)  or  ^  square  mm.  The  second  wire  might  be  replaced  by  a  copper 
wire  a  metre  in  length  with  a  section  of  f  square  mm.  These  two  wires 
would  present  the  same  resistance  as  a  copper  wire  a  metre  in  length,  and 
with  a  section  of  ^  +  f  =  -^  'square  millimetres. 

The  principal  current  would  divide  along  the  wires  into  two  portions, 
which  would  be  as  ~  :  f . 

The  .most  important  laws  of  divided  circuits  are  as  follows  : — 
i.  The  sum  of  the  strengths  in  the  divided  parts  of  a  circuit  is  equal  to 
the  strength  of  the  principal  ctirrent. 

ii.  The  strengths  of  the  currents  in  the  divided  parts  of  a  circuit  are 
inversely  as  their  resistances;  or,  what  is  the  same,  the  division  of  a  current 
into  partial  currents  which  lie  between  two  points  is  directly  as  the  respective 
conductivities  of  these  branches. 


-963]  Absolute  Electrical  Units.  937 

And  as  problems  on  divided  or  shunt  circuits  frequently  occur  in  tele- 
graphy, the  following  formulae,  which  include  these  laws,  are  given  for  a  simple 
case. 

If  C  be  the  strength  of  the  current  in  the  undivided  part  of  the  circuit 
rqpnm,  and  if  c  is  the  strength  in  one  branch  (say)  in  the  above  figure  qpn 
and  c '  in  qxn  ;  if  R,  r,  and  t\  are  the  corresponding  resistances,  the  electro- 
motive force  being  E,  then 

E  r  Er, 


Rr  +  r^  +  rrl  Rr  +  R 

The  resistance  R,  of  the  whole  circuit  is 


c  =?s 


Rr+  Rr 


!— 

r+r 
and  therefore  the  total  resistance  of  the  branch  currents  qpn  and  qxn  is 


r+r, 

962.  The  electrodynamometer. — The  principle  of  the  electrodynamo- 
meter  is  that  of  measuring  the  repulsion  between  parallel  currents  moving 
in  opposite  directions,  one  of  them  being  fixed  and  the  other  movable.     Fig. 
902  represents  the  essential  features  of  a  form  devised  by  Messrs.  Siemens 
for  measuring  the  strength  of  the  powerful  currents  used  in  electric  lighting  : 
TV  is  a  coil  of  stout  insulated  copper  wire,  and  w'  a  single  wire  ;  nn  are 
mercury  cups,  and  k  k  binding  screw,  by  which  connection 

is  made  with  the  main  circuit  L  L. 

The  wire  vu'  is  surrounded  by  a  stout  spiral  spring, 
which  is  connected  at  one  end  with  this  wire,  and  at  the 
other  with  a  screw,  s ;  this  is  provided  with  an  index,  z, 
which  moves  over  a  graduated  scale,  S.  An  index,  z'z', 
is  also  fixed  to  the  wire  iv'.  At  the  outset  both  indexes 
point  to  zero ;  when  the  current  passes  it  will  be  seen 
from  the  direction  of  the  arrows  that  it  traverses  the 
fixed  and  movable  coils  in  opposite  directions,  and  the 
point  z'  is  displaced  along  the  scale.  By  turning  the 
screw  s  it  is  brought  back  to  zero,  in  doing  which  the 
index  z  is  moved  through  an  angle  which  is  a  measure 
of  the  torsion  of  the  spiral  spring  f,  and  this  angle  is 
proportional  to  the  square  of  the  strength  of  the  current 
by  which  the  movable  coil  is  deflected. 

963.  Absolute  electrical  units. — The  great  import- 
ance of  having  a  uniform  system  of  measurements  of  phy- 
sical magnitudes  which  should  be  universally  adopted  is  at 
once  obvious,  and  this  has  been  more  especially  felt  in  the 
applications  of  electricity.    The  first  step  in  this  direction 
was  taken  by  the  British  Association,  which  adopted  the 
system  of  absolute  units  known  as  the  C.G.S.  system,  of 

which  mention  has  already  been  made  (610,  709),  and  which  this  account  is 
intended  to  supplement. 

The  essence  of  an  absolute  system  of  physical  measurements  is  that  the 
various  units  may  be  directly  expressed  in  mechanical  units  (610).     A  system 


Fig.  902. 


93  8  Dynamical  Electricity.  [963- 

of  absolute  electrical  units  may  be  based  on  either  the  electrostatic,  the  electro- 
magnetic, or  again  on  the  electrodynamic  actions.  There  is  no  theoretical 
reason  why  one  should  be  preferred  to  another  of  these,  but  in  practice  only 
the  two  former  are  used.  Of  these  the  electrostatic  system  is  perhaps  the 
simpler,  but  that  based  on  electromagnetism  is  most  convenient,  and  best 
lends  itself  to  the  practical  determination  of  the  most  important  standards, 
such  as  those  of  electromotive  force  and  resistance. 

Electrostatic  Units. 

We  shall  distinguish  the  dimensions  of  these  units  by  small  letters  placed 
in  brackets. 

Quantity  of  Electricity,  q.  Coulomb's  law  given  for  the  repulsive  force 

between  two  equal  quantities  q,  of  electricity  at  the  distance  /,  f—  *L  (734), 

from  which  q  =  I  ^/f.  Hence  we  have  for  the  dimensions  of  unit  quantity 
of  electricity  [>]  =  //£  =  LlMiT'1. 

Potential,  v.    The  potential  of  a  quantity  of  electricity  at  the  distance  / 

is  the  quotient  of  the  quantity  by  the  distance.     Hence  \y\  =  ?-  =  UMiT"1. 

Capacity,  c.  The  capacity  of  a  conductor  is  the  quotient  of  the  quantity 
of  electricity  with  which  it  is  charged,  by  the  potential  which  this  quantity 

produces  in  it;   \c\  =£  from  which   <;]=L.     Hence  the  capacity  of  a  con- 

ductor is  expressed  by  a  length.  Unit  capacity  is  thus  that  of  a  body  which 
is  raised  by  unit  quantity.  to  unit  potential.  An  insulated  conducting  sphere 
which  has  a  diameter  of  one  centimetre  has  unit  capacity. 

Current,  i.  The  strength  of  a  current  is  the  quantity  of  electricity  which 

passes  in  a  given  time  ;  [*]  =  ?  =  UM>T2.     Accordingly  unit  current  is  that 

which  conveys  unit  quantity  of  electricity  in  a  second. 

Resistance,  r.  From  Ohm's  law  (825),  the  resistance  of  a  conductor  is 
the  quotient  of  difference  of  potentials  at  the  two  ends  of  a  wire  by  the 

strength  of  a  current.  Hence  [V]  =  ?  =  I/^T,  which  shows  that  the  dimen- 
sions of  resistance  are  the  inverse  of  a  velocity. 

Electromagnetic  Units. 
Quantity  of  magnetism.     From  Coulomb's  law/=—  -.  from  which  [M]  = 


-X,  that  is,  the  same  as  that  of  quantity  of  electricity  on  the  electro- 
static system.  Unit  magnetic  pole  is  that  which  repels  an  equal  pole  at  a 
distance  of  a  centimetre  with  a  force  of  a  dyne. 

Magnetic  Field.  H.     Unit   magnetic  field  is  that   field  in   which  unit 
quantity  magnetism  is  acted  on  by  unit  force.     Hence  F  =  HM,  from  which 


Current.  I.  The  unit  of  electrical  current  in  the  electromagnetic  system 
is  that  which,  traversing  unit  length  of  an  arc  of  a  circle  of  unit  radius, 
exerts  unit  force  on  unit  pole,  or  unit  magnetism  at  its  centre.  Its  dimen- 
sions are  [Q]  =  UM*!"1. 


-964]  Practical  Units.  939 

Quantity  of  electricity,  O.  The  quantity  of  electricity  conveyed  by  a  con- 
ductor is  the  product  of  the  current  by  the  time  that  it  lasts.  Hence  unit 
quantity  is  that  which  passes  in  a  second  in  a  conductor  in  which  unit  current 
is  flowing,  [O]  =  IT  =  L*M*. 

Resistance.  R.     The  resistance  of  a  conductor  may  be  defined  by  Joule's 

law,  W  =  PRT.    Hence  [R]  =     ,  that   is,   the  resistance  of  a   conductor   is 

expressed  by  a  velocity. 

Electromotive  force.      Difference  of  potentials  [E].     From  Ohm's  law, 


964.  Practical  units.  —  The  values  of  the  absolute  units  in  the  C.G.S. 
system  are  not  convenient  for  measuring  the  magnitudes  which  ordinarily 
occur.  Thus  the  absolute  unit  of  resistance  is  that  represented  by  the 
twenty-thousandth  part  of  a  millimetre  of  pure  copper  wire  a  millimetre  in 
diameter.  It  has  therefore  been  necessary  to  choose  units  better  suited 
for  practical  uses,  and  at  the  International  Congress  of  Electricians  at  Paris 
in  1  88  1  an  International  Commission  was  formed  for  the  purpose  of  deciding 
on  such  units  and  determining  their  value.  In  1884  the  Commission  agreed 
to  recommend  the  following,  which  are  in  the  main  those  introduced  by  the 
British  Association. 

The  practical  unit  of  resistance  is  equal  to  io9  absolute  electromagnetic 
C.G.S.  units  of  resistance,  and  is  called  the  Ohm.  It  has  been  decided  to 
represent  it  by  a  column  of  pure  mercury  with  a  cross  section  of  a  square 
millimetre  ;  its  exact  length  has  been  determined  experimentally  by  the  Com- 
mission, and  has  been  taken  at  i  -06  metre.  This  is  known  as  the  legal  or 
Congress  ohm.  A  wire  of  pure  copper,  a  millimetre  in  diameter  and  46*25 
metres  in  length,  has  a  resistance  of  one  ohm.  Siemens'  unit  (952)  has  a 
resistance  of  0-94339  ohm.  The  copper  conducting  wire  of  an  ordinary  sub- 
marine cable  has  a  resistance  of  about  1  1  ohms  per  mile. 

In  order  to  express  multiples  and  sub-multiples  the  prefixes  mega  or 
micro  are  used,  which  are  respectively  a  million  times  as  great  or  as  small. 
Thus  a  megohm  is  io6  ohms,  that  is,  io15  absolute  units  of  resistance.  In 
like  manner  a  microhm  is  icr6  ohm,  that  is,  io3  =  1000  such  units. 

The  Volt  is  the  practical  unit  of  electromotive  force  or  of  difference  of 
potentials,  and  is  equal  to  io8  absolute  units.  From  the  difficulty  of  getting 
an  element  which  is  perfectly  constant,  more  especially  when  it  is  closed,  the 
standard  of  EMF  is  best  derived  from  measurements  of  resistance  and  of 
strength  of  current,  which  are  both  convenient  and  very  accurate.  The 
electromotive  force  of  a  Daniell's  cell  is  about  a  twelfth  greater  than  a  volt. 
According  to  the  latest  determinations  of  Lord  Rayleigh  a  Latimer  Clark's 
element  has  the  EMF  1*433  volt. 

The  Ampere  is  the  unit  of  current,  and  is  the  current  produced  by  the 
electromotive  force  of  a  volt  in  a  circuit  having  a  resistance  of  an  ohm.  It 
is  therefore  equal  to  icr1  C.G.S.  units.  A  millampere  is  the  thousandth  of 
an  ampere. 

The  resistance  of  a  Daniell's  element  with  an  external  cylinder  of  zinc, 
8  inches  high  and  3.^  in  diameter,  surrounding  the  porous  pot,  is  about  1-3 
ohm,  and  as  its  EMF  is  ro8  volt  its  current  when  on  short  circuit  is  about 
0-8  ampere.  In  like  manner  a  medium-sized  Bunsen  has  a  resistance  of 


940  Dynamical  Electricity.  [964- 

about  o-i  ohm,  and  as  its  EMF  is  r8  volt,  the  current  on  short  circuit  is 
1 8  amperes.  A  Brush  machine  the  current  of  which  ignited  16  lamps  had  an 
EMF  of  839  volts  ;  its  internal  resistance  was  10-55  and  the  external,  in- 
cluding the  lamps,  was  73  ohms.  Accordingly  the  current  was  10-04  amperes. 
A  Holtz  machine  has  in  electromagnetic  measure  the  EMF  of  90000  volts  ; 
its  internal  resistance,  when  it  makes  two  turns  in  a  second,  is  calculated  at 
27  x  ios  ohms,  and  accordingly  its  current  is  jo^oo  °f  an  ampere,  or  g1-  of  a 
millampere.  Such  a  current  is  too  weak  for  telegraph  work  ;  the  currents 
which  are  used  with  the  ordinary  Morse  receivers  have  a  strength  of  14  to 
1 6  millamperes. 

The  Coulomb  is  the  unit  of  quantity  of  electricity,  and  is  that  quantity 
which  traverses  the  section  of  a  conductor  in  a  second,  when  a  current 
of  an  ampere  is  passing  though  it. 

The  Farad  is  the  unit  of  capacity,  and  is  such  that  in  a  condenser  of 
that  capacity  the  quantity  of  a  coulomb  produces  a  difference  of  potential 
of  a  volt.  It  is  io-9  C.G.S.  units. 

The  farad  is  too  large  a  unit  for  praptical  use,  thus  the  capacity  of  the 
globe  is  only  joiiloo  °f  a  farad.  Accordingly  the  technical  unit  of  capacity 
is  the  millionth  part  of  this,  and  is  called  the  microfarad.  This  is  io~15  units. 
A  Leyden  jar  with  a  total  coated  surface  of  a  square 
metre,  and  the  glass  of  which  is  i  mm.  thick,  has  a 
capacity  of  ^  of  a  microfarad.  The  capacity  of  an 
ordinary  submarine  cable  may  be  taken  at  about  g  of  a 
microfarad  per  knot  or  nautical  mile  of  1852  metres. 

The  practical  standards  consist  of  circular  or 
square  sheets  of  tinfoil  with  projecting  tongues,  a  and^' 
(fig.  903),  fastened  on  thin  sheets  of  mica.  Between 
each  such  coated  sheet  is  placed  an  uncoated  one  of 
mica,  the  two  sets  of  tongues  being  severally  con- 
nected with  each  other,  and  thus  the  coatings  repre- 
sent the  coated  surfaces  of  a  condenser.  The  whole 
is  enclosed  in  a  box  ;  a  condenser  having  a  capacity 
of  a  microfarad  will  represent  a  coated  surface  of  over  6  square  yards. 

Watt. — The  energy,  W,  of  an  electrical  current  in  unit  time  may  be 

variously  expressed  ;  thus  W  =  C~R  =  —   =  CE.    This  latter  expression  is  the 

R 

most  convenient  for  practical  purposes,  and  represents  the  work  done  by  unit 
current  (ampere)  when  impelled  by  an  EMF  of  a  volt.  It  is  thus  a 
voltampere,  and  on  the  proposal  of  the  late  Sir  W.  Siemens  has  been 
called  a  Watt.  It  is  equal  to  io7  ergs.  It  may  also  be  defined  as  the  work 
done  by  the  quantity  of  electricity  of  a  coulomb  falling  through  a  difference 
of  potentials  equal  to  a  volt,  and  in  this  form  the  definition  is  closely 
analogous  to  that  of  a  kilogramme  metre. 

The  watt  is  ^  of  an  English  horse-power,  or  one  horse-power  =  746  watts. 

965.  Relation  of  the  electrostatic  to  tlie  electromagnetic  unit. — If 
we  compare  the  dimensions  of  the  units  of  quantity  and  the  other  electrical 
magnitudes,  in  the  electrostatic  with  those  of  the  corresponding  dimensions 
as  expressed  in  the.  electromagnetic  system,  we  find  that  the  ratios  are 


-965]       Relation  of  Electrostatic  to  Electromagnetic  Unit.        941 

independent  of  the  unit  of  mass,  and  that  — ,  that  is,  the  expression  of  a 

velocity,  always  enters  into  the  ratio  between  them.  Now  the  ratio  of  the 
two  sets  of  units  may  be  determined  experimentally.  Suppose,  for  in- 
stance, that  a  condenser  is  charged  with  electricity.  Knowing  its  dimen- 
sions, the  quantity,  q,  of  the  charge  may  be  determined  in  electrostatic 
measure,  by  measuring,  for  instance,  the  repulsion  which  a  given  proportion 
of  the  total  charge  produces  in  a  torsion  balance  of  known  dimensions.  The 
same  condenser,  being  charged  to  the  same  extent,  may  be  discharged 
through  a  galvanometer,  and  by  measuring  the  deflection  produced,  and 
knowing  the  constants  of  the  instrument,  the  quantity  may  be  obtained  in 
electromagnetic  units,  and  thus  the  ratio  of  the  quantity  expressed  in  the  two 
sets  of  units  may  be  deduced.  Or,  again,  the  EMF  of  a  Daniell's  cell  may 
be  measured  first  by  the  aid  of  an  absolute  electrometer,  which  will  give  in 
electrostatic  units  of  potential  about  0*0036.  On  the  other  hand  the  potential 
determined  in  electromagnetic  measure  has  the  value  ro88  x  io8.  Hence 
it  would  thus  be  found  that  in  round  numbers  the  electromagnetic  unit 
of  quantity  is  equal  to  3-10  °  electrostatic  units  of  quantity.  This  is  easily 
intelligible,  since  the  latter  is  the  quantity  of  electricity  which  attracts  or 
repels  another  equal  quantity  at  a  distance  of  I  cm.  with  a  force  of  a  dyne, 
while  the  latter  is  the  quantity  which  traverses  the  wire  in  a  second  when 
the  current  has  unit  intensity.  Similarly,  by  making  determinations  of  the 
ratio  in  all  cases  in  which  the  same  magnitude  may  be  determined  in  elec- 
trostatic as  well  as  in  electromagnetic  measure,  it  is  found  that  the  agree- 
ment in  the  numbers  found  is  very  close,  and  as  the  mean  of  the  best 
results  is  2-9857  x  io10.  As  the  ratio  between  the  units  is  always  of  the 
dimensions  of  a  velocity,  and  holds  under  the  condition  that  the  centimetre 
is  the  unit  of  length,  and  the  second  is  the  unit  of  time,  this  velocity  is 
298,570  kilometres,  or  185,530  miles,  in  a  second.  Now  this  number  agrees 
very  closely  with  that  for  the  velocity  of  light — 185,420  miles  (507).  This 
coincidence  can  scarcely  be  accidental,  but,  no  doubt,  arises  from  the  fact 
that  the  phenomena  are  correlated,  and  that  the  medium  in  which  the  two 
actions  take  place  is  the  same. 


942  Dynamical  Electricity.  [966- 


CHAPTER   X. 

ANIMAL   ELECTRICITY. 

966.  Muscular  currents. — The  existence  of  electrical  currents  in  living 
muscle. was  first  indicated  by  Galvani,  but  his  researches  fell  into  oblivion 
after  the  discovery  of  the  voltaic  pile,  which  was  supposed  to  explain  all  the 
phenomena.     Since  then,  Nobili,  Matteucci,  and  others,  especially,  in  late 
years,  Du  Bois  Reymond,  have  shown  that  electric  currents  do  exist  in  living 
muscles  and  nerves,  and  have  investigated  their  laws. 

For  investigating  these  currents  it  is  necessary  to  have  a  delicate  gal- 
vanometer, and  also  electrodes  which  will  not  become  polarised  or  give  a 
current  of  their  own,  and  which  will  not  in  any  way  alter  the  muscle  when 
placed  in  contact  with  it  ;  the  electrodes  which  satisfy  these  conditions  best 
are  those  of  Du  Bois  Reymond,  as  modified  by  Bonders.  Each  consists^of 
a  glass  tube,  one  end  of  which  is  narrowed  and  stopped  by  a  plug  of  paste 
made  by  moistening  china-clay  with  a  half  per  cent,  solution  of  common  salt  ; 
the  tube  is  then  partially  filled  with  a  saturated  solution  of  sulphate  of  zinc  ; 
and  into  this  dips  the  end  of  a  piece  of  thoroughly  amalgamated  zinc  wire, 
the  other  end  of  which  is  connected  by  a  copper  wire  with  the  galvanometer  ; 
the  moistened  china-clay  is  a  conducting  medium  which  is  perfectly  neutral 
to  the  muscle,  and  amalgamated  zinc  in  solution  of  sulphate  of  zinc  does  not 
become  polarised. 

967.  Currents  of  muscle  at  rest. — In  describing  these  experiments -the 
surface  of  the  muscle  is  called  the  natural  longitudinal  section  ;  the  tendon 
the  natural  transverse  section  ;    and  the  services  obtained  by  cutting  the 
muscle  longitudinally  or  transversely  are  respectively  the  artificial  longitu- 
dinal and  artificial  transverse  sections. 

If  a  living  irritable  muscle  be  removed  from  a  recently  killed  frog,  and 
the  clay  of  one  electrode  be  placed  in  contact  with  its  surface,  and  of  the 
other  with  its  tendon,  the  galvanometer  will  indicate  a  current  from  the 
former  to  the  latter  ;  showing,  therefore,  that  the  surface  of  the  muscle  is 
positive  with  respect  to  the  tendon.  By  varying  the  position  of  the  elec- 
trodes, and  making  various  artificial  sections,  it  is  found — 

1.  That  any  longitudinal  section  is  positive  to  any  transverse  section. 

2.  That  any  point  of  a  longitudinal  section  nearer  the   middle   of  the 
muscle  is  positive   to  any  other  point  of  the  same  section  farther  from  the 
centre. 

3.  In  any  artificial  transverse  section  any  point  nearer  the  periphery  is 
positive  to  one  nearer  the  centre. 

4.  The  current  obtained  between  two  points  in  a  longitudinal  or  in  a 


-967J 


Currents  of  Muscle  at  Rest. 


943 


Fig.  904. 


transverse  section  is  always  much  more  feeble  than  that  obtained  between 
two  different  sections. 

5.  No  current  is  obtained  if  two  points  of  the  same  section  equidistant 
from  its  centre  be  taken. 

6.  To  obtain  these  currents  it  is  not  necessary  to  employ  a  whole  muscle, 
or  a  considerable  part  of  one,  but  the  smallesrfragment  that  can  be  experi- 
mented with  is  sufficient. 

7.  If  a  muscle  be  cut  straight  across,  the  most  -powerful  current  is  that 
from  the  centre  of  the  natural  longitudinal  section  to  the  centre  of  the  arti- 
ficial transverse  ;  but  if  the  muscle  be 

cut  across  obliquely,  as  in  fig.  904,  the 
most  positive  point  is  moved  from  c 
towards  <£,  and  the  most  negative  from 
dT  towards  a  (^  currents  of  inclination'1*}. 

To  explain  the  existence  and  rela- 
tions of  these  muscular  currents,  it  may  be  supposed  that  each  muscle  is 
made  up  of  regularly  disposed  electromotor  elements,  which  may  be  re- 
garded as  cylinders  whose  axes  are  parallel  to  that  of  the  muscle,  and 
whose  sides  are  charged  with  positive  and  their  ends  with  negative  electri- 
city ;  and,  further,  that  all  are  suspended  and  enveloped  in  a  conducting 
medium.  In  such  a  case  (fig.  904)  it  is  clear  that  throughout  most  of  the 
muscle  the  positive  electricities  of  the  opposed  surfaces  would  neutralise  one 
another,  as  would  also  the  negative  charges  of  the  ends  of  the  cylinders  ;  so 
that,  so  long  as  the  muscle  was  intact,  only  the  charges  at  its  sides  and  ends 
would  be  left  to  manifest  themselves  by  the  production  of  electromotive 
phenomena ;  the  whole  muscle  being  enveloped  in  a  conducting  stratum,  a 
current  would  constantly  be  passing  from  the  longitudinal  to  the  transverse 
section,  and,  a  part  of  this  being  led  off  by  the  wire  circuit,  would  manifest 
itself  in  the  galvanometer. 

This  theory  also  explains  the  currents  between  two  different  points  on  the 
same  section  ;  the  positive  charge  at  <£,  for  instance  (fig.  905),  would  have  more 
resistance  to  overcome  in  get- 
ting to  the  transverse  section 
than  that  at  d,  therefore  it  has 
a  higher  tension  ;  and  if  b  and 
d  are  connected  by  the  elec- 
trodes, b  will  be  found  positive  — —      — —      — —      -^—      — —        x 

to  d,  and  a  current  will  pass 
from  the  former  to  the  latter. 

What  are  called  currents 
of  inclination  are  also  explic- 
able on  the  above  hypothesis,  p. 
for  the  oblique  section  can  be 

represented  as  a  number  of  elements  arranged  as  in  fig.  906,  so  that  both  the 
longitudinal  surfaces  and  the  ends  of  the  cylinders  are  laid  bare,  and  it  can 
thus  be  regarded  as  a  sort  of  oblique  pile  whose  positive  pole  is  towards  b 
and  its  negative  at  a,  and  whose  current  adds  itself  algebraically  to  the 
ordinary  current  and  displaces  its  poles  as  above  mentioned. 

A  perfectly  fresh  muscle,  very  carefully  removed,  with  the  least  possible 


+  -f 
zf- 


944  Dynamical  Electricity.  [967- 

contact  with  foreign  matters,  sometimes  gives  almost  no  current  between  its 
different  natural  sections,  and  the  current  always  becomes  more  marked 
after  the  muscle  has  been  exposed  a  short  time  ;  nevertheless,  the  pheno- 
mena are  vital,  for  the  currents  disappear  completely  with  the  life  of  the 
muscle,  sometimes  becoming  first  irregular  or  even  reversed  in  direction. 

968.  Rheoscopic  frog-.     Contraction  without  metals. — The  existence 
of  the  muscular  currents  can  be  manifested  without  a  galvanometer,  by  using 
/s  another  muscle  as  a  galvanoscope. 

Thus,  if  the  nerve  of  one  living 
muscle  of  a  frog  be  dropped  sud- 
denly on  another  living  muscle,  so 
as  to  come  in  contact  with  its 
longitudinal  and  transverse  sec- 


a  tions,    a   contraction    of    the    first 
muscle  will  occur,  due  to  the  stimu- 
lation of  its  nerve  by  the  passage  through  it  of  the  electric  current  derived 
from  the  surface  of  the  second. 

969.  Currents  in  active  muscle. — When  a  muscle  is  made  to  contract 
there  occurs  a  sudden  diminution  of  its  natural  electric  current,  as  indicated 
by  the  galvanometer.     This  is  so  instantaneous  that,  in  the  case  of  a  single 
muscular  contraction,  it  does  not  overcome  the  inertia  of  the  needle  of  the 
galvanometer  ;  but  if  the  contractions  be  made  to  succeed  one  another  very 
rapidly — that  is,  if  the  muscle  be  tetanised  (827) — then  the  needle  swings 
steadily  back  towards  zero  from  the  position  in  which  the  current  of  the 
resting  muscle  had  kept  it,  often  gaining  such  momentum  in  the  swing  as  to 
pass  beyond  the  zero  point,  but  soon  reverting  to  some  point  between  zero 
and  its  original  position. 

The  negative  variation  in  the  case  of  a  simple  muscular  contraction  can, 
however,  be  made  manifest  by  using  another  muscle  as  a  rheoscope  ;  if  the 
nerve  of  this  second  muscle  be  laid  over  the  first  muscle  in  such  a  position 
that  the  muscular  current  passes  through  it,  and  the  first  muscle  be  then  made 
to  contract,  the  sudden  alteration  in  the  strength  of  its  current  stimulates 
the  nerve  laid  on  it  (827),  and  so  causes  a  contraction  of  the  muscle  to  which 
the  latter  belongs. 

The  same  phenomenon  can  be  demonstrated  in  the  muscles  of  warm- 
blooded animals  ;  but  with  less  ease,  on  account  of  the  difficulty  of  keeping 
them  alive  after  they  are  laid  bare  or  removed  from  the  body.  Experiments 
made  by  placing  electrodes  outside  the  skin,  or  passing  them  through  it,  are 
inexact  and  unsatisfactory. 

970.  Electric  currents  in  nerve. — The  same  electromotor  indications 
can  be  obtained  from  nerves  as  from  muscles  ;  at  least,  as  far  as  their  smaller 
size  will  permit ;   the  currents  are  more  feeble  than  the  muscular  ones,  but 
can  be  demonstrated  by  the  galvanometer  in  a  similar  way.     Negative  vari- 
ation has  been  proved  to  occur  in  active  nerve  as  in  active  muscle.      The 
effect  of  a  constant  current  passed  through  one  part  of  a  nerve  on  the  amount 
of  the  normal  nerve-current,  measured  at  another  part,  has  already  been 
described  (Chap.  III.,  Electrotonus). 

971.  Electrical  fish. — Electrical  fish  are  those  fish  which  have  the  re- 
markable property  of  giving,  when  touched,  shocks  like  those  of  the  Leyden 


-971]  Electrical  Fish.  945 

jar.  Of  these  fish  there  are  several  species,  the  best  known  of  which  are  the 
torpedo,  the  gymnotus,  and  the  silurus.  The  torpedo,  which  is  very  common 
in  the  Mediterranean,  has  been  carefully  studied  by  Becquerel  and  Breschet 
in  France,  and  by  Matteuccj  in  Italy.  The  gymnotus  was  investigated  by 
Humboldt  and  Bonpland  in  South  America,  and  in  England  by  Faraday, 
who  had  the  opportunity  of  examining  live  specimens. 

The  shock  which  they  give  serves  both  as  a  means  of  offence  and  of 
defence.  It  is  purely  voluntary,  and  becomes  gradually  weaker  as  it  is 
repeated  and  as  these  animals  lose  their  vitality,  for  the  electrical  action 
soon  exhausts  them  materially.  According  to  Faraday,  the  shock  which  the 
gymnotus  gives  is  equal  to  that  of  a  battery  of  15  jars  exposing  a  coating  of 
25  square  feet,  which  explains  how  it  is  that  horses  frequently  give  way  under 
the  repeated  attacks  of  the  gymnotus. 

Numerous  experiments  show  that  these  shocks  are  due  to  ordinary 
electricity.  For  if,  touching  with  one  hand  the  back  of  the  animal,  the 
belly  is  touched  with  the  other,  or  with  a  metal  rod,  a  violent  shock  is  felt 
in  the  wrists  and  arms  ;  while  no  shock  is  felt  if  the  animal  is  touched  with 
an  insulating  body.  Further,  when  the  back  is  connected  with  one  end  of  a 
galvanometer  wire  and  the  belly  with  the  other,  at  each  discharge  the  needle 
is  reflected,  but  immediately  turns  to  zero,  which  shows  that  there  is  an 
instantaneous  current  ;  and,  moreover,  the  direction  of  the  needle  shows  that 
the  current  goes  from  the  back  to  the  belly  of  the  fish.  Lastly,  if  the  current 
of  a  torpedo  be  passed  through  a  helix  in  the  centre  of  which  is  a  small  steel 
bar,  the  latter  is  magnetised  by  the  passage  of  a  discharge. 

By  means  of  the  galvanometer,  Matteucci  established  the  following 
facts  :— 

i.  When  a  torpedo  is  lively,  it  can  give  a  shock  in  any  part  of  its  body, 
but  as  its  vitality  diminishes,  the  parts  at  which  it  can  give  a  shock  are 
nearer  the  organ  which  is  the  seat  of  the  development  of  electricity.  2.  Any 
point  of  the  back  is  always  positive  as  compared  with  the  corresponding 
point  of  the  belly.  3.  Of  any  two  points  at  different  distances  from  the  elec- 
trical organ,  the  nearest  always  plays  the  part  of  a  positive  pole,  and  the 
farthest  that  of  negative  pole.  With  the  belly  the  reverse  is  the  case. 

The  organ  where  the  electricity  is  produced  in  the  torpedo  is  double,  and 
formed  of  two  parts  symmetrically  situated  on  two  sides  of  the  head  and 
attached  to  the  skull-bone  by  the  internal  face.  Each  part  consists  of  nearly 
parallel  lamellae  of  connective  tissue  inclosing  small  chambers,  in  which  lie 
the  so-called  electrical  plates,  each  of  which  has  a  final  nerve-ramification 
distributed  on  one  of  its  faces.  This  face,  on  which  the  nerve  ends,  is  turned 
the  same  way  in  all  the  plates,  and  when  the  discharge  takes  place  is  always 
negative  to  the  other. 

Matteucci  investigated  the  influence  of  the  brain  on  the  discharge.  For 
this  purpose  he  laid  bare  the  brain  of  a  living  torpedo,  and  found  that  the 
first  three  lobes  could  be  irritated  without  the  discharge  being  produced,  and 
that  when  they  were  removed  the  animal  still  possessed  the  faculty  of  giving 
a  shock.  The  fourth  lobe,  on  the  contrary,  could  not  be  irritated  without 
an  immediate  production  of  the  discharge ;  but  if  it  was  removed,  all  dis- 
engagement of  electricity  disappeared,  even  if  the  other  lobes  remained 
untouched.  Hence  it  would  appear  that  the  primary  source  of  the  electricity 

3P 


946  Dynamical  Electricity.  [971- 

elaborated  is  the  fourth  lobe,  whence  it  is  transmitted  by  means  of  the  nerves 
to  the  two  organs  described  above,  which  act  as  multipliers.  In  the  silurus 
the  head  appears  also  to  be  the  seat  of  the  electricity  ;  but  in  the  gymnotus 
it  is  found  in  the  tail. 

972.  Application  of  electricity  to  medicine.— The  first  applications  of 
electricity  to  medicine  date  from  the  discovery  of  the  Leyden  jar.  Nollet 
and  Boze  appear  to  have  been  the  first  who  thought  of  the  application,  and 
soon  the  spark  and  electrical  friction  became  a  universal  panacea,  but  it 
must  be  admitted  that  the  results  of  subsequent  trials  did  not  come  up  to  the 
hopes  of  the  early  experimentalists. 

After  the  discovery  of  dynamic  electricity  Galvani  proposed  its  applica- 
tion to  medicine  ;  since  which  time  many  physicists  and  physiologists  have 
been  engaged  upon  this  subject,  and  yet  there  is  still  much  uncertainty  as  to 
the  real  effects  of  electricity,  the  cases  in  which  it  is  to  be  applied,  and  the 
best  mode  of  applying  it.  Practical  men  prefer  the  use  of  currents  to  that 
of  statical  electricity,  and,  except  in  a  few  cases,  discontinuous  to  con- 
tinuous currents.  There  is,  finally,  a  choice  between  the  currents  of  the 
battery  and  induction  currents  ;  further,  the  effects  of  the  latter  differ, 
according  as  induction  currents  of  the  first  or  second  order  are  used.  In 
fact,  since  induction  currents,  although  very  intense,  have  a  very  feeble 
chemical  action,  it  follows  that  when  they  traverse  the  organs,  they  do  not 
produce  the  chemical  effects  of  the  current  of  the  battery,  and  hence  do  not 
tend  to  produce  the  same  disorganisation.  Further,  in  electrifying  the 
muscles  of  the  face,  induction  currents  are  to  be  preferred,  for  these  currents 
only  act  feebly  on  the  retina,  while  the  currents  of  the  battery  act  energetically 
on  this  organ,  and  may  affect  it  dangerously.  There  is  a  difference  in  the 
action  of  induced  currents  of  different  orders  ;  for  while  the  primary  induced 
current  causes  lively  muscular  actions,  but  has  little  action  on  the  cutaneous 
sensibility,  the  secondary  induced  current,  on  the  contrary,  increases  the 
cutaneous  sensibility  to  such  a  point  that  its  use  ought  to  be  proscribed  to 
persons  whose  skin  is  very  irritable. 

Hence  electrical  currents  should  not  be  applied  in  therapeutics  without  a 
thorough  knowledge  of  their  various  properties.  They  ought  to  be  used 
with  great  prudence,  for  their  continued  action  may  produce  serious  accidents. 
Matteucci  says  :  '  In  commencing,  a  feeble  current  must  always  be  used. 
This  precaution  now  seems  to  me  the  more  important  as  I  did  not  think  it 
so  before  seeing  a  paralytic  person  seized  with  almost  tetanic  convulsions 
under  the  action  of  a  current  formed  of  a  single  element.  Take  care  not  to 
continue  the  application  too  long,  especially  if  the  current  is  energetic. 
Rather  apply  a  frequently  interrupted  current  than  a  continuous  one,  espe- 
cially if  it  be  strong  ;  but  after  twenty  or  thirty  shocks,  at  most,  let  the 
patient  take  a  few  moments'  rest.' 

Of  late  years,  however,  feeble  continuous  currents  have  come  more  into 
use.  They  are  frequently  of  great  service  when  applied  skilfully,  so  as  to 
throw  the  nerves  of  the  diseased  part  into  a  state  of  cathelectrotonus  or 
anelectrotonus  (827),  according  to  the  object  which  is  wished  for  in  any 
given  case. 


-974]  Meteorograph.  947 


ELEMENTARY   OUTLINES 


METEOROLOGY  AND  CLIMATOLOGY. 


METEOROLOGY. 

973.  Meteorology. — The  phenomena  which  are  produced  in  the  atmo- 
sphere are  called  meteors  ;  and  meteorology  is  that  part  of  physics  which  is 
concerned  with  the  study  of  these  phenomena. 

A  distinction  is  made  between  aerial  meteors,  such  as  winds,  hurricanes, 
and  whirlwinds  ;  aqueous  meteors,  comprising  fogs,  clouds,  rain,  dew,  snow, 
and  hail ;  and  luminous  meteors,  as  lightning,  the  rainbow,  and  the  aurora 
borealis. 

974.  Meteorograph. — The  importance  of  being  able  to  make  continuous 
observations  of  various  meteorological  phenomena  has  led  to  the  construc- 
tion of  various  forms  of  automatic  arrangements  for  this  purpose,  of  which 
that  of  Osier  in  England  may  be  specially  mentioned.     One  of  the  most  com- 
prehensive and  complete  is  Secchi's  meteorograph,  of  which  we  will  give  here 
a  description. 

It  consists  of  a  base  of  masonry  about  2  feet  high  (fig.  907)  ;  on  this  are 
fixed  four  columns,  about  2.\  yards  high,  which  support  a  table  on  which  is 
a  clockwork  regulating  the  whole  of  the  movements  of  the  machine.  The 
phenomena  are  registered  on  two  sheets  which  move  downwards  on  two 
opposite  sides,  their  motion  being  regulated  by  clockwork.  One  of  them 
occupies  ten  days  in  so  doing,  and  on  it  are  registered  the  direction  and 
velocity  of  the  wind,  the  temperature  of  the  air,  the  height  of  the  barometer, 
and  the  occurrence  of  rain  ;  on  the  second,  which  only  takes  two  days,  the 
barometric  height  and  the  occurrence  of  rain  are  repeated,  but  on  a  much 
larger  scale  ;  this  gives,  moreover,  the  moisture  of  the  air. 

Direction  of  the  wind. — The  four  principal  directions  of  the  wind  are 
registered  by  means  of  four  pencils  fixed  at  the  top  of  thin  brass  rods, «,  b,  c, 
d  (fig.  907),  which  are  provided  at  the  bottom  ends  with  soft  iron  keepers 
attracted  by  two  electromagnets,  E  E',  for  west  and  north,  and  by  two  other 
electromagnets  lower  down  for  south  and  east.  These  four  electromagnets, 
as  well  as  all  the  others  on  the  apparatus,  are  worked  by  a  single  sand 
battery  (886)  of  twenty-four  elements.  The  passage  of  the  current  in  one  or 

3P2 


948 


Meteorology. 


[974 


the  other  of  these  electromagnets  is  regulated  by  means  of  a  vane  (fig.  908) 
consisting  of  two  plates  at  an  angle  of  thirty  degrees  with  each  other,  by 


Jlf^^  : 

Fig.  907. 

which  greater  steadiness  is  obtained  than  with  a  single  plate.     In  the  rod  of 
the  vane  is  a  small  brass  plate,  o  ;  this  part  is  in  the  centre  of  four  metal 


974]  Meteorograph.  949 

sectors  insulated  from  each  other,  and  each  provided  with  a  binding  screw, 

by  which  connection  is  established  with  the  binding  screw  K,  and  the  electro- 

magnets   E  E'.       The    battery    current 

reaches  the  rod  of  the  vane  by  the  wire  <z, 

and  thence  the  sliding  contact  o,  which 

leads  it  to  the  electromagnet  for  the  north, 

for  instance. 

If  the  current  passed  constantly  in  this 
electromagnet,  the  pencil  on  the  rod  d 
would  be  stationary  ;  but  from  the  electro- 
magnet E'  the  current  passes  into  a  second 
electromagnet,  n,  over  the  clockwork,  and 
is  thereby  alternately  opened  and  closed, 
as  will  be  seen  in  speaking  of  the  velocity 
of  the  wind.  Hence  the  armature  of  the 
rod  d,  alternately  free  and  attracted,  os- 
cillates ;  and  its  pencil,  which  is  always 
pressed  against  the  paper  AD  by  the 
elasticity  of  the  rod,  traces  on  it  a  series 
of  parallel  dashes  as  the  paper  descends, 
and  so  long  as  the  wind  is  in  the  north. 
If  the  wind  changes  then  to  west,  for 
instance,  the  rod  a  oscillates,  and  its 
pencil  traces  a  different  series  of  marks. 

The  rate  of  displacement  of  the  paper  being  known,  we  get  the  direction  of 
the  prevalent  wind  at  a  given  moment. 

Velocity  of  the  wind.  —  This  is  indi- 
cated by  a  Robinson's  anemometer,  and 
is  registered  in  two  ways  ;  by  two  counters 
which  mark  in  decametres  and  kilometres 
the  distance  travelled  by  the  wind  ;  and 
by  a  pencil  which  traces  on  a  table  a  curve, 
the  ordinates  of  which  are  proportional  to 
the  velocity  of  the  wind. 

Robinson,  who  originally  devised  this 
form  of  anemometer  (fig.  909),  proved  that 
its  velocity  is  proportional  to  that  of  the 
wind  ;  in  the  present  apparatus  the  length 
of  the  arms  is  so  calculated  that  each  revo- 
lution corresponds  to  a  velocity  of  ten 
metres  (975).  The  anemometer  is  placed 
at  a  considerable  distance  from  the  meteor- 
ograph, and  is  connected  with  it  by  a 
copper  wire,  d,  which  passes  to  the  electro- 
magnet, n,  of  the  counter.  On  its  rod  there 
is,  moreover,  an  excentric,  which  at  each 
turn  touches  a  metallic  contact  in  connec- 
tion with  the  wire  d.  The  battery  current  reaches  the  anemometer  by  a  wire, 
#,  the  current  is  closed  once  at  each  rotation,  and  passes  to  the  electro- 


Fig.  909. 


950  Meteorology.  [974 

magnet  «,  which  moves  the  needle  of  the  dial  through  one  division.  There 
are  fifty  such  divisions,  which  represent  as  many  turns  of  the  vane,  and 
therefore  so  many  multiples  of  ten  metres.  The  lower  dial  marks  the  kilo- 
metres. 

The  curve  of  velocities  is  traced  on  the  sheet  by  a  pencil,  /,  fixed  to  a 
horizontal  rod.  This  is  joined  at  its  two  ends  to  two  guide-rods,  o  and  j, 
which  keep  it  parallel.  The  pencil  and  the  rod  are  moved  laterally  by  a 
chain  which  passes  over  two  pulleys,  r'  and  r,  and  is  then  coiled  over  a  pulley 
placed  on  the  shaft  of  the  counter,  but  connected  with  it  merely  by  a  ratchet- 
wheel  :  and  moved  thus  by  the  counter  and  the  chain,  the  pencil  traces 
every  hour  on  the  sheet  a  line  the  length  of  which  is  proportioned  to  the 
velocity  of  the  wind.  From  hour  to  hour  an  excentric  moved  by  clockwork 
detaches,  from  the  shaft  of  the  counter,  the  pulley  on  which  is  coiled  the 
chain,  and  this  pulley  becoming  out  of  gear,  a  weight,  p,  connected  with  the 
pencil  /',  restores  this  to  its  starting-point.  All  the  lines,  V,  traced  succes- 
sively by  the  pencil,  start  from  the  same  straight  line  as  ordinates,  and  their 
ends  give  the  curve  of  velocities. 

The  counters  on  the  right  and  left  are  worked  by  electromagnets,  m  m', 
and  are  intended  to  denote  the  velocity  of  special  winds  ;  for  instance,  those 
of  the  north  and  south,  by  connecting  their  electromagnets  with  the  north 
and  south  sectors  of  the  vane  (fig.  909). 

Temperature  of  the  air. — This  is  indicated  by  the  expansion  and  con- 
traction of  a  copper  wire  of  16  metres  in  length  stretched  backwards  and 
forwards  on  a  fir  post  8  metres  in  length.  The  whole  being  placed  on  the 
outside — on  the  roof,  for  instance — the  expansion  and  contraction  are  trans- 
mitted by  a  system  of  levers  to  a  wire,  <?,  which  passes  to  the  meteorograph, 
where  it  is  jointed  to  a  bent  lever,  /.  This  is  jointed  to  a  horizontal  rod,  s, 
which  supports  a  pencil,  and  at  the  other  end  is  jointed  to 'a  guide-rod,  x. 
Thus  the  pencil,  sharing  the  oscillations  of  the  whole  system,  traces  the  curve 
of  the  temperatures. 

Pressure  of  the  atmosphere. — This  is  registered  by  the  oscillations  of  a 
barometer,  B,  suspended  at  one  end  of  a  bent  scale-beam,  I  F,  playing  on  a 
knife-edge  (fig.  911).  The  arm  F  supports  a  counterpoise  ;  to  the  arm  I  is 
suspended  the  barometer  B,  which  is  wider  at  the  top  than  at  the  bottom. 
A  wooden  flange  or  floater,  O,  fixed  to  the  lower  part  of  the  tube,  plunges  in 
a  bath  of  mercury,  so  that  the  buoyancy  of  the  liquid  counterbalances  part  of 
the  weight  of  the  barometer.  Owing  to  the  large  diameter  of  the  barometric 
chamber,  a  very  slight  variation  of  level  in  this  chamber  makes  the  tube 
oscillate,  and  with' it  the  scale-beam  IF.  To  the  axis  of  this  is  a  triangle, 
ghk,  jointed  to  a  horizontal  rod,  which  in  turn  is  connected  with  a  guide-rod, 
z.  In  the  middle  of  this  rod  is  a  pencil  which,  sharing  in  the  oscillations 
of  the  triangle  ghk^  traces  the  curve  H  of  pressure.  A  bent  lever  at  the 
bottom  of  the  barometer  tube  keeps  this  in  a  vertical  position. 

Rainfall. — This  is  registered  between  the  direction  of  the  winds  and  the 
curve  H  by  a  pencil  at  the  end  of  a  rod,  u,  which  is  worked  by  an  electro- 
magnet, e.  On  the  roof  is  a  funnel  which  collects  the  rain,  and  a  long  tube 
leads  the  water  to  a  small  water-balance,  with  the  cups  placed  near  the 
meteorograph  (fig.  910).  To  the  axis  of  the  scale  beam  one  pole  of  the  battery 
is  connected  ;  the  left  cup  being  full,  tips  up,  and  a  contact,  «,  closes  the 
current,  which  passes  then  to  one  of  the  binding  screws,  C,  and  hence  to  the 


974]  Measurement  of  the  Rainfall.  95  i 

electromagnet,  e.  Then  the  right  cup,  being  in  turn  full,  tips  in  the  opposite 
direction,  and  the  contact  b  now  transmits  the  current  to  the  electromagnet. 
Thus,  at  each  oscillation  this  latter  attracts  its  armature,  and  with  it  the 
rod  a,  which  makes  a  mark  by  means  of  a  pencil  at  the  end.  If  the  rain  is 
abundant  the  oscillations  of  the  beam  are  rapid,  and  the  marks  being  very 
close  together  give  a  deep  shade  ;  if,  on  the  contrary,  the  oscillations  are 
slow,  the  marks  are  at  a  greater  distance  and  give  a  light  shade.  When 
the  rain  ceases  the  oscillations  cease  also,  and  the 
pencil  makes  no  mark. 

To  complete  this  description  of  the  first  face  of 
the  meteorograph :  S  is  the  alarum-bell  of  the  clock- 
work, OO  a  cord  supporting  a  weight  which  moves 
the  works  of  the  hour-hand.  L  Z  is  a  second  cord  that 
supports  the  weight  which  works  the  alarum ;  the 
wheel  U,  placed  below  the  clockwork,  winds  up  the 
sheet  AD  when  it  is  at  the  bottom  of  its  course. 

The  second  sheet  (fig.  911)  gives  the  barometric 
height  and  the  rainfall  like  the  first,  but  on  a  larger 
scale,  since  the  motion  of  the  sheet  is  five  times  as 
rapid.  Its  principal  function  is  that  of  registering  the 
moisture  of  the  air.  This  is  effected  by  means  of  the 
psychrometer  (fig.  912).  T  and  T'  are  two  thermo- 
meters fixed  on  two  plates.  The  muslin  which  covers 

the  second  is  kept  continually  moist  by  water  dropping  on  it.  In  each  of 
the  bulbs  are  fused  two  platinum  wires  ;  the  stems  of  the  thermometers  are 
open  at  the  top,  and  in  them  are  two  platinum  wires,  m  and  n,  suspended 
to  a  metal  frame  movable  on  four  pulleys  supported  by  a  fixed  piece,  B. 
The  frame  A,  in  contact  with  the  current  of  the  battery,  is  suspended 
to  a  steel  wire,  L,  which  passes  over  a  pulley  to  the  meteorograph 
(fig.  910).  Here  is  a  long  triangular  lever,  W,  which  supports  a  small  wheel, 
to  which  is  fixed  the  wire  L.  The  lever  W,  which  turns  about  an  axis,  f,  is 
moved  by  a  rod,  #,  by  means  of  an  excentric,  which  the  clock  works  every 
quarter  of  an  hour.  At  each  oscillation  the  lever  W  transmits  its  motion 
to  a  small  chariot,  on  which  is  an  electromagnet,  .r,  and  at  the  same  time  to 
the  steel  wire  L,  which  supports  the  frame  A  (fig.  912).  The  chariot,  moved 
towards  the  left  by  the  rotation  of  the  excentric,  lets  the  frame  sink.  The 
moment  the  first  platinum  wire  reaches  the  mercurial  column  of  the  dry 
bulb  thermometer,  which  is  the  highest,  the  current  is  closed,  and  passes  into 
the  electromagnet  of  the  chariot.  An  armature  at  once  causes  a  pencil  to 
mark  a  point  on  the  sheet  which  is  the  beginning  of  a  line  representing  the 
path  of  the  dry  bulb  thermometer.  As  the  frame  continues  to  descend,  the 
second  platinum  wire  touches  the  mercury  of  the  wet  bulb,  and  closes  a 
current  in  a  relay,  M,  which  opens  the  circuit  of  the  electromagnet,  x.  The 
pencil  is  then  detached  ;  then,  returning  upon  itself,  the  chariot  reproduces 
the  closing  and  opening  of  the  circuit  in  the  opposite  direction,  the  pencil 
makes  another  mark,  which  is  the  end  of  the  line.  There  are  thus  formed 
two  series  of  dots  arranged  in  two  curves,  one  of  which  represents  the  path  of 
the  dry,  and  the  other  the  path  of  the  wet,  bulb.  The  horizontal  distance  of  the 
two  points  of  these  curves  is  proportional  to  the  difference  / — tv  of  the  tem- 
peratures indicated  at  the  same  moment  by  the  thermometers  (fig.  912). 


952 


Meteorology. 


[974- 


Quantity  of  rain. —  The  quantity  of  rain  which  falls  in  a  given  time 
is  registered  on  a  disc  of  paper  on  a  pulley,  R.  On  the  groove  of  this  is 
coiled  a  chain,  to  which  is  suspended  a  brass  tube,  P.  This  is  fixed  at  the 


Fig.  911. 


bottom  to  a  float,  which  plunges  in  a  reservoir  placed  in  the  base  of  the 
meteorograph.      On  passing  out  of  the  water-balance  (fig.  911)  the  water 


-976] 


Causes  of  Winds. 


953 


passes  into  this  reservoir,  and  as  its  section  is  one-fourth  that  of  the  funnel, 
the  height  of  water  which  falls  is  quadrupled ;  it  is  measured  on  a  scale,  G, 
divided  into  millimetres. 

As  the  float  rises,  a  weight,  Z,  moves  the  pulley  in  the  contrary  direction, 
and  its  rotation  is  proportional  to  the  height  of 
water  which  has  fallen.  A  pencil  moves  at  the 
same  time  from  the  centre  to  one  circumference  of 
the  paper  disc  with  a  velocity  of  5  mm.  in  24 
hours  :  hence  the  quantity  of  rain  which  falls  every 
day  is  noted  on  a  different  place  on  the  paper 
disc. 

975.  Direction  and  velocity  of  winds. — 
Winds  are  currents  moving  in  the  atmosphere  with 
variable  directions  and  velocities.  There  are  eight 
principal  directions  in  which  they  blow — north, 
north-east,  east,  south-east,  south,  south-west,  west, 
and  north-west.  Mariners  further  divide  each  of 
the  distances  between  these  eight  directions  into 
four  others,  making  in  all  32  directions,  which  are 
called  points  or  rhumbs.  A  figure  of  32  rhumbs 
on  a  circle,  in  the  form  of  a  star,  is  known  as  the 
mariner's  card. 

Velocity  is  determined  by  means  of  the 
anemometer  (fig.  909),  a  small  vane  with  fans, 
which  the  wind  turns  ;  the  velocity  is  deduced  from 
the  number  of  turns  made  in  a  given  time.  In  our 
climate  the  mean  velocity  is  from  1 8  to  20  feet  in  a 
second.  With  a  velocity  of  less  than  18  inches  in 
a  second  no  movement  is  perceptible,  and  smoke 
ascends  straight ;  with  a  velocity  between  i^  and 
2  feet  per  second  the  wind  is  perceptible  and  moves  a  pennant ;  from  13  to 
22  feet  it  is  moderate,  it  stretches  a  flag  and  moves  the  leaves  of  trees  ; 
with  from  23  to  36  feet  velocity  it  is  fresh  and  moves  the  branches  of 
trees  ;  with  36  to  56  feet  it  is  strong  and  moves  the  larger  branches  and 
the  smaller  stems  ;  with  a  velocity  of  56  to  90  feet  it  is  a  storm,  and  entire 
trees  are  moved  ;  and  from  90  to  120  it  is  a  hurricane. 

To  measure  the  pressure  of  the  wind  a  plate  is  used,  which  by  means  of  a 
vane  is  always  kept  in  a  direction  opposite  that  of  the  wind.  Behind  the 
plate  are  one  or  more  springs  which  are  the  more  pressed  the  greater  is  the 
pressure  of  the  wind  against  the  plate.  Knowing  the  distance  through  which 
the  plate  is  pressed,  we  can  calculate  the  pressure  which  the  wind  exerts  on 
the  plate  in  question. 

With  some  degree  of  approximation,  and  for  low  velocities,  the  pressure 
may  be  taken  as  proportional  to  the  square  of  the  velocity.  Thus,  if  the 
pressure  on  the  square  foot  is  0^005  pound,  with  a  velocity  of  1*5  foot  in 
a  second,  it  is  0*02  pound  with  a  velocity  of  3  feet,  and  0-123  with  a  velocity 
of  7-33  feet. 

976.  Causes  of  winds. — Winds  are  produced  by  a  disturbance  of  the 
equilibrium  in  some  part  of  the  atmosphere  :  a  disturbance  always  resulting 


Fig.  912. 


954  Meteorology.  [976- 

from  a  difference  in  temperature  between  adjacent  countries.  Thus,  if  the 
temperature  of  a  certain  extent  of  ground  becomes  higher,  the  air  in  contact 
with  it  becomes  heated,  it  expands  and  rises  towards  the  higher  regions  of 
the  atmosphere  ;  whence  it  flows,  producing  winds  which  blow  from  hot  to 
cold  countries.  But  at  the  same  time  the  equilibrium  is  destroyed  at  the 
surface  of  the  earth,  for  the  barometric  pressure  on  the  colder  adjacent  parts 
is  greater  than  on  that  which  has  been  heated,  and  hence  a  current  will  be 
produced  with  a  velocity  dependent  on  the  difference  between  these  pres- 
sures ;  thus  two  distinct  winds  will  be  produced — an  upper  one  setting  out- 
wards from  the  heated  region,  and  a  lower  one  setting  inwards  towards  it. 

977.  Regular,  periodical,  and  variable  winds. — According  to  the  more 
or  less  constant  directions  in  which  winds  blow,  they  may  be  classed  as 
regular,  periodical,  and  variable  winds. 

i.  Regular  winds  are  those  which  blow  all  the  year  through  in  a  virtually 
constant  direction.  These  winds,  which  are  also  known  as  the  trade  winds, 
are  uninterruptedly  observed  far  from  the  land  in  equatorial  regions,  blowing 
from  the  north-east  to  the  south-west  in  the  Northern  Hemisphere,  and  from 
the  south-east  to  the  north-west  in  the  Southern  Hemisphere.  They  prevail 
on  the  two  sides  of  the  equator  as  far  as  30°  of  latitude,  and  they  blow  in 
the  same  direction  as  the  apparent  motion  of  the  sun — that  is,  from  east  to 
west. 

The  air  above  the  equator  being  gradually  heated,  rises  as  the  sun  passes 
round  from  east  to  west,  and  its  place  is  supplied  by  the  colder  air  from  the 
north  or  south.  The  direction  of  the  wind,  however,  is  modified  by  this  fact, 
that  the  velocity  which  this  colder  air  has  derived  from  the  rotation  of  the 
earth— namely,  the  velocity  of  the  surface  of  the  earth  at  the  point  from 
which  it  started — is  less  than  the  velocity  of  the  surface  of  the  earth  at  the 
point  at  which  it  has  now  arrived  :  hence  the  currents  acquire,  in  reference 
to  the  equator,  the  constant  direction  which  constitutes  the  trade-winds. 

ii.  Periodical  winds  are  those  which  blow  regularly  in  the  same  direction 
at  the  same  seasons  and  at  the  same  hours  of  the  day  :  the  monsoon, 
simoom,  and  the  land  and  sea  breeze  are  examples  of  this  class.  The  name 
monsoon  is  given  to  winds  which  blow  for  six  months  in  one  direction  and 
for  six  months  in  another.  They  are  principally  observed  in  the  Red  Sea 
and  in  the  Arabian  Gulf,  in  the  Bay  of  Bengal  and  in  the  Chinese  Sea. 
These  winds  blow  towards  the  continents  in  summer,  and  in  a  contrary 
direction  in  winter.  The  simoom  is  a  hot  wind  that  blows  over  the  deserts 
of  Asia  and  Africa,  and  which  is  characterised  by  its  high  temperature  and 
by  the  sands  which  it  raises  in  the  atmosphere  and  carries  with  it.  During 
the  prevalence  of  this  wind  the  air  is  darkened,  the  skin  feels  dry,  the 
respiration  is  accelerated,  and  a  burning  thirst  is  experienced. 

This  wind  is  known  under  the  name  of  sirocco  in  Italy  and  Algiers,  where 
t  blows  from  the  great  desert  of  Sahara.  In  Egypt,  where  it  prevails  from 
the  end  of  April  to  June,  it  is  called  kamsin.  The  natives  of  Africa,  in  order 
to  protect  themselves  from  the  effects  of  the  too  rapid  perspiration  occasioned 
by  this  wind,  cover  themselves  with  fatty  substances. 

The  land  and  sea  breeze  is  a  wind  which  blows  on  the  sea-coast,  during 
the  day  from  the  sea  towards  the  land,  and  during  the  night  from  the  land  to 
the  sea.  For  during  the  day  the  land  becomes  more  heated  than  the  sea,  in 


-979] 


Weather  Charts.  955 


consequence  of  its  lower  specific  heat  and  greater  conductivity,  and  hence  as 
the  superincumbent  air  becomes  more  heated  than  that  upon  the  sea,  it  as- 
cends and  is  replaced  by  a  current  of  colder  and  denser  air  flowing  from  the 
sea  towards  the  land.  During  the  night  the  land  cools  more  rapidly  than  the 
sea,  and  hence  the  same  phenomenon  is  produced,  but  in  a  contrary  direction. 
The  sea  breeze  commences  after  sunrise,  increases  up  to  three  o'clock  in  the 
afternoon,  decreases  towards  evening,  and  is  changed  into  a  land  breeze 
after  sunset.  These  winds  are  only  perceived  at  a  slight  distance  from  the 
shores.  They  are  regular  in  the  tropics,  but  less  so  in  our  climates  ;  and 
traces  of  them  are  seen  as  far  as  the  coasts  of  Greenland.  The  proximity  of 
mountains  also  gives  rise  to  periodical  daily  breezes. 

iii.  Variable  winds  are  those  which  blow  sometimes  in  one  direction  and 
sometimes  in  another,  alternately,  without  being  subject  to  any  law.  In  mean 
latitudes  the  direction  of  the  winds  is  very  variable  ;  towards  the  poles  this 
irregularity  increases,  and  under  the  arctic  zone  the  winds  frequently  blow 
from  several  points  of  the  horizon  at  once.  On  the  other  hand,  in  approach- 
ing the  torrid  zone,  they  become  more  regular.  The  south-west  wind  prevails 
in  England,  in  the  north  of  France,  and  in  Germany  ;  in  the  south  of  France 
the  direction  inclines  towards  the  north,  and  in  Spain  and  Italy  the  north 
wind  predominates. 

978.  taw  of  the  rotation  of  winds.— Spite    of  the  great  irregularity 
which  characterises  the  direction  of  the  winds  in  our  latitude,  it  has  been  as- 
certained that  the  wind  has  a  preponderating  tendency  to  veer  round  accord- 
ing to  the  sun's  motion— that  is,  to  pass  from  north,  through  north-east,  east- 
south-east  to  south,  and  so  on  round  in  the  same  direction  from  west  to 
north  ;    that  it  often  makes  a  complete  circuit  in  that  direction,  or  more 
than  one  in  succession,  occupying  many  days  in  doing  so,  but  that  it  rarely 
veers,  and  very  rarely  or  never  makes  a  complete  circuit  in  the  opposite 
direction.     This  course  of  the  winds  is  most  regularly  observed  in  winter. 
According  to  Leverrier,  the  displacement  of  the  north-east  by  the  south- 
west wind  rises  from  the  occurrence  of  a  whirlwind  formed  upon  the  Gulf 
Stream.     For  a  station  in  south  latitude  a  contrary  law  of  rotation  prevails. 

This  law,  though  more  or  less  suspected  for  a  long  time,  was  first  formally 
enunciated  and  explained  by  Dove,  and  is  known  as  Dove's  law  of  rotation 
of  winds. 

979.  Weather   charts. — A   considerable   advance   has   been   made   in 
weather  forecasts  by  the  frequent  and  systematic  publication  of  weather 
charts ;  that  is  to  say,  maps  in  which  the  barometric  pressure,  the  tempe- 
rature, the  force  of  the  wind,  &c.,  are  expressed  for  considerable  areas,  in  an 
exact  and  comprehensive  manner.     A  careful  study  of  such  maps  renders 
possible  a  forecast  of  the  weather  for  a  day  or  more  in  advance.     We  can 
here  do  little  more  than  explain  the  meaning  of  the  principal  terms  in  use. 

If  lines  are  drawn  through  those  places  on  the  earth's  surface  where  the 
corrected  barometric  height  at  a  given  time  is  the  same,  such  lines  are 
called  isobarometric  lines,  or  more  briefly,  isobaric  lines,  or  isobars.  Between 
any  two  points  on  the  same  isobar  there  is  no  difference  of  pressure. 
Isobars  are  usually  drawn  for  a  difference  of  5  mm.,  or  of  ~  of  an  inch. 

If  we  take  a  horizontal  line  between  two  isobars,  and  at  that  point  at 
which  the  pressure  is  greatest  draw  a  perpendicular  line  on  any  suitable 


956  Meteorology.  [979- 

scale,  which  shall  represent  the  difference  in  pressure  between  the  two  places, 
the  line  drawn  from  the  top  of  this  perpendicular  to  the  lower  isobar  will 
form  an  angle  with  the  horizontal,  and  the  steepness  of  this  angle  is  a 
measure  of  the  fall  in  pressure  between  the  two  stations,  and  is  called  the 
barometric  gradient.  Gradients  are  usually  expressed  in  England  and 
America  in  hundredths  of  an  inch  of  mercury  for  one  degree  of  sixty  nautical 
miles,  and  on  the  Continent  in  millimetres  for  the  same  distance.  The 
closer  are  the  isobars  the  steeper  is  the  gradient,  and  the  more  powerful 
the  wind  ;  and  though  no  exact  numerical  relationship  can  be  proved  to  exist 
between  the  steepness  of  the  gradient  and  the  force  of  the  wind,  it  may  be 
mentioned  that  a  gradient  of  about  6  represents  a  strong  breeze  ;  and  a 
gradient  of  10,  or  a  difference  in  pressure  of  ^  of  an  inch  for  60  miles, 
is  a  stiff  gale. 

The  direction  of  the  wind  is  from  the  place  of  higher  pressure  to  that  of 
lower,  and  in  this  respect  the  law  of  Buys  Ballot  may  be  mentioned,  which 
has  been  found  to  hold  in  all  cases  in  the  Northern  Hemisphere,  where 
local  configuration  does  not  come  into  play.  If  we  stand  with  our  back  to 
the  wind  the  line  of  lower  pressure  is  on  the  left  hand.  For  places  in  the 
Southern  Hemisphere  exactly  the  opposite  law  holds. 

If  within  any  area  the  pressure  is  lower,  the  wind  blows  round  that  area, 
the  place  of  lowest  pressure  being  on  the  left.  The  direction  of  the  wind  is, 
in  short,  opposite  that  of  the  hands  of  a  watch.  Such  a  circulation  is  called 
cyclonic ;  it  is  that  which  is  characteristic  of  the  West  Indian  hurricanes, 
which  are  known  as  cyclones.  Conversely  the  wind  blows  round  an  area  of 
higher  pressure  in  the  same  direction  as  the  hands  of  a  watch  ;  and  this  cir- 
culation is  called  anti-cyclonic. 

Cyclonic  systems  are  by  far  the  most  frequent,  and  are  characterised  by 
steep  gradients  ;  the  air  in  them  tends  to  move  in  towards  the  centre,  and 
thence  to  the  upper  regions  of  the  atmosphere.  They  bring  with  them,  over 
the  greater  part  of  the  region  which  they  cover,  much  moisture,  an  abundance 
of  cloud,  and  heavy  rain.  Anti-cyclonic  systems  have  the  opposite  charac- 
teristics ;  the  gradients  are  slight,  the  wind  light,  and  it  moves  with  the  hands 
of  a  watch.  The  air  is  dry,  so  that  there  is  but  little  cloud,  and  no  rain. 
Cyclonic  systems,  from  the  dampness  of  the  air,  produce'warm  weather  in 
winter,  and  cold,  wet  weather  in  summer.  Anti-cyclonic  systems  bring  our 
hardest  frosts  in  winter  and  greatest  heat  in  summer,  as  there  is  but  little 
moisture  in  the  air  to  temper  the  extremes  of  climate.  Both  systems  travel  over 
the  earth's  surface— the  cyclones  rapidly,  but  the  anti-cyclones  more  slowly. 

980.  Fogs  and  Mists. — When  aqueous  vapour  rising  from  a  vessel  of 
boiling  water  diffuses  in  the  colder  air,  it  is  condensed  ;  a  sort  of  cloud  is 
formed  which  consists  of  a  number  of  small  hollow  vesicles  of  water,  which 
remain  suspended  in  the  air.  These  are  usually  spoken  of  as  vapour,  yet 
they  are  not  so — at  any  rate  not  in  the  physical  sense  of  the  word,  for  in 
reality  they  are  partially  condensed  vapour. 

When  this  condensation  of  aqueous  vapour  is  not  occasioned  by  contact 
with  cold  solid  bodies,  but  takes  place  throughout  large  spaces  of  the  atmo- 
sphere, it  constitutes  fogs  or  mists  ^  which,  in  fact,  are  nothing  more  than  the 
appearance  seen  over  a  vessel  of  hot  water. 

A  chief  cause  of  fogs  consists  in  the  moist  soil  being  at  a  higher  tern- 


-981]  Clouds.  957 

perature  than  the  air.  The  vapours  which  then  ascend  condense  and  become 
visible.  In  all  cases,  however,  the  air  must  have  reached  its  point  of  satura- 
tion before  condensation  takes  place.  Fogs  may  also  be  produced  when  a 
current  of  hot  and  moist  air  passes  over  a  river  at  a  lower  temperature  than 
its  own,  for  then,  the  air  being  cooled,  as  soon  as  it  is  saturated,  the  excess 
of  vapour  present  is  condensed.  The  distinction  between  mists  and  fogs  is 
one  of  degree  rather  than  of  kind.  A  fog  is  a  very  thick  mist. 

When  water  is  coated  with  a  layer  of  coal-tar,  it  is  prevented  from  eva- 
porating. Frankland  ascribes  the  dry  fog  met  with  in  London  to  the  large 
quantities  of  coal-tar  and  paraffine  vapour  which  are  sent  into  the  atmosphere, 
and  which,  condensing  on  the  vesicles  of  fog,  prevent  their  evaporation. 

Aitkin  has  shown  that  aqueous  vapour  never  condenses  unless  some 
liquid  or  solid  is  present  on  which  it  is  deposited.  Particles  of  dust  in  the 
air  are  the  nuclei  for  clouds  and  fogs.  This  he  showed  by  passing  steam 
into  filtered  air  ;  it  remained  quite  clear,  while  a  turbidity  was  produced 
under  the  same  circumstances  in  unfiltered  air.  The  density  of  the  cloud 
was  found  to  depend  on  the  number  of  particles  of  dust  in  the  air.  A  most 
abundant  source  of  dust  is  the  combustion  of  coal.  The  sulphur  in  the  coal 
in  burning  also  forms  sulphurous  acid,  which,  though  a  gas,  is  found  to  act 
as  a  nucleus. 

981.  Clouds. — Clouds  are  masses  of  vapour,  condensed  into  little  drops 
or  vesicles  of  extreme  minuteness,  like  fogs.  There  is  no  difference  of  kind 
between  fogs  and  clouds.  Fogs  are  clouds  resting  on  the  ground.  To  a 
person  enveloped  in  it,  a  cloud  on  a  mountain  appears  like  a  fog.  They 
always  result  from  the  condensation  of  vapour  which  rises  from  the  earth. 
According  to  their  appearance,  they  have  been  divided  by  Howard  into  four 
principal  kinds  :  the  nimbus,  the  stratus,  the  cumulus,  and  the  cirrus.  These 
four  kinds  are  represented  in  fig.  913,  and  are  designated  respectively  by  one, 
two,  three,  and  four  birds  on  the  wing. 

The  cirrus  consists  of  small  whitish  clouds,  which  have  a  fibrous  or  wispy 
appearance,  and  occupy  the  highest  regions  of  the  atmosphere.  The  name 
of  mares'  tails,  by  which  they  are  generally  known,  well  describes  their 
appearance.  From  the  low  temperature  of  the  spaces  which  they  occupy, 
it  is  more  than  probable  that  cirrus  clouds  consist  of  frozen  particles  ;  and 
hence  it  is  that  halos,  coronse,  and  other  optical  appearances,  produced  by 
refraction  and  reflection  from  ice-crystals,  appear  almost  always  in  these 
clouds  and  their  derivatives.  Their  appearance  often  precedes  a  change  of 
weather. 

The  cumulus  are  rounded  spherical  forms  which  look  like  mountains 
piled  one  on  the  other.  They  are  more  frequent  in  summer  than  in  winter, 
and  after  being  formed  in  the  morning  they  generally  disappear  towards 
evening.  If,  on  the  contrary,  they  become  more  numerous,  and  especially 
if  surmounted  by  cirrus  clouds,  rain  or  storms  may  be  expected. 

Stratus  clouds  consist  of  very  large  and  continuous  horizontal  sheets, 
which  form  chiefly  at  sunset  and  disappear  at  sunrise.  They  are  frequent 
in  autumn  and  unusual  in  spring-time,  and  are  lower  than  the  preceding. 

The  nimbus,  or  rain  clouds,  which  are  sometimes  classed  as  one  of  the 
fundamental  varieties,  are  properly  a  combination  of  the  three  preceding 
kinds.  They  affect  no  particular  form,  and  are  solely  distinguished  by  a 


958 


Meteorology. 


[981- 


uniform  grey  tint  and  by  fringed  edges.    They  are  indicated  on  the  right  of 
the  figure  by  the  presence  of  one  bird. 

The  fundamental  forms  pass  into  one  another  in  the  most  varied  manner  ; 
Howard  has  classed  these  transitional  forms  as  cirro-cumulus •,  cirro-stratus, 
and  cumulo-stratus,  and  it  is  often  very  difficult  to  tell,  from  the  appearance 
of  a  cloud,  which  type  it  most  resembles.  The  cirro-cumulus  is  most  cha- 
racteristically known  as  a  'mackerel  sky;'  it  consists  of  small  roundish 
masses,  disposed  with  more  or  less  irregularity  and  connection.  It  is  fre- 
quent in  summer,  and  attendant  on  warm  and  dry  weather.  Cirro-stratus 
appears  to  result  from  the  subsidence  of  the  fibres  of  cirrus  to  a  horizontal 
position  at  the  same  time  approaching  laterally.  The  form  and  relative 
position,  when  seen  in  the  distance  frequently  give  the  idea  of  shoals  of  fish. 
The  tendency  of  cumulo-stratus  is  to  spread,  settle  down  into  the  nimbus, 
and  finally  fall  as  rain. 


Fig.  9*3- 

The  height  of  clouds  varies  greatly  ;  in  the  mean  it  is  from  1,300  to  1,500 
yards  in  winter,  and  from  3,300  to  4,300  yards  in  summer.  But  they  often 
exist  at  greater  heights  ;  Gay-Lussac,  in  his  balloon  ascent,  at  a  height  of 
7,630  yards,  observed  cirrus  clouds  above  him,  which  appeared  to  be  at  a 
considerable  height.  In  Ethiopia,  D'Abbadie  observed  storm-clouds  whose 
height  was  only  230  yards  above  the  ground. 

In  order  to  explain  the  suspension  of  clouds  in  the  atmosphere,  Halley 
first  proposed  the  hypothesis  of  vesicular  vapours.  He  supposed  that  clouds 
are  formed  of  an  infinity  of  extremely  minute  vesicles,  hollow,  like  soap- 
bubbles  filled  with  air,  which  are  hotter  than  the  surrounding  air  ;  so  that 
these  vesicles  float  in  the  air  like  so  many  small  balloons.  Others  assume 
that  clouds  and  fogs  consist  of  extremely  minute  droplets  of  water  which  are 
retained  in  the  atmosphere  by  the  ascensional  force  of  currents  of  hot  air, 


-982]  Formation  of  Clouds.  959 

just  as  light  powders  are  raised  by  the  wind.  Ordinarily,  clouds  do  not 
appear  to  descend,  but  this  absence  of  downward  motion  is  only  apparent. 
In  fact,  clouds  do  usually  fall  slowly,  but  then  the  lower  part  is  continually 
dissipated  on  coming  in  contact  with  the  lower  and  more  heated  layers  ;  at 
the  same  time  the  upper  part  is  always  increasing  from  the  condensation  of 
new  vapours,  so  that  from  these  two  actions  clouds  appear  to  retain  the 
same  height. 

982.  Formation  of  clouds. — Many  causes  may  concur  in  the  formation 
of  clouds.  The  usual  cause  of  the  formation  of  a  cloud  is  the  ascent,  into 
higher  regions  of  the  atmosphere,  of  air  laden  with  aqueous  vapour  ;  it 
thereby  expands,  being  under  diminished  pressure  ;  and  in  consequence 
of  this  expansion  it  is  cooled,  and  this  cooling  produces  a  condensation  of 
vapour.  Hence  it  is  that  high  mountains,  stopping  the  currents  of  air  and 
forcing  them  to  rise,  are  an  abundant  source  of  rain.  If  the  air  is  quite  dry 
its  temperature  would  be  one  degree  lower  for  every  300  metres.  The  case 
is  different  with  moist  air  ;  for  when  the  air  has  ascended  so  high  that  its 
temperature  has  fallen  to  the  dew-point,  aqueous  vapour  is  condensed,  and 
in  consequence  of  this  heat  is  liberated  ;  when  the  dew-point  is  thus  attained, 
and  the  air  is  saturated,  the  cooling  due  to  the  ascent  and  expansion  of  air 
is  counteracted  by  this  liberation  of  latent  heat,  so  that  the  diminution  of 
temperature  with  the  height  is  considerably  slower  in  the  case  of  moist  than 
of  dry  air. 

The  following  calculation  will  give  us  the  quantity  of  water  separated  in 
a  given  case  :  Suppose  air  at  a  temperature  of  20°  to  be  saturated  with 
aqueous  vapour  at  that  temperature  ;  the  pressure  of  the  vapour  will  be  17-4 
mm.,  and  the  weight  contained  in  one  cubic  metre  of  air  17-1  grammes. 

If  the  air  has  risen  to  a  height  of  3,500  metres,  it  has  come  under  a 
pressure  which  is  only  f  of  what  it  was  ;  its  temperature  is  4°,  and  its 
volume  about  i^  time  what  it  originally  was.  As  it  remains  saturated  the 
pressure  will  be  6'i  mm.,  and  the  quantity  of  vapour  will  be  6-4  grammes 
in  a  cubic  metre,  that  is  to  say,  6-4  x  11  =  9-6  grammes  in  the  whole  mass  of 
what  was  originally  a  cubic  metre.  The  pressure  of  aqueous  vapour  has 
sunk  during  the  ascent  from  17-4  mm.  to  6'i  mm.,  and  its  weight  17-1 
grammes  to  9-6  grammes ;  that  is,  a  weight  of  7*5  grammes  has  been  deposited 
for  that  mass  of  air  which  at  the  sea-level  occupied  a  space  of  one  cubic 
metre.  These  7-5  grammes  are  in  the  form  of  the  small  droplets  which 
constitute  fogs  or  clouds. 

If  the  mass  of  air  had  risen  to  a  height  of  8,500  metres,  where  the  pres- 
sure is  only  one-third  that  on  the  sea-level,  the  temperature  is  —28°,  and 
the  space  it  occupies  three  times  as  great  as  at  first.  The  pressure  of 
aqueous  vapour  is  0-5  mm.,  and  its  weight  o-6  gramme  in  a  cubic  metre. 
Hence  there  are  now  only  r8  gramme  left  of  the  entire  quantity  of  aqueous 
vapour  originally  present,  and  the  remaining  15*3  grammes  would  be 
separated  as  water  or  ice.  A  similar  calculation  will  show  that  at  a  height 
of  4,200  metres,  where  the  temperature  is  zero  and  the  pressure  f,  the  quan- 
tity of  water  present  in  the  original  cubic  metre  is  only  "82  gramme,  the 
rest  being  deposited. 

Thus,  a  mass  of  air  which,  at  the  sea-level,  occupies  a  space  of  a  cubic 
metre,  and  is  saturated  with  aqueous  vapour  at  20°,  and  then  contains  17-1 


960 


Meteorology. 


[982- 


grammes,  will  only  contain  9-6  grammes  at  a  height  of  3,500  metres,  8-2 
grammes  at  4,200  metres,  and  1*8  gramme  at  8,500  metres.  Hence,  while 
a  mass  of  air  rises  from  the  sea-level  to  a  height  of  4,200  ft.,  8-9  grammes  of 
aqueous  vapour  are  separated  as  cloud-vesicles  :  at  8,500  metres,  or  about 
double  the  height,  6-4  grammes  are  separated  in  the  form  of  ice. 

A  hot  moist  current  of  air  mixing  with  a  colder  current  undergoes  a 
cooling,  which  brings  about  a  condensation  of  the  vapour.  Thus  the  hot 
and  moist  winds  of  the  south  and  south-west,  mixing  with  the  colder  air  of 
our  latitudes,  give  rain.  The  winds  of  the  north  and  north-east  tend  also, 
in  mixing  with  our  atmosphere,  to  condense  the  vapours  ;  but  as  these  winds, 
owing  to  their  low  temperature,  are  very  dry,  the  mixture  rarely  attains 
saturation,  and  generally  gives  no  rain. 

The  formation  of  clouds  in  this  way  is  thus  explained  by  Hutton.  The 
tension  of  aqueous  vapour,  and  therewith  the  quantity  present  in  a  given 
space  when  saturated,  diminishes  according  to  a  geometric  progression, 
while  the  temperature  falls  in  arithmetical  progression,  and  therefore  the 
elasticity  of  the  vapour  present  at  any  time  is  reduced  by  a  fall  of  temperature 
more  rapidly  than  in  direct  proportion  to  the  fall.  Hence,  if  a  current  of 
warm  air,  saturated  with  aqueous  vapour,  meets  a  current  of  cold  air  also 
saturated,  the  air  acquires  the  mean  temperature  of  the  two,  but  can  only 
retain  a  portion  of  the  vapour  in  the  invisible  condition,  and  a  cloud  or  mist 
is  formed.  Thus,  suppose  a  cubic  metre  of  air  at  10°  C.  mixes  with  a  cubic 
metre  of  air  at  20°  C.,  and  that  they  are  respectively  saturated  with  aqueous 
vapour.  By  formula  (401)  it  is  easily  calculated  that  the  weight  of  water 
contained  in  the  cubic  metre  of  air  at  10°  C.  is  9-397  grammes,  and  in  that 
at  20°  C.  is  17*632  grammes,  or  27-029  grammes  in  all.  When  mixed  they 
produce  two  cubic  metres  of  air  at  15°  C.  ;  but  as  the  weight  of  water  re- 
quired to  saturate  this  is  only  2x12-8  =  25-6  grammes,  the  excess,  1*429 
gramme,  will  be  deposited  in  the  form  of  mist  or  clouds. 

983.  Rain.  —  When  the  individual  vapour-vesicles  become  larger  and 
heavier  by  the  constant  condensation  of  aqueous  vapour,  and  when  finally 
individual  vesicles  unite,  they  form  regular  drops,  which  fall  as  rain. 

The  quantity  of  rain  which  falls  annually  in  any  given  place,  or  the  annual 
rainfall,  is  measured  by  means  of  a  rain-gauge,  or  pluviometer.  Ordinarily  it 

consists  of  a  cylindrical  vessel 
M  (figs.  914  and  915),  closed  at 
the  top  by  a  funnel-shaped  lid, 
in  which  there  is  a  very  small 
hole,  through  which  the  rain 
falls.  At  the  bottom  of  the 
vessel  is  a  glass  tube,  A,  in 
which  the  water  rises  to  the 
same  height  as  inside  the  rain- 
gauge,  and  is  measured  by  a 
scale  on  the  side,  as  shown  in 
the  figures. 

The  apparatus  being  placed 
in   an   exposed   situation,   if  at 
the  end  of  a  month  the  height  of  water  in  the  tube  is  two  inches,  for  example, 


Fig.  914. 


Fig.  915. 


-983]  Rain.  961 

it  shows  that  the  water  has  attained  this  height  in  the  vessel,  and,  conse- 
quently, that  a  layer  of  two  inches  in  depth  expresses  the  quantity  of  rain 
which  this  extent  of  surface  has  received. 

It  has  been  noticed  that  the  quantity  of  rain  indicated  by  the  rain-gauge 
is  greater  as  this  instrument  is  nearer  the  ground.  This  has  been  ascribed 
to  the  fact  that  the  raindrops,  which  are  generally  colder  than  the  layers  of 
air  which  they  traverse,  condense  the  vapour  in  these  layers,  and  therefore 
constantly  increase  in  volume.  Hence  more  rain  falls  on  the  surface  of  the 
ground  than  at  a  certain  height.  But  it  has  been  objected  that  the  excess 
of  the  quantity  of  rain  which  falls,  over  that  at  a  certain  height,  is  six  or 
seven  times  that  which  could  arise  from  condensation,  even  during  the  whole 
course  of  the  raindrops  from  the  clouds  to  the  earth.  The  difference  must 
therefore  be  ascribed  to  purely  local  causes,  and  it  is  now  assumed  that  the 
difference  arises  from  eddies  produced  in  the  air  about  the  rain-gauge,  which 
are  more  perceptible  as  it  is  higher  above  the  ground  ;  as  these  eddies  dis- 
perse the  drops  which  would  otherwise  fall  into  the  instrument,  they  diminish 
the  quantity  of  water  which  it  receives. 

In  any  case  it  is  clear  that  if  raindrops  traverse  moist  air,  they  will,  from 
their  temperature,  condense  aqueous  vapour  and  increase  in  volume.  If,  on 
the  contrary,  they  traverse  dry  air,  the  drops  tend  to  vaporise,  and  less  rain 
falls  than  at  a  certain  height  ;  it  might  even  happen  that  the  rain  did  not 
reach  the  earth. 

From  measurements  of  the  coronas  (981)  Delezenne  determined  the 
diameter  of  the  globules  in  the  case  of  rain-clouds  just  about  to  fall,  and  in  the 
case  of  the  cloud  from  a  low-pressure  steam-engine  (471).  The  former 
was  found  to  vary  from  0*0565  to  0*0226  mm.,  and  the  latter  from  0-0051  to 
0-0042  mm.  With  the  former  5,500  droplets  would  be  needed  to  make  a 
drop  of  water  a  millimetre  in  diameter,  and  with  the  latter  50,000. 

According  to  the  same  author  there  would  be  about  I5mgr.  of  globules  in 
a  cubic  metre  of  a  cloud  which  produced  a  rainfall  of  lomm.  of  water  in  an 
hour.  With  this  number  the  mean  distances  of  the  vesicles  with  the  above 
magnitudes  are  respectively  1*845,  0-706,  0-167,  and  o-i48mm. 

The  rainfall  varies  with  the  height  of  a  station  above  the  sea-level,  at 
the  rate  of  3  or  4  per  cent,  for  each  100  feet  of  altitude  above  the  sea. 

Many  local  circumstances  may  effect  the  quantity  of  rain  which  falls  in 
different  countries  ;  but,  other  things  being  equal,  most  rain  falls  in  hot  cli- 
mates, for  there  the  vaporisation  is  most  abundant.  The  rainfall  decreases, 
in  fact,  from  the  equator  to  the  poles.  At  London  it  is  23-5  inches  ;  at 
Bordeaux  it  is  25-8  ;  at  Madeira  it  is  27-7  ;  at  Havannah  it  is  91-2  ;  and  at 
St.  Domingo  it  is  107*6.  The  quantity  varies  with  the  season  :  in  Paris,  in 
winter,  it  is  4-2  inches  ;  in  spring,  6*9  ;  in  summer,  6*3  ;  and  in  autumn,  4*8 
inches.  The  heaviest  annual  rainfall  at  any  place  on  the  globe  is  on  the 
Khasi  Hills  in  Bengal,  where  it  is  600  inches  ;  of  which  500  inches  fall  in 
seven  months.  On  July  i,  1851,  a  rainfall  of  25^  inches  on  one  day  was 
observed  at  Cherrapoonjee.  At  Kurrachee,  in  the  north-west  of  India,  the 
rainfall  is  only  7  inches. 

The  driest  recorded  place  in  England  is  Lincoln,  where  the  mean  rainfall 
is  20  inches  ;  and  the  wettest  is  Stye,  at  the  head  of  Borrowdale  in  Cumber- 
land, where  it  amounts  to  165  inches.  The  greatest  average  amount  of  rain- 

3Q 


962 


Meteorology. 


[983- 


fall  in  any  one  day,  taking  the  means  of  all  stations,  is  i£  inch  ;  though 
individual  stations  far  exceed  this  amount,  sometimes  reaching  4  inches. 

An  inch  of  rain  on  a  square  yard  of  surface  expresses  a  fall  of  4674 
pounds,  or  4-67  gallons.  On  an  acre  it  corresponds  to  22,622  gallons,  or 
100-9935  tons.  100  tons  per  inch  per  acre  is  a  ready  way  of  remembering 
this. 

984.  Waterspouts. — These  are  masses  of  vapour  suspended  in  the  lower 
layers  of  the  atmosphere  which  they  traverse,  and  endowed  with  a  gyratory 
motion  rapid  enough  to  uproot  trees,  upset  houses,  and  break  and  destroy 
everything  with  which  they  come  in  contact. 

These  meteors,  which  are  generally  accompanied  by  hail  and  rain,  often 
emit  lightning  and  thunder,  producing  the  sound  of  carriages  rolling  over  a 
stony  road.  Many  of  them  have  no  gyratory  motion,  and  about  a  quarter  of 
those  observed  are  produced  in  a  calm  atmosphere. 

When  they  take  place  on  the  sea  they  present  a  curious  phenomenon. 
The_water  is  disturbed,  and  rises  in  the  form  of  a  cone,  while  the  clouds  are 


Fig.  916. 

depressed  in  the  form  of  an  inverted  cone  ;  the  two  cones  then  unite  and 
form  a  continuous  column  from  the  sea  to  the  clouds  (fig.  916).  Even, 
however,  on  the  high  seas  the  water  of  these  waterspouts  is  never  salt, 
proving  that  they  are  formed  of  condensed  vapour,  and  not  of  sea-water 
raised  by  aspiration. 

The  origin  of  these  is  not  known.  Kaemtz  assumes  that  they  are  due 
principally  to  two  opposite  winds  which  pass  by  the  side  of  each  other,  or  to 
a  very  high  wind  which  prevails  in  the  higher  regions  of  the  atmosphere. 
Peltier  and  many  others  ascribe  to  them  an  electric  origin. 


-986]  Influence  of  Aqueous  Vapour  on  Climate.  963 

985.  Influence  of  aqueous  vapour  on  climate. — Tyndall  applied  the 
property  possessed  by  aqueous  vapour  of  powerfully  absorbing  and  radiating 
heat  to  the  explanation  of  some  obscure  points  in  meteorology.  He  estab- 
lished the  fact  that  in  a  tube  4  feet  long  the  atmospheric  vapour  on  a  day  of 
average  dryness  absorbs  10  per  cent  of  obscure  heat.  With  the  earth  warmed 
by  the  sun  as  a  source,  at  the  very  least  10  per  cent,  of  its  heat  is  intercepted 
within  10  feet  of  the  surface.  The  absorption  and  radiation  of  aqueous 
vapour  is  more  than  16,000  times  that  possessed  by  air. 

The  radiative  power  of  aqueous  vapour  may  be  the  main  cause  of  the 
torrent-like  rains  that  occur  in  the  tropics,  and  also  of  the  formation  of 
cumulus  clouds  in  our  own  latitudes.  The  same  property  probably  causes  the 
descent  of  very  fine  rain,  called  serein,  which  has  more  the  characteristics  of 
falling  dew,  as  it  appears  a  short  time  after  sunset,  when  the  sky  is  clear  ; 
its  production  has  therefore  been  attributed  to  the  cold  resulting  from  the 
radiation  of  the  air.  It  is  not  the  air,  however,  but  the  aqueous  vapour  in 
the  air,  which  by  its  own  radiation  chills  itself,  so  that  it  condenses  into  serein. 

The  absorbent  power  of  aqueous  vapour  is  of  even  greater  importance. 
Whenever  the  air  is  dry  terrestrial  radiation  at  night  is  so  rapid  as  to  cause 
intense  cold.  Thus,  in  the  central  parts  of  Asia,  Africa,  and  Australia,  the 
daily  range  of  the  thermometer  is  enormous  ;  in  the  interior  of  the  last-named 
continent  a  difference  in  temperature  of  no  less  than  40°  C.  has  been  recorded 
within  24  hours.  In  India,  and  even  in  the  Sahara,  owing  to  the  copious 
radiation,  ice  has  been  formed  at  night.  But  the  heat  which  aqueous  vapour 
absorbs  most  largely  is  of  the  kind  emitted  from  sources  of  low  temperature  ; 
it  is  to  a  large  extent  transparent  to  the  heat  emitted  from  the  sun  whilst  it 
is  almost  opaque  to  the  heat  radiated  from  the  earth.  Consequently,  the 
solar  rays  penetrate  our  atmosphere  with  a  loss,  as  estimated  by  Pouillet,  of 
only  25  per  cent.,  when  directed  vertically  downwards,  but  after  warming 
the  earth  they  cannot  re-traverse  the  atmosphere.  Through  thus  preventing 
the  escape  of  terrestrial  heat,  the  aqueous  vapour  in  the  air  moderates  the 
extreme  chilling  which  is  due  to  the  unchecked  radiation  from  the  earth, 
and  raises  the  temperature  of  that  region  over  which  it  is  spread.  In 
TyndalFs  words,  'aqueous  vapour  is  a  blanket  more  necessary  to  the 
vegetable  life  of  England  than  clothing  is  to  man.  Remove  for  a  single 
summer  night  the  aqueous  vapour  from  the  air  which  overspreads  this 
country,  and  every  plant  capable  of  being  destroyed  by  a  freezing  tempera- 
ture would  perish.  The  warmth  of  our  fields  and  gardens  would  pour  itself 
unrequited  into  space,  and  the  sun  would  rise  upon  an  island  held  fast  in  the 
iron  grip  of  frost.' 

986.  Tyndall's  researches. — Tyndall  found  that  by  the  action  of  solar 
and  of  the  electric  light  on  vapours  under  a  great  degree  of  attenuation,  they 
are  decomposed.  This  new  reaction  not  only  puts  a  powerful  agent  of 
chemical  decomposition  into  the  hands  of  chemists,  but  it  has  led  Tyndall 
to  important  conclusions  regarding  the  origin  of  the  blue  colour  of  the  sky 
and  the  polarisation  of  daylight. 

He  used  a  glass  tube  with  glass  ends,  which  could  be  exhausted  and  then 
filled  with  air  charged  with  the  vapours  of  volatile  liquids,  by  allowing  the 
air  to  bubble  through  small  Wolff  bottles  containing  them.  By  mixing  the  air 
charged  with  vapour  with  different  proportions  of  pure  air,  and  by  varying 

3  Q  2 


964  Meteorology.  [986- 

the  degree  of  exhaustion,  it  was  possible  to  have  a  vapour  under  any  degree 
of  attenuation.  The  tube  could  also  be  filled  with  the  vapour  of  a  liquid 
alone.  The  tube  having  been  filled  with  air  charged  with  vapour  of  nitrite  of 
amyle,  a  somewhat  convergent  beam  from  the  electric  lamp  was  passed  into 
the  tube.  For  a  moment  the  tube  appeared  optically  empty,  but  suddenly  a 
shower  of  liquid  spherules  was  precipitated  on  the  path  of  the  beam,  forming 
a  luminous  white  cloud.  The  nature  of  the  substance  thus  precipitated  was 
not  specially  investigated. 

This  effect  was  not  due  to  any  chemical  action  between  the  vapour  and 
the  air,  for  when  either  dry  oxygen  or  dry  hydrogen  was  used  instead  of  air, 
or  when  the  vapour  was  admitted  alone,  the  effect  was  substantially  the  same. 
Nor  was  it  due  to  any  heating  effect,  for  the  beam  had  been  previously  sifted 
by  passing  through  a  solution  of  alum,  and  through  the  thick  glass  of  the 
lens.  The  unsifted  beam  produced  the  same  effect ;  the  obscure  calorific 
rays  did  not  seem  to  affect  the  result. 

The  sun's  light  also  effects  the  decomposition  of  the  nitrite  of  amyle 
vapour  ;  and  this  decomposition  was  found  to  be  mainly  due  to  the  more 
refrangible  rays. 

When  the  electric  light,  before  entering  the  experimental  tube,  was  made 
to  pass  through  a  layer  of  liquid  nitrite  of  amyle  an  eighth  of  an  inch  in 
thickness,  the  luminous  effect  was  not  appreciably  diminished,  but  the 
chemical  action  was  almost  entirely  stopped.  Thus  that  special  constituent 
of  the  luminous  radiation  which  effects  the  decomposition  of  the  vapour  is 
absorbed.by  the  liquid.  The  decomposition  of  liquid  nitrite  of  amyle  by  light, 
if  it  take  place  at  all,  is  far  less  rapid  and  distinct  than  that  of  the  vapour. 
The  circumstance  that  the  absorption  is  the  same  whether  the  nitrite  is  in 
the  liquid  or  in  the  vaporous  state,  is  considered  by  Tyndall  as  a  proof  that 
the  absorption  is  not  the  act  of  the  molecule  as  a  whole,  but  that  it  is  atomic  ; 
that  is,  that  it  is  to  the  atoms  that  the  peculiar  rate  of  vibration  is  trans- 
ferred which  brings  about  the  decomposition  of  the  body.  By  varying  the 
nature  of  the  vapour  the  shape  of  a  cloud  could  be  greatly  varied,  and 
in  many  cases  presented  the  most  fantastic  and  beautiful  forms. 

It  was  also  found  that  a  vapour  which  when  alone  resists  the  action  of 
light  may,  by  being  associated  with  another  gas  or  vapour,  exhibit  a  vigor- 
ous action.  Thus  when  the  tube  was  filled  with  atmospheric  air,  mixed  with 
nitrite  of  butyle  vapour,  the  electric  light  produced  very  little  effect ;  but  with 
half  an  atmosphere  of  this  mixture,  and  half  an  atmosphere  of  air  which  had 
passed  through  hydrochloric  acid,  the  action  of  the  light  was  almost  instan- 
taneous. In  another  case  mixed  air  and  nitrite  of  butyle  vapour  were  passed 
into  the  tube  so  that  the  mixture  was  under  a  pressure  of  2-5  mm.  Air 
passed  through  aqueous  hydrochloric  acid  was  introduced  until  the  pressure 
was  3  inches.  The  condensed  beam  passed  through  at  first  without  change, 
but  afterwards  a  superb  blue  cloud  was  formed. 

In  cases  where  the  vapours  are  under  a  sufficient  degree  of  attenuation, 
whatever  otherwise  be  their  nature,  the  visible  action  commences  with  the 
formation  of  a  blue  cloud.  The  term  cloud,  however,  must  not  be  understood 
in  its  ordinary  sense  ;  the  blue  cloud  is  invisible  in  ordinary  daylight,  and 
to  be  seen  must  be  surrounded  by  darkness,  it  alone  being  illuminated  by  a 
powerful  beam  of  light.  The  blue  cloud  differs  in  many  important  particulars 


-987]  Dew.     Hoarfrost.  965 

from  the  finest  ordinary  clouds,  and  may  be  considered  to  occupy  an  inter- 
mediate position  between  these  clouds  and  true  cloudless  vapour. 

By  graduating  the  quantity  of  vapour,  the  precipitation  may  be  obtained 
of  any  required  degree  of  fineness  ;  forming  either  particles  distinguishable 
by  the  naked  eye,  or  particles  beyond  the  reach  of  the  highest  microscopic 
power.  The  case  is  similar  to  that  of  carbonic  acid  gas,  which,  diffused 
in  the  atmosphere,  resists  the  decomposing  action  of  solar  light,  but  is 
decomposed  when  in  contact  with  the  chlorophyle  in  the  leaves  of  plants. 

When  the  blue  cloud  produced  in  these  experiments  was  examined  by 
any  polarising  arrangement,  the  light  emitted  laterally  from  the  beam — that 
is,  in  a  direction  at  right  angles  to  its  axis — was  found  to  be  perfectly  polar- 
ised. This  phenomenon  was  observed  in  its  greatest  perfection  the  more 
perfect  the  blue  of  the  sky.  It  is  produced  by  any  particles,  provided  they 
are  sufficiently  fine.  This  is  quite  analogous  to  the  light  of  the  blue  sky. 
When  this  is  examined  by  a  Nicol's  prism,  or  any  other  analyser,  it  is  found 
that  the  light  emitted  at  right  angles  to  the  path  of  the  sun's  rays  is  polarised. 

The  phenomena  of  the  firmamental  blue,  and  the  polarisation  of  the 
sky  light,  thus  find  definite  explanations  in  these  experiments.  We  need  only 
assume  the  existence,  in  the  higher  regions  of  the  atmosphere,  of  excessively 
fine  particles  of  water ;  for  particles  of  any  kind  produce  this  effect.  It 
is  easy  to  conceive  the  existence  of  such  particles  in  the  higher  regions, 
even  on  a  hot  summer's  day.  For  the  vapour  must  there  be  in  a  state  of 
extreme  attenuation  ;  and  inasmuch  as  the  oxygen  and  nitrogen  of  the  atmo- 
sphere behave  like  a  vacuum  to  radiant  heat,  the  extremely  attenuated  particles 
of  aqueous  vapour  are  practically  in  contact  with  the  absolute  cold  of  space. 

'  Suppose  the  atmosphere  surrounded  by  an  envelope  impervious  to 
light,  but  with  an  aperture  on  the  sunward  side,  through  which  a  parallel 
beam  of  solar  light  could  enter  and  traverse  the  atmosphere.  Surrounded 
on  all  sides  by  air  not  directly  illuminated,  the  track  of  such  a  beam  would 
resemble  that  of  the  parallel  beam  of  the  electric  light  through  an  incipient 
cloud.  The  sunbeam  would  be  blue,  and  it  would  discharge  light  laterally  in 
the  same  condition  as  that  discharged  by  the  incipient  cloud.  The  azure  re- 
vealed by  such  a  beam  would  be  to  all  intents  and  purposes  a  blue  cloud.' 

987.  Dew.  Hoarfrost. — Dew  is  aqueous  vapour  which  has  condensed 
on  bodies  during  the  night  in  the  form  of  minute  globules.  It  is  occasioned 
by  the  chilling  which  bodies  near  the  surface  of  the  earth  experience  in 
consequence  of  nocturnal  radiation.  Their  temperature  having  then  sunk 
several  degrees  below  that  of  the  air,  it  frequently  happens,  especially 
in  hot  seasons,  that  this  temperature  is  below  that  at  which  the  atmo- 
sphere is  saturated.  The  layer  of  air  which  is  immediately  in  contact  with 
the  chilled  bodies,  and  which  has  virtually  the  same  temperature,  then  de- 
posits a  portion  of  the  vapour  which  it  contains  (396) ;  just  as  when  a  bottle 
of  cold  water  is  brought  into  a  warm  room  it  becomes  covered  with  moisture, 
owing  to  the  condensation  of  aqueous  vapour  upon  it. 

According  to  this  theory,  which  was  first  propounded  by  Dr.  Wells,  all 
causes  which  promote  the  cooling  of  bodies  increase  the  quantity  of  dew. 
These  causes  are  the  emissive  power  of  bodies,  the  state  of  the  sky,  and  the 
agitation  of  the  air.  Bodies  which  have  a  great  radiating  power  more  readily 
become  cool,  and  therefore  ought  to  condense  more  vapour.  In  fact  there  is 


966 


Meteorology. 


[987- 


generally  no  deposit  of  dew  on  metals,  whose  radiating  power  is  very  small, 
especially  when  they  are  polished ;  while  the  ground,  sand,  glass  and  plants, 
which  have  a  great  radiating  power,  become  abundantly  covered  with  dew. 

The  state  of  the  sky  also  exercises  a  great  influence  on  the  formation  of 
dew.  If  the  sky  is  cloudless,  the  planetary  spaces  send  to  the  earth  an  in- 
appreciable quantity  of  heat,  while  the  earth  radiates  very  considerably,  and 
therefore  becoming  very  much  chilled,  there  is  an  abundant  deposit  of  dew. 
But  if  there  are  clouds,  as  their  temperature  is  far  higher  than  that  of  theplanet- 
ary  spaces,  they  radiate  in  turn  towards  the  earth,  and  as  bodies  on  the  surface 
of  the  earth  only  experience  a  feeble  chilling,  no  deposit  of  dew  takes  place. 

Wind  also  influences  the  quantity  of  vapour  deposited.  If  it  is  feeble,  it 
increases  it,  inasmuch  as  it  renews  the  air ;  if  it  is  strong,  it  diminishes  it, 
as  it  heats  the  bodies  by  contact,  and  thus  does  not  allow  the  air  time  to 
become  cooled.  Finally,  the  deposit  of  dew  is  more  abundant  according  as 
the  air  is  moister,  for  then  it  is  nearer  its  point  of  saturation. 

Hoarfrost  and  rime  are  dew  which  has  been  deposited  on  bodies 
cooled  below  zero,  and  has  become  frozen.  The  flocculent  form  which  the 
small  crystals  present,  of  which  rime  is  formed,  shows  that  the  vapour 
solidifies  directly  without  passing  through  the  liquid  state.  Hoarfrost,  like 
dew,  is  formed  on  bodies  which  radiate  most,  such  as  the  stalks  and  leaves 
of  vegetables,  and  is  chiefly  deposited  on  the  parts  turned  towards  the  sky. 

988.  Snow.  Sleet. — Snow  is  water  solidified  in  stellate  crystals,  vari- 
ously modified,  and  floating  in  the  atmosphere.  These  crystals  arise  from 


Fig.  917. 

the  congelation  of  the  minute  vesicles  which  constitute  the  clouds,  when  the 
temperature  of  the  latter  is  below  zero.  They  are  more  regular  when  formed 
m  a  calm  atmosphere.  Their  form  may  be  investigated  by  collecting  them 
on  a  black  surface,  and  viewing  them  through  a  strong  lens.  The  regularity, 
and  at  the  same  time  variety,  of  their  forms  are  truly  beautiful.  Fig.  917 
shows  some  of  these  forms  as  seen  through  a  microscope.  Very  roughly  a 
fall  of  one  foot  of  snow  may  be  taken  as  equal  to  an  inch  of  rain. 

It  snows  most  in  countries  near  the  poles,  or  which  are  high  above  the 
sea-level.    By  the  limit  of  perpetual  snow—  or,  briefly  snow-line— is  meant  that 


-990]  Ice.     Regelation.  967 

height  above  the  sea-level  at  which  the  snow  does  not  melt,  even  in  the 
hottest  summers.  It  is  lower  nearer  the  poles  than  the  equator  :  it  does  not 
depend  solely  on  the  latitude,  but  is  influenced  by  many  local  circumstances. 
Sleet  is  also  solidified  water,  and  consists  of  small  icy  needles  pressed 
together  in  a  confused  manner.  Its  formation  is  ascribed  to  the  sudden 
congelation  of  the  minute  globules  of  the  clouds  in  an  agitated  atmosphere. 

989.  Bail. — Hail  is  a  mass  of  compact  globules  of  ice  of  different  sizes, 
which  fall  in  the  atmosphere.     In  our  climate  hail  falls  principally  during 
spring  and  summer,  and  at  the  hottest  times  of  the  day  ;  it  rarely  falls  at 
night.     The  fall  of  hail  is  always  preceded  by  a  peculiar  noise. 

Hail  is  generally  the  precursor  of  storms,  it  rarely  accompanies  them, 
and  follows  them  more  rarely  still.  Hail  falls  from  the  size  of  small  peas  to 
that  of  an  egg  or  an  orange.  The  formation  of  hailstones  has  never  been  alto- 
gether satisfactorily  accounted  for  ;  nor  more  especially  their  great  size. 

990.  Ice.     Regelation. — Ice  is  an  aggregate  of  snow-crystals,  such  as 
are  shown  in  fig.  917.     The  transparency  of  ice  is  due  to  the  close  contact 
of  these  crystals,  which  causes  the  individual  particles  to  blend  into  an  un- 
broken mass,  and  renders  the  substance  optically,  as  well  as  mechanically, 
continuous.     When  large  masses  of  ice  slowly  melt  away,  a  crystalline  form 
is  sometimes  seen  by  the  gradual  disintegration  into  rude  hexagonal  prisms  ; 
a  similar  structure  is  frequently  met  with,  but  in  greater  perfection,  in  the  ice- 
caves  or  glaciers  of  cold  regions. 

An  experiment  of  Tyndall  shows  the  beautiful  structure  of  ice.  When  a 
piece  of  ice  is  cut  parallel  to  its  planes  of  freezing,  and  the  radiation  from 
any  source  of  light  is  permitted  to  pass  through  it,  the  disintegration  of 
the  substance  proceeds  in  a  remarkable  way.  By  observing  the  plate  of 
ice  through  a  lens,  numerous  small  crystals  will  be  seen  studding  the 
interior  of  the  block  ;  as  the  heat  continues  these  crystals  expand,  and 
finally  assume  the  shape  of  six-rayed  stars  of  exquisite  beauty. 

This  is  a  kind  of  negative  crystallisation,  the  crystals  produced  being 
composed  of  water  :  they  owe  their  formation  to  the  molecular  disturbance 
caused  by  the  absorption  of  heat  from  the  source.  Nothing  is  easier  than  to 
reproduce  this  phenomenon,  if  care  be  taken  in  cutting  the  ice.  The  planes 
of  freezing  can  be  found  by  noting  the  direction  of  the  bubbles  in  ice,  which 
are  either  spaisely  arranged  in  striae  at  right  angles  to  the  surface,  or  thickly 
collected  in  beds  parallel  to  the  surface  of  the  water.  A  warm  and  smooth 
metal  plate  should  be  used  to  level  and  reduce  the  ice  to  a  slab  not  exceeding 
half  an  inch  in  thickness. 

A  still  more  important  property  of  ice  remains  to  be  noticed.  Faraday 
discovered  that  when  two  pieces  of  melting  ice  are  pressed  together  they 
freeze  into  one  at  their  points  of  contact.  This  curious  phenomenon  is  now 
known  under  the  name  of  Regelation,  The  cause  of  it  has  been  the  subject 
of  much  controversy,  but  the  simplest  explanation  seems  to  be  that  given 
by  its  discoverer.  The  particles  on  the  exterior  of  a  block  of  ice  are  held  by 
cohesion  on  one  side  only  ;  when  the  temperature  is  at  o°  C.,  these  exterior 
particles  being  partly  free  are  the  first  to  pass  into  the  liquid  state,  and  a  film 
of  water  covers  the  solid.  But  the  particles  in  the  interior  of  the  block  are 
bounded  on  all  sides  by  the  solid  ice,  the  force  of  cohesion  is  here  a  maximum, 
and  hence  the  interior  ice  has  no  tendency  to  pass  into  a  liquid,  even  when 


968  Meteorology.  [990- 

the  whole  mass  is  at  o°.  If  the  block  be  now  split  in  halves,  a  liquid  film 
instantly  covers  the  fractured  surfaces,  for  the  force  of  cohesion  on  the 
fractured  surfaces  has  been  lessened  by  the  act.  By  placing  the  halves 
together,  so  that  their  original  position  shall  be  regained,  the  liquid  films 
on  the  two  fractured  surfaces  again  become  bounded  by  ice  on  both  sides. 
The  film  being  excessively  thin,  the  force  of  cohesion  is  able  to  act  across 
it ;  the  consequence  of  this  is,  the  liquid  particles  pass  back  into  the  solid 
state,  and  the  block  is  reunited  by  regelation.  Not  only  do  ice  and  ice  thus 
freeze  together,  but  regelation  also  takes  place  between  moist  ice  and  any 
non-conducting  solid  body,  as  flannel  or  sawdust ;  a  similar  explanation  to 
that  just  given  has  been  applied  here,  substituting  another  solid  for  the  ice 
on  one  side.  It  must  be  remarked,  however,  that  many  eminent  philosophers 
dissent  frdm  the  explanation  here  given. 

Whatever  may  be  the  true  cause  of  regelation,  there  can  be  no  doubt  that 
this  interesting  observation  of  Faraday's  explains  many  natural  phenomena. 
For  example,  the  formation  of  a  snowball  depends  on  the  regelation  of  the 
snow-granules  composing  it ;  and  as  regelation  cannot  take  place  at  tem- 
peratures below  o°  C.,  for  then  both  snow  and  ice  are  dry,  it  is  only  possible 
to  make  a  coherent  snowball  when  the  snow  is  melting. 

The  snow-bridges,  also,  which  span  wide  chasms  in  the  Alps  and  else- 
where, and  over  which  men  can  walk  in  safety,  owe  their  existence  to  the 
regelation  of  gradually  accumulating  particles  of  snow. 

Bottomley  has  made  a  very  instructive  experiment  which  illustrates  rege- 
lation. A  block  of  ice  is  suspended  on  two  supports,  and  a  fine  piano  wire 
with  heavy  weights  at  each  end  is  laid  across  it.  After  some  time  the  wire 
has  slowly  cut  its  way  through,  but  the  cut  surfaces  have  reunited,  and  except- 
ing a  few  bubbles,  show  no  trace  of  the  operation  ;  the  wire  is  below  zero,  as 
is  proved  by  placing  it  in  cold  water,  upon  which  some  ice  forms  round  it. 

991.  Claciers. — Tyndall  has  applied  this  regelating  property  of  ice  to 
an  explanation  of  the  formation  and  motion  of  glaciers,  of  which  the  fol- 
lowing is  a  brief  description  :  In  elevated  regions,  the  snow-line  (988) 
marks  the  boundary  of  eternal  snow,  for  above  this  the  heat  of  summer  is 
unable  to  melt  the  winter's  snow.  By  the  heat  of  the  sun  and  the  con- 
sequent percolation  of  water  melted  from  the  surface,  the  lower  portions  of 
the  snow-field  are  raised  to  o°  C.  ;  at  the  same  time  this  part  is  closely 
pressed  together  by  the  weight  of  the  snow  above ;  regelation  therefore  sets 
in,  converting  the  loose  snow  into  a  coherent  mass. 

By  increasing  pressure  the  intermingled  air  which  renders  snow  opaque 
becomes  ejected  and  transparent;  ice  then  results.  Its  own  gravity,  and 
the  pressure  from  behind,  urge  downwards  the  glacier  which  has  thus  been 
formed.  In  its  descent  from  the  mountain  the  glacier  behaves  in  all 
respects  like  a  river,  passing  through  narrow  gorges  with  comparative 
velocity,  and  then  spreading  out  and  moving  slowly  as  its  bed  widens. 
Further,  just  as  the  central  portions  of  a  river  move  faster  than  the  sides, 
so  Forbes  ascertained  that  the  centre  of  a  glacier  moves  quicker  than  its 
margin,  and  from  the  same  reason  (the  difference  in  the  friction  encoun- 
tered) the  surface  moves  more  rapidly  than  the  bottom.  To  explain  these 
facts  Forbes  assumed  ice  to  be  a  viscous  body  capable  of  flexure,  and 
flowing  like  lava  ;  but  as  ice  has  not  the  properties  of  a  viscous  sub- 


-993]      Apparatus  to  Investigate  Electricity  of  Atmosphere.     969 

stance,  the  now  generally  accepted  explanation  of  glacier  motion  is  that 
supplied  by  the  theory  of  regelation.  According  to  this  theory,  the  brittle 
ice  of  the  glacier  is  crushed  and  broken  in  its  passage  through  narrow 
channels,  such  as  that  of  Tre'laporte  on  Mont  Blanc  ;  and  then,  as  it 
emerges  from  the  gorge  which  confined  it,  becomes  reunited  by  virtue  of 
regelation  ;  in  this  instance  forming  the  well-known  Mer  de  Glace.  By 
numerous  experiments  Tyndall  has  established  that  regelation  is  adequate 
to  furnish  this  explanation,  and  has  artificially  imitated,  on  a  small  scale, 
the  moulding  of  glaciers  by  the  crushing  and  subsequent  regelation  of  ice. 

992.  Atmospheric    electricity.     Franklin's   experiment. — The    most 
frequent  luminous  phenomena,  and  the  most  remarkable  for  their  effects, 
are  those  produced  by  the  free  electricity  in  the  atmosphere.     The  first 
physicists  who  observed  the  electric  spark   compared  it   to  the  gleam  of 
lightning,  and  its  crackling  to  the  sound  of  thunder.     But  Franklin,  by  the 
aid   of  powerful  electrical  batteries,  first  established   a   complete  parallel 
between  lightning  and  electricity  ;  and  he  indicated,  in  a  memoir  published 
in  1749,  the  experiments  necessary  to  attract  electricity  from  the  clouds  by 
means  of  pointed  rods.     The  experiment  was  tried  by 

Dalibard  in  France  ;  and  Franklin,  pending  the  erec- 
tion of  a  pointed  rod  on  a  spire  in  Philadelphia,  had  the 
happy  idea  of  flying  a  kite,  provided  with  a  metal 
point,  which  could  reach  the  higher  regions  of  the 
atmosphere.  In  June  1752,  during  stormy  weather, 
he  flew  the  kite  in  a  field  near  Philadelphia.  The 
kite  was  flown  with  ordinary  pack-thread,  at  the  end 
of  which  Franklin  attached  a  key,  and  to  the  key  a 
silk  cord,  in  order  to  insulate  the  apparatus  :  he  then 
fixed  the  silk  cord  to  a  tree,  and  having  presented 
his  hand  to  the  key,  at  first  he  obtained  no  spark. 
He  was  beginning  to  despair  of  success,  when,  rain 
having  fallen,  the  cord  became  a  good  conductor,  and 
a  spark  passed.  Franklin,  in  his  letters,  describes  his 
emotion  on  witnessing  the  success  of  the  experiment  as 
being  so  great  that  he  could  not  refrain  from  tears. 

Franklin  imagined  that  the  kite  drew  from  the 
cloud  its  electricity ;  it  is,  in  fact,  a  simple  case  of 
induction,  and  depends  on  the  inductive  action  which 
the  thunder-cloud  exerts  upon  the  kite  and  the  cord. 

993.  Apparatus  to  investigate  the  electricity  of 
the  atmosphere. — To  observe  the  electricity  in  fine 
weather,  when  the  quantity  is  generally  small,  an  ap- 
paratus may  be  used,  as  devised  by  Saussure  for  this 
kind  of  investigation.     It  is  an  electroscope  similar  to 
that  already  described  (751),  but  the  rod  to  which  the 
gold  leaves  are  fixed  is  surmounted  by  a  conductor 
2  feet  in  length,  and  terminates  either  in  a  knob  or 
a  point  (fig.  918).     To  protect  the  apparatus  against 

rain,  it  is  covered  with  a  metal  shield  4  inches   in  Fig.  918. 

diameter.     The  glass  case  is  square,  instead  of  being  round,  and  a  divided 


970 


Meteorology. 


[993 


scale  on  its  inside  face  indicates  the  divergence  of  the  gold  leaves.  This 
electrometer  only  gives  signs  of  atmospheric  electricity  as  long  as  it  is 
raised  in  the  atmosphere  so  that  it  is  in  layers  of  air  of  higher  electrical 
potential  than  its  own. 

To  ascertain  the  electricity  of  the  atmosphere,  Saussure  also  used  a 
copper  ball,  which  he  projected  vertically  with  his  hand.  This  ball  was 
fixed  to  one  end  of  a  metal  wire,  the  other  end  of  which  was  attached  to  a 
ring,  which  could  glide  along  the  conductor  of  the  electrometer.  From  the 
divergence  of  the  gold  leaves,  the  electrical  condition  of  the  air  at  the 
height  which  the  ball  attained  could  be  determined.  Becquerel,  in  experi- 
ments made  on  the  St.  Bernard,  improved  Saussure's  apparatus  by  substi- 
tuting for  the  knob  an  arrow,  which  was  projected  into  the  atmosphere  by 
means  of  a  bow.  A  gilt  silk  thread,  88  yards  long,  was  fixed  with  one  end 
to  the  arrow,  while  the  other  end  was  attached  to  the  stem  of  an  electro- 
scope. Peltier  used  a  gold-leaf  electroscope,  at  the  top  of  which  was  a 
somewhat  large  copper  globe.  Provided  with  this  instrument,  the  observer 


Fig.  919. 

places  himself  in  a  prominent  position  ;  it  is  then  quite  sufficient  to  raise  the 
electroscope  even  a  foot  or  so  to  obtain  signs  of  electricity. 

To  observe  the  electricity  of  clouds,  where  the  potential  is  very  con- 
siderable, use  is  made  of  a  long  bar  terminating  in  a  point.  This  bar, 
which  is  insulated  with  care,  is  fixed  to  the  summit  of  a  building,  and  its 
lower  end  is  connected  with  an  electrometer,  or  even  with  electric  chimes 
(fig.  659),  which  announce  the  presence  of  thunder-clouds.  As,  however,  the 
bar  can  then  give  dangerous  shocks,  a  metal  ball  must  be  placed  near  it, 
which  is  well  connected  with  the  ground,  and  which  is  nearer  the  bar  than 
the  observer  himself;  so  that  if  a  discharge  should  ensue,  it  will  strike 
the  ball  and  not  the  observer.  Richmann,  of  St.  Petersburg,  was  killed  in  an 
experiment  of  this  kind,  by  a  discharge  which  struck  him  on  the  forehead. 


993] 


Ordinary  Electricity  of  the  Atmosphere. 


971 


Sometimes  also  captive  balloons  or  kites  have  been  used,  provided 
with  a  point,  and  connected  by  means  of  a  gilt  cord  with  an  electrometer. 

A  good  collector  of  atmospheric  electricity  consists  of  a  fishing-rod  with 
an  insulated  handle  which  projects  from  an  upper  window.  At  the  top  is 
a  bit  of  lighted  tinder  held  in  a  metallic  forceps,  the  smoke  of  which,  being 
an  excellent  conductor,  conveys  the  electricity  of  the  air  down  a  wire  attached 
to  the  rod.  A  sponge  moistened  with  alcohol,  and  set  on  fire,  is  also  an 
excellent  conductor. 

A  convenient  instrument  for  investigating  atmospheric  electricity  has 
been  introduced  by  Sir  W.  Thomson  ;  one  form  of  which,  used  in  the 
Meteorological  Observatory  of  Montsouris,  is  represented  in  fig.  919.  It 
consists  of  a  large  metal  vessel  A  resting  on  three  insulating  glass  legs  fixed 


Fig.  920. 

to  the  top  of  a  tall  column  of  cast  iron.  A  sheet  metal  mantle  B  protects  the 
supports  from  the  rain.  The  apparatus  is  arranged  in  the  open,  and  can  be 
filled  with  water  from  a  pipe  C.  The  water  issues  through  a  long  lateral 
jet  in  A,  in  a  stream  so  fine  that  the  volume  of  the  water  is  not  appreciably 
altered.  An  insulated  wire  /  passing  through  the  column,  connects  the  vessel 
A  with  an  electrometer  placed  indoors. 

The  manner  in  which  the  electricity  of  the  atmosphere  is  registered  is  seen 
from  fig.  920,  which  represents  the  form  in  use  at  the  above  observatory.  In 
a  light  tight  box  is  a  band  of  sensitised  photographic  paper,  stretched  on 
the  surface  of  a  cylinder  and  moved  by  clockwork. 

In  one  side  of  the  box  is  a  long  cylindrical  glass  lens,  in  front  of  which 
at  E  are  two  quadrant  electrometers  (780).  Both  of  these  are  connected  with 


972  Meteorology.  [993- 

the  same  collector  of  electricity,  placed  outside,  and  their  sectors  are  charged 
by  the  same  source  of  electricity,  but  one  of  them  is  ten  times  as  sensitive 
as  the  other.  Near  one  side  of  the  box  is  a  gas  burner  with  an  opaque 
chimney  A,  in  two  opposite  sides  of  which  are  longitudinal  slits,  through 
which  the  light  passes  to  two  total-reflection  prisms  (545)  pp',  which  are 
arranged  so  as  to  send  two  pencils  of  light  on  the  mirrors  m  m'~  of  the 
electrometer.  This  is  shown  on  a  larger  scale  on  the  left  of  the  figure  :  the 
two  pencils  fall  upon  the  lens  L,  which  concentrates  in  a  point  the  slices  of 
light  issuing  from  the  chimney  and  reflected  from  the  mirror.  These  follow 
the  motion  of  the  mirror,  and  thus  impress  on  the  sensitive  paper  the  curves 
which  measure  the  electrical  potential  of  the  air. 

There  is  also  an  arrangement  by  which  an  electromagnet  puts  the  electro- 
meters to  earth  for  a  few  minutes  at  every  hour,  and  thus  discharges  them. 
The  mirrors  revert  then  to  their  original  position  and  commence  a  new  trace. 

If  we  replace  the  electrometer  with  its  mirror  attached,  by  a  magneto- 
meter, we  can  easily  see  how  the  variations  in  the  magnetic  declination  may 
be  recorded  (702). 

994.  Ordinary  electricity  of  the  atmosphere. — By  means  of  the  dif- 
ferent apparatus  which  have  been  described,  it  has  been  found  that  the 
presence  of  electricity  in  the  atmosphere  is  not  confined  to  stormy  weather, 
but  that  the  atmosphere  always  contains  free  electricity,  usually  positive,  but 
occasionally  negative.  When  the  sky  is  cloudless,  the  electricity  is  always 
positive,  but  it  increases  with  the  height  above  the  ground.  The  amount  is 
greatest  in  the  highest  and  most  isolated  places.  No  trace  of  positive  elec- 
tricity is  found  in  houses,  streets,  and  under  trees  :  in  towns  positive  elec- 
tricity is  most  perceptible  in  large  open  spaces,  on  quays,  or  on  bridges.  In 
all  cases  positive  electricity  is  only  found  at  a  certain  height  above  the  ground. 
Sir  W.  Thomson  found  in  the  Isle  of  Arran  at  a  height  of  9  feet  above 
the  ground  a  difference  of  potential  equal  to  200  to  400  Daniell's  elements 
or  from  218  to  236  volts.  This  represents  a  rise  of  potential  of  from  24 
to  48  volts  for  each  foot  of  ascent.  This  is  subject  to  great  variation  ;  with 
winds  from  the  north  and  north-east  the  potential  was  often  6  to  10  times 
as  much  as  the  higher  of  these  amounts. 

At  sunrise  the  positive  electricity  in  the  air  is  feeble  ;  it  increases  up  to  1 1 
o'clock,  according  to  the  season,  and  then  attains  its  first  maximum.  It 
then  decreases  rapidly  until  a  little  before  sunset,  and  then  increases  till  it 
reaches  its  second  maximum,  a  few  hours  after  sunset  ;  the  remainder  of 
the  night  the  electricity  decreases  until  sunrise.  Thus  the  greatest  amount 
of  electricity  is  observed  when  the  barometric  pressure  is  highest.  These 
increasing  and  decreasing  periods,  which  are  observed  all  the  year,  are 
more  perceptible  when  the  sky  is  clearer,  and  the  weather  more  settled.  The 
positive  electricity  of  fine  weather  is  much  stronger  in  winter  than  in  summer. 

When  the  sky  is  clouded,  the  electricity  is  sometimes  positive  and  some- 
times negative.  It  often  happens  that  the  electricity  changes  its  sign 
several  times  in  the  course  of  the  day,  owing  to  the  passage  of  an  electrified 
cloud.  During  storms,  and  when  it  rains  or  snows,  the  atmosphere  may  be 
positively  electrified  one  day,  and  negatively  the  next,  and  the  number  of  the 
two  sets  of  days  are  virtually  equal. 

During  a  thunderstorm  the  changes  in  potential  and  sign  of  electricity 
are  so  rapid  that  the  photographic  method  of  registration  fails. 


-996]  Electricity  of  Clouds.  973 

From  a  long  series  of  observations  on  the  electricity  of  the  atmosphere 
made  in  the  early  morning,  Dellman  found  that  the  electricity  increased 
with  the  density  of  the  fog,  but  in  a  far  more  rapid  ratio. 

The  electricity  of  the  ground  has  been  found  by  Peltier  to  be  always 
negative,  but  to  different  extents,  according  to  the  hygrometric  state  and 
temperature  of  the  air. 

The  density  is,  however,  exceedingly  small,  being  calculated  at  0*00036 
dynes  per  square  centimetre,  from  which  it  follows  that  the  electrical 
pressure  (737)  is  0-00000082  dynes  per  square  centimetre,  or  less  than  the 
millionth  of  a  milligramme  in  weight.  Even  if  the  pressure  were  10  times 
as  great  it  would  be  insufficient  to  raise  even  the  lightest  bodies. 

995.  Causes  of  the    atmospheric  electricity. — Although  many  hypo- 
theses have  been  propounded  to  explain  the  origin  of  atmospheric  electricity 
it  must  be  confessed  that  our  knowledge  is  in  an  unsatisfactory  state. 

Volta  first  showed  that  the  evaporation  of  water  produced  electricity. 
Pouillet  subsequently  showed  that  no  electricity  is  produced  by  the  evapo- 
ration of  distilled  water  ;  but  that  if  an  alkali  or  a  salt  is  dissolved,  even 
in  small  quantity,  the  vapour  is  positively  and  the  solution  is  negatively 
electrified.  The  reverse  is  the  case  if  the  water  contains  acid.  Hence  it 
has  been  assumed  that  as  the  waters  which  exist  on  the  surface  of  the  earth 
and  on  the  sea  always  contain  salt  dissolved,  the  vapours  disengaged  ought 
to  be  positively  and  the  earth  negatively  electrified.  The  development  of 
electricity  by  evaporation  may  be  observed  by  heating  strongly  a  platinum 
dish,  adding  to  it  a  small  quantity  of  liquid,  and  placing  it  on  the  upper 
plate  of  the  condensing  electroscope  (fig.  679),  taking  care  to  connect  the 
lower  plate  with  the  ground.  When  the  water  of  the  capsule  is  evaporated, 
the  connection  with  the  ground  is  broken,  and  the  upper  plate  raised.  The 
gold  leaves  then  diverge  if  the  water  contained  salts,  but  remain  quiescent 
if  the  water  was  pure. 

Reasoning  from  such  experiments,  Pouillet  ascribed  the  development 
of  electricity  by  evaporation  to  the  separation  of  particles  of  water  from 
the  substances  dissolved  ;  but  Reich  and  Riess  showed  that  the  electricity 
disengaged  during  evaporation  could  be  attributed  to  the  friction  which 
the  particles  of  water  carried  away  in  the  current  of  vapour  exercise 
against  the  sides  of  the  vessel,  just  as  in  Armstrong's  electrical  machine 
(758).  By  a  recent  series  of  experiments,  Gaugain  has  arrived  at  the  same 
result. 

Sohncke  recalls  an  experiment  of  Faraday  which  he  has  repeated — that 
the  friction  of  minute  vesicles  of  water  against  dry  ice  is  an  abundant  source 
of  electricity ;  he  ascribes  atmospheric  electricity  to  this  origin,  showing  that 
in  the  upper  regions  both  particles  of  water  and  of  ice  may  coexist.  The  ice 
particles  become  positively  electrified  while  those  of  water  are  negative. 
When  these  fall  in  rain,  they  carry  with  them  their  negative  electricity. 

996.  Electricity  of  clouds. — Clouds  are  in  general  electrified,  usually 
positively  but  sometimes   negatively,  and   only  differ   in   their   higher    or 
lower   potential.      The  formation   of  positive   clouds    is    ascribed    to   the 
vapour  disengaged  from  the  ground  and  condensed  in  the  higher  regions. 
Negative  clouds  are  supposed  to  result  from  fogs,  which,  by  their  contact 
with  the  ground,  become  charged  with  negative  electricity,  which  they  retain 
on  rising  into  the  atmosphere  ;  or  that,  separated  from  the  ground  by  layers 


974  Meteorology.  [996- 

of  moist  air,  they  have  been  negatively  electrified  by  induction  from  the 
positive  clouds,  which  have  repelled  into  the  ground  positive  electricity. 

Whatever  be  the  origin  of  atmospheric  electricity,  there  can  be  no  doubt 
that  the  invisible  aqueous  vapour  is  the  carrier  of  it.  For  suppose  1,000 
vapour-particles,  each  possessing  the  same  charge  of  electricity,  coalesce  to 
form  a  single  droplet,  the  diameter  of  such  a  droplet  will  be  ten  times  that 
of  the  individual  particles,  that  is,  its  capacity  is  ten  times  as  great  (739)  ; 
but  the  quantity  of  electricity  will  be  1,000  times  as  great  as  on  the  small 
one,  and  therefore  the  potential  will  be  100  times  as  great.  But  the  number 
of  vapour-particles  which  go  to  form  a  single  droplet  is  rather  to  be  counted 
by  billions  ;  hence,  however  small  be  the  finite  value  which  we  assign  to 
the  potentials  of  the  electricity  of  the  vapour-particles,  that  of  the  drops  will 
be  infinitely  greater  and  sufficient  to  account  for  the  high  potential  of  clouds. 

997.  lightning. — This,  as  is  well  known,  is  the  dazzling  light  emitted  by 
the  electric  spark  when  it  shoots  from  clouds  charged  with  electricity.  In 
the  lower  regions  of  the  atmosphere  the  light  is  white,  but  in  the  higher 
regions,  where  the  air  is  more  rarefied,  it  takes  a  violet  tint ;  as  does  the 
spark  of  the  electrical  machine  in  a  rarefied  medium  (787). 

The  flashes  of  lightning  are  often  more  than  a  mile,  and  sometimes 
extend  to  four  or  five  miles,  in  length ;  they  generally  pass  through  the 
atmosphere  in  a  zigzag  direction — a  phenomenon  ascribed  to  the  resistance 
offered  by  the  air  condensed  by  the  passage  of  a  strong  discharge.  The 
spark  then  diverges  from  a  right  line,  and  takes  the  direction  of  least  resist- 
ance. In  vacuo,  electricity  passes  in  a  straight  line. 

De  la  Rue  and  Miiller  have  calculated  that  the  potential  required  to  pro- 
duce a  flash  a  mile  in  length,  would  be  that  of  3,516,480  of  their  cells  (812). 

We  cannot,  however,  regard  the  length  of  a  lightning  flash  as  the  direct 
striking  distance  between  two  conductors.  Owing  to  the  number  of  droplets 
met  on  its  path  the  discharge  is  rather  to  be  compared  with  that  of  the 
luminous  tubes  (789).  The  experiments  of  Mascart  on  the  relation  between 
the  striking  distance  (777)  and  the  potential  required  to  produce  it  show 
that  the  striking  distance  increases  far  more  rapidly  than  the  potential.  Thus 
while  the  potential  required  for  a  striking  distance  of  I  cm.  is  8-3  ;  for  4  cm. 
it  is  15-9  ;  for  8  cm.  20-5  ;  and  for  15  cm.  23-3.  From  this  it  is  possible  that  a 
lightning  discharge  is  produced  by  a  difference  of  potentials  between  two  clouds 
which  is  not  out  of  proportion  with  those  obtained  by  our  electrical  machines. 

Several  kinds  of  lightning  flashes  may  be  distinguished— i,  the  zigzag 
flashes,  which  move  with  extreme  velocity  in  the  form  of  a  line  of  fire  with 
sharp  outlines,  and  which  closely  resemble  the  spark  of  an  electrical 
machine ;  2,  the  sheet  flashes,  which,  instead  of  being  linear,  like  the  pre- 
ceding, fill  the  entire  horizon  without  having  any  distinct  shape.  This  kind, 
which  is  most  frequent,  appears  to  be  produced  in  the  cloud  itself,  and  to 
illuminate  the  mass.  According  to  Kundt,  the  number  of  sheet  discharges 
are  to  the  zigzag  discharged  as  n:6;  and  from  spectrum  observations  it 
would  appear  that  the  former  are  brush  discharges  between  clouds,  while 
the  latter  are  true  electrical  discharges  between  the  clouds  and  the  earth. 
Another  kind,  called  heat  lightning,  is  ascribed  to  distant  lightning  flashes 
which  are  below  the  horizon,  but  illuminate  the  higher  strata  of  clouds  so 
that  their  brightness  is  visible  at  great  distances ;  they  produce  no  sound, 


-998]  Thunder.  975 

probably  in  consequence  of  the  fact  of  their  being  so  far  off  that  the  rolling 
of  thunder  cannot  reach  the  ear  of  the  observer.  There  is  further  the  very 
unusual  phenomenon  of  globe  lightning,  or  the  flashes  which  appear  in  the 
form  of  globes  of  fire.  These,  which  are  sometimes  visible  for  as  much  as 
ten  seconds,  descend  from  the  clouds  to  the  earth  with  such  slowness  that 
the  eye  can  follow  them.  They  often  rebound  on  reaching  the  ground  ;  at 
other  times  they  burst  and  explode  with  a  noise  like  that  of  the  report  of 
many  cannon.  No  adequate  explanation  has  been  given  of  these. 

The  duration  of  the  light  of  the  first  three  kinds  does  not  amount  to  the 
millionth  of  a  second,  as  was  determined  by  Wheatstone  by  means  of  his 
rotating  wheel,  which  was  turned  so  rapidly  that  the  spokes  were  invisible  ; 
on  illuminating  it  by  the  lightning  flash,  its  duration  was  so  short  that 
whatever  the  velocity  of  rotation  of  the  wheel,  it  appeared  quite  stationary  ; 
that  is,  its  displacement  is  not  perceptible  during  the  time  the  lightning  exists. 
The  light  produced  by  a  lightning  flash  must  be  comparable  to  the  sun 
in  brightness,  though  it  does  not  appear  to  us  brighter  than  ordinary  moon- 
light. But  considering  its  excessively  brief  duration,  and  that  the  full 
effect  of  any  light  on  the  eye  is  only  produced  when  its  duration  is  at 
least  the  tenth  of  a  second,  it  follows  that  a  landscape  continuously  illu- 
minated by  the  lightning  flash  would  appear  100,000  times  as  bright  as  it 
actually  appears  to  us  during  the  flash. 

998.  Thunder. —  Thunder  is  the  violent  report  which  succeeds  lightning  in 
stormy  weather.  The  lightning  and  the  thunder  are  practically  simultaneous, 
but  an  interval  of  several  seconds  is  always  observed  between  these  two 
phenomena,  which  arises  from  the  fact  that  sound  only  travels  at  the  rate  of 
about  i, 100  feet  in  a  second  (232),  while  the  passage  of  light  is  almost  instan- 
taneous. Hence  an  observer  will  only  hear  the  noise  of  thunder  five  or  six 
seconds,  for  instance,  after  the  lightning,  according  as  the  distance  of  the 
thunder- cloud  is  five  or  six  times  1,100  feet.  The  noise  of  thunder  arises 
from  the  disturbance  which  the  electric  discharge  produces  in  the  air,  and 
which  may  be  witnessed  in  Kinnersley's  thermometer  (fig.  691).  Near  the 
place  where  the  lightning  strikes,  the  sound  is  sharp  and  of  short  duration. 
At  a  greater  distance  a  series  of  reports  are  heard  in  rapid  succession.  At  a 
still  greater  distance  the  noise,  feeble  at  first,  changes  into  a  prolonged  rolling 
sound  of  varying  intensity.  If  the  lightning  is  at  a  greater  distance  than  14 
or  1 5  miles  it  is  no  longer  heard,  for  sound  is  more  imperfectly  propagated 
through  air  than  through  solid  bodies  :  hence  there  are  lightning  discharges 
without  thunder  ;  these  occur  at  times  when  the  sky  is  cloudless. 

Some  attribute  the  noise  of  the  rolling  of  thunder  to  the  reflection  of 
sound  from  the  ground  and  from  the  clouds.  Others  have  considered  the 
lightning  not  as  a  single  discharge,  but  as  a  series  of  discharges,  each  of 
which  gives  rise  to  a  particular  sound.  But  as  these  partial  discharges 
proceed  from  points  at  different  distances,  and  from  zones  of  unequal  density 
it  follows  not  only  that  they  reach  the  ear  of  the  observer  successively,  but 
that  they  bring  sounds  of  unequal  density,  which  occasion  the  duration  and 
inequality  of  the  rolling.  The  phenomenon  has  finally  been  ascribed  to 
the  zigzags  of  lightning  themselves,  assuming  that  the  air  at  each  salient 
angle  is  at  its  greatest  compression,  which  would  produce  the  unequal  in- 
tensity of  the  sound. 


976  Meteorology.  [999- 

999.  Effects   of    lightning-. — The  lightning    discharge   is   the    electric 
discharge  which  strikes  between  a  thunder-cloud  and  the  ground.    The  latter, 
by  the  induction  from  the  electricity  of  the  cloud,  becomes  charged  with 
contrary  electricity ;  and  when  the  tendency  of  the  two  electricities  to  com- 
bine exceeds  the  resistance  of  the  air,  the  spark  passes,  which  is  often  ex- 
pressed by  saying,  that  *  a  thunder-bolt  has  fallen.'     Lightning  in  general 
strikes  from  above,  but  ascending  lightning  is  also  sometimes  observed  ;  pro- 
bably this  is  the  case  when  the  clouds  being  negatively  the  earth  is  positively 
electrified,  for  experiments  show  that  at  the  ordinary  pressure  the  positive 
fluid  passes  through  the  atmosphere  more  easily  than  negative  electricity. 

From  the  first  law  of  electrical  attraction  the  discharge  ought  to  fall  first 
on  the  nearest  and  best  conducting  objects,  and,  in  fact,  trees,  elevated 
buildings,  metals,  are  particularly  struck  by  the  discharge.  Hence  it  is  im- 
prudent to  stand  under  trees  during  a  thunderstorm. 

The  effects  of  lightning  are  very  varied,  and  of  the  same  kind  as  those 
of  batteries  (783),  but  of  far  greater  power.  The  lightning  discharge  kills 
men  and  animals,  ignites  combustibles,  melts  metals,  breaks  bad  con- 
ductors in  pieces.  When  it  penetrates  the  ground  it  melts  the  siliceous 
substances  on  its  path,  and  thus  produces  in  the  direction  of  the  discharge 
those  remarkable  vitrified  tubes  called  fulgurites,  some  of  which  are  as  much 
as  12  yards  in  length  ;  in  most  cases  there  are  found  to  be  accumulations  of 
water  below  such  fulgurites.  When  it  strikes  bars  of  iron,  it  magnetises 
them,  and  often  inverts  the  poles  of  compass  needles. 

After  the  passage  of  lightning  a  highly  peculiar  odour  is  frequently 
produced,  like  that  perceived  in  a  room  in  which  an  electrical  machine 
is  being  worked.  This  is  due  to  the  formation  of  ozone,  a  peculiar  allotro- 
pic  modification  of  oxygen  (793).  An  electrified  cloud  forms  with  the  earth 
below  a  condenser,  the  intervening  mass  of  air  being  the  dieletric.  This 
mass  of  air  is  therefore  in  a  state  of  strain  like  the  dieletric  in  a  Leyden 
jar,  and  it  is  to  this  state  of  strain  which  precedes  the  actual  discharge,  rather 
than  to  the  discharge  itself,  that  is  due  the  production  of  ozone. 

Heated  air  conducts  better  than  cold  air,  probably  only  owing  to  its 
lesser  density.  Hence  it  is  that  large  numbers  of  animals  are  often  killed 
by  a  single  discharge,  as  they  crowd  together  in  a  storm,  and  a  column  of 
warm  air  rises  from  the  group. 

1000.  Return  shock. — This  is  a  violent  and  sometimes  fatal  shock  which 
men  and  animals  experience,  even  when  at  a  great  distance  from  the  place 
where  the  lightning  discharge  passes.     It  is  caused  by  the  inductive  action 
which  the  thunder-cloud  exerts  on  bodies  placed  within  the  sphere  of  its 
activity.     These  bodies  are  then,  like  the  ground,  charged  with  the  opposite 
electricity  to  that  of  the  cloud;  but  when  the  latter  is  discharged  by  the 
recombination  of  its  electricity  with  that  of  the  ground,  the  induction  ceases, 
and  the  bodies  reverting  rapidly  from  the  electrical  state  to  the  neutral  state, 
the  concussion  in  question  is  reproduced— the  return  shock.     A  gradual  de- 
composition and  reunion  of  the  electricity  produces  no  visible  effects  ;  yet  it 
is  alleged  that  such  disturbances  of  the  electrical  equilibrium  are  perceived 
by  nervous  persons. 

The  return  shock  is  always  less  violent  than  the  direct  one  ;  there  is  no 
instance  of  its  having  produced  any  inflammation,  yet  plenty  of  cases  in 


-1001]  LigJ Lining  Conductor.  977 

which  it  has  killed  both  men  and  animals  ;  in  such  cases  no  broken  limbs, 
wounds,  or  burns  are  observed. 

The  return  shock  may  be  imitated  by  placing  a  gold-leaf  electroscope 
connected  by  a  wire  with  the  ground  near  an  electrical  machine  ;  when  the 
machine  is  worked,  at  each  spark  taken  from  the  prime  conductor  the  gold 
leaves  of  the  electroscope  suddenly  diverge. 

i oo i.  Lightning -conductor. — This  was  invented  by  Franklin,  in  1755. 

There  are  two  principal  parts  in  a  lightning-conductor,  the  rod  and  the 
conductor.  The  rod  is  a  pointed  bar  of  iron,  fixed  vertically  to  the  roof  of 
the  edifice  to  be  protected  ;  it  is  from  6  to  10  feet  in  height,  and  its  basal 
section  is  about  2  or  3  inches-in  diameter.  The  conductor  is  a  bar  of  iron, 
which  descends  from  the  bottom  of  the  rod  to  the  ground,  which  it  penetrates 
to  some  distance.  As  iron  bars  cannot  always  be  well  adapted  to  the  exterior 
of  buildings,  in  consequence  of  their  rigidity,  the  conductors  are  best  formed 
of  wire  ropes,  such  as  are  used  for  rigging  and  for  suspension  bridges.  In  a 
report  made  by  the  Academy  of  Sciences  on  the  construction  of  lightning- 
conductors,  the  use  of  copper  instead  of  iron  wire  in  these  conductors  is 
recommended,  inasmuch  as  copper  is  a  better  conductor  than  iron.  The 
metallic  section  of  the  cords  ought  to  be  about  f  a  square  inch,  and  the 
individual  wires  0-04  to  0-06  inch  in  diameter ;  they  ought  to  be  twisted 
in  three  strands,  like  an  ordinary  cord.  The  conductor  is  usually  led  into  a 
well,  and  to  connect  it  better  with  the  soil  it  ends  in  two  or  three  branches. 
If  there  is  no  well  near,  a  hole  is  dug  in  the  soil  to  the  depth  of  6  or  7  yards, 
and  the  foot  of  the  conductor  having  been  introduced,  the  hole  is  filled 
with  powdered  coke,  which  conducts  very  well. 

The  action  of  a  lightning-conductor  is  an  illustration  of  the  action  of 
induction  and  of  the  property  of  points  (731) ;  when  a  storm  cloud  positively 
electrified,  for  instance,  forms  in  the  atmosphere,  it  acts  inductively  on  the 
earth,  repels  the  positive  and  attracts  the  negative  electricity,  which  accu- 
mulates on  bodies  placed  on  the  surface  of  the  soil,  the  more  abundantly 
as  these  bodies  are  at  a  greater  height.  The  density  is  then  greatest  on  the 
highest  bodies,  which  are  therefore  most  exposed  to  the  electric  discharge ; 
but  if  these  bodies  are  provided  with  metal  points,  like  the  rods  of  conductors, 
the  negative  electricity,  withdrawn  from  the  soil  by  the  influence  of  the  cloud, 
flows  into  the  atmosphere,  and  neutralises  the  positive  electricity  of  the  cloud. 
Hence,  not  only  does  a  lightning-conductor  tend  to  prevent  the  accumulation 
of  electricity  on  the  surface  of  the  earth,  but  it  also  tends  to  restore  the 
clouds  to  their  natural  state,  both  which  concur  in  preventing  lightning  dis- 
charges. This  mode  of  action  of  lightning-conductors  is  often  overlooked  ; 
it  is  stated  in  reference  to  Pietermaritzburg  that  until  lightning-conductors 
became  common  in  that  town  it  was  constantly  visited  by  thunderstorms  at 
certain  seasons.  They  come  as  frequently  as  ever,  but  cease  to  give  flashes 
on  reaching  the  town  ;  they  do  so,  however,  when  they  have  passed  over  it. 
The  disengagement  of  electricity  is,  however,  sometimes  so  abundant  that 
the  lightning-conductor  is  inadequate  to  discharge  the  electricity  accumulated, 
and  the  lightning  strikes  ;  but  the  conductor  receives  the  discharge,  in  con- 
sequence of  its  greater  conductivity,  and  the  edifice  is  preserved. 

A  conductor,  to  be  efficient,  ought  to  satisfy  the  following  conditions  : — 

3R 


978  Meteorology.  [1001- 

i.  the  rod  ought  to  be  so  large  as  not  to  be  melted  if  the  discharge  passes ; 
ii.  it  ought  to  terminate  in  a  point,  or  in  several  points,  to  give  readier  issue  to 
the  electricity  disengaged  by  induction  from  the  ground  ;  iii.  the  conductor 
must  be  continuous  from  the  point  to  the  ground,  and  the  connection  between 
the  rod  and  the  ground  must  be  as  intimate  as  possible  ;  iv.  if  the  building 
which  is  provided  with  a  lightning-conductor  contains  metallic  surfaces  of  any 
extent,  such  as  zinc  roofs,  metal  gutters,  or  ironwork,  these  ought  to  be  con- 
nected with  the  conductor.  If  the  last  two  conditions  are  not  fulfilled,  there  is 
a  great  danger  of  lateral  discharges  ;  that  is  to  say,  that  the  discharge  takes 
place  between  the  conductor  and  the  edifice,  and  then  it  increases  the  danger. 

Colladon  concludes,  from  the  observation  of  a  series  of  lightning  dis- 
charges, that  a  tall  tree,  such  as  a  poplar,  whose  roots  are  in  dry  ground, 
may  act  as  a  good  lightning-conductor,  if  on  the  other  side  of  the  house 
there  does  not  happen  to  be  a  well  or  pool,  towards  which  the  electricity  can 
spring  through  the  house. 

1 002.  Rainbow. — The  rainbow  is  a  luminous  phenomenon  which  appears 
in  the  clouds  opposite  the  sun  when  they  are  resolved  into  rain.  It  consists 
of  seven  concentric  arcs,  presenting  successively  the  colours  of  the  solar 
spectrum.  Sometimes  only  a  single  bow  is  perceived,  but  there  are  usually 
two  :  a  lower  one,  the  colours  of  which  are  very  bright ;  and  an  external  or 
secondary  one,  which  is  paler,  and  in  which  the  order  of  the  colours  is  re- 
versed. In  the  interior  rainbow  the  red  is  the  highest  colour  ;  in  the  other 
rainbow  the  violet  is.  It  is  seldom  that  three  bows  are  seen  ;  theoretically 
a  greater  number  may  exist,  but  their  colours  become  so  faint  that  they  cannot 
be  perceived. 

The  phenomenon  of  the  rainbow  is  produced  by  the  decomposition  of  the 
white  light  of  the  sun  when  it  passes  into  the  drops,  and  by  its  reflection 
from  their  inside  face.  In  fact,  the  same  phenomenon  is  witnessed  in  dew- 
drops  and  in  jets  of  water  ;  in  short,  wherever  sunlight  passes  into  drops 
of  water  under  a  certain  angle. 

The  appearance  and  the  extent  of  the  rainbow  depend  on  the  position  ol 
the  observer,  and  on  the  height  of  the  sun  above  the  horizon  ;  hence  only 
some  of  the  rays  refracted  by  the  raindrops,  and  reflected  in  their  concavity 
to  the  eye  of  the  spectator,  are  adapted  to  produce  the  phenomenon.  Those 
which  do  so  are  called  effective  rays. 

To  explain  this  let  n  (fig.  921)  be  a  drop  of  water,  into  which  a  solar  ray 
S  a  penetrates.  At  a  point  of  incidence,  #,  part  of  the  light  is  reflected  from 
the  surface  of  the  liquid  ;  another,  entering  it,  is  decomposed  and  traverses 
the  drop  in  the  direction  a  b.  Arrived  at  £,  part  of  the  light  emerges  from 
the  raindrop,  the  other  part  is  reflected  from  the  concave  surface,  and  tends 
to  emerge  at^-.  At  this  point  the  light  is  again  partially  reflected  ;  the  re- 
mainder emerges  in  a  direction  g  O,  which  forms  with  the  incident  ray,  S  a, 
an  angle  called  the  angle  of  deviation.  It  is  such  rays  as  g  O,  proceeding 
from  the  side  next  the  observer,  which  produce  on  the  retina  the  sensation 
of  colours,  provided  the  light  is  sufficiently  intense. 

It  can  be  shown  mathematically  that  in  the  case  of  a  series  of  rays  which 
impinge  on  the  same  drop,  and  only  undergo  a  reflection  in  the  interior,  the 
angle  of  deviation  increases  from  the  ray  S"»,  for  which  it  is  zero,  up  to  a 
certain  limit,  beyond  which  it  decreases,  and  that  near  this  limit  rays  passing 


1002J 


Rainbbw. 


979 


parallel  into  a  drop  of  rain  also  emerge  parallel.  From  this  parallelism  a 
beam  of  light  is  produced  sufficiently  intense  to  impress  the  retina  ;  these 
are  the  rays  which  emerge  parallel  and  are  efficient. 

As  the  different  colours  which  compose  white  light  are  unequally  refran- 
gible, the  maximum  angle  of  deviation  is  not  the  same  for  all.  For  red  rays 
the  angle  of  deviation  corresponding  to  the  active  rays  is  42°  2',  and  for  violet 
rays  it  is  40°  17'.  Hence,  for  all  drops  placed  so  that  rays  proceeding  from 
the  sun  to  the  drop  make,  with  those  proceeding  from  the  drop  to  the  eye,  an 
angle  of  42°  2',  this  organ  will  receive  the  sensation  of  red  light ;  this  will  be 
the  case  with  all  drops  situated  on  the  circumference  of  the  base  of  a  cone, 
the  summit  of  which  is  the  spectator's  eye  ;  the  axis  of  this  cone  is  parallel 
to  the  sun's  rays,  and  the  angle  formed  by  the  two  opposed  generating  lines 
is  84°  4".  This  explains  the  formation  of  the  red  band  in  the  rainbow  ;  the 
angle  of  the  cone  in  the  case  of  the  violet  band  is  80°  34'. 
.  -  The  cones  corresponding  to  each  band  have  a  common  axis  called  the 
-visual  axis.  As  this  right  line  is  parallel  to  the  rays  of  the  sun,  it  follows 


Fig.  921. 

that  when  this  axis  is  on  the  horizon,  the  visual  axis  is  itself  horizontal,  and 
the  rainbow  appears  as  a  semicircle.  If  the  sun  rises,  the  visual  axis  sinks, 
and  with  it  the  rainbow.  Lastly,  when  the  sun  is  at  a  height  of  42°  2',  the 
arc  disappears  entirely  below  the  horizon.  Hence  the  phenomenon  of  the 
rainbow  never  takes  place  except  in  the  morning  and  evening. 

What  has  been  said  refers  to  the  interior  arc.  The  secondary  bow  is 
formed  by  rays  which  have  undergone  two  reflections,  as  shown  by  the  ray 
S'  idfeQ,  in  the  drop  p.  The  angle  S'  I  O  formed  by  the  emergent  and 
incident  rays  is  called  the  angle  of  deviation.  The  angle  is  no  longer  suscep- 
tible of  a  maximum,  but  of  a  minimum,  which  varies  for  each  kind  of  rays, 
and  to  which  also  efficient  rays  correspond.  It  is  calculated  that  the  mini- 
mum angle  from  violet  rays  is  54°  7',  and  for  red  rays  only  50°  57' ;  hence  it 
is  that  the  red  bow  is  here  on  the  inside,  and  the  violet  arc  on  the  outside. 
There  is  a  loss  of  light  for  every  internal  reflection  in  the  drop  of  rain,  and 
therefore  the  colours  of  the  secondary  bow  are  always  feebler  than  those  of 
the  internal  one.  The  secondary  bow  ceases  to  be  visible  when  the  sun  is 
54°  above  the  horizon. 

3  R  2 


980  Meteorology.  [1002- 

The  moon  sometimes  produces  rainbows  like  the  sun,  but  they  are  very 
pale. 

1003.  Aurora  borealis. — The  aurora  borealis,  or  northern  light,  or  more 
properly  polar  aurora,  is  a  remarkable  luminous  phenomenon  which  is  fre- 
quently seen  in  the  atmosphere  at  the  two  terrestrial  poles.  The  following 
is  a  description  of  an  aurora  borealis  observed  at  Bossekop,  in  Lapland,  lat. 
70°,  in  the  winter  of  1838-9  : — 

In  the  evening,  between  4  and  8  o'clock,  the  upper  part  of  the  fog  which 
usually  prevails  to  the  north  of  Bossekop  became  coloured.  This  light 
became  more  regular,  and  formed  an  indistinct  arc  of  a  pale  yellow,  with  its 
concave  side  turned  towards  the  earth,  while  its  summit  was  in  the  magnetic 
meridian. 

Blackish  rays  soon  separated  the  luminous  parts  of  the  arc.  Luminous 
rays  formed,  becoming  alternately  rapidly  and  slowly  longer  and  shorter, 
their  lustre  suddenly  increasing  and  diminishing.  The  bottom  of  these  rays 
always  showed  the  brightest  light,  and  formed  a  more  or  less  regular  arc. 
The  length  of  the  rays  was  very  variable,  but  they  always  converged  towards 
the  same  point  of  the  horizon,  which  was  in  the  prolongation  of  the  north 
end  of  the  dipping-needle  ;  sometimes  the  rays  were  prolonged  as  far  as 


Fig.  922. 

their  point  of  meeting,  and  thus  appeared  like  a  fragment  of  an  immense 
cupola. 

The  arc  continued  to  rise  in  an  undulatory  motion  towards  the  zenith. 
Sometimes  one  of  its  feet  or  even  both  left  the  horizon  ;  the  folds  became 
more  distinct  and  more  numerous ;  the  arc  was  now  nothing  more  than  a 
long  band  of  rays  convoluted  in  very  graceful  shapes,  forming  what  is  called 
the  boreal  crown.  The  lustre  of  the  rays  varied  suddenly  in  intensity,  and 
attained  that  of  stars  of  the  first  magnitude  ;  the  rays  darted  with  rapidity, 
the  curves  formed  and  re-formed  like  the  folds  of  a  serpent  (fig.  922),  the  base 
was  red,  the  middle  green,  while  the  remainder  retained  its  bright  yellow 


-1003]  Aurora  Borealis.  981 

colour.  Lastly,  the  lustre  diminished,  the  colours  disappeared  ;  everything 
became  feebler  or  suddenly  went  out. 

A  French  scientific  commission  to  the  North  observed  150  auroras 
boreales  in  200  days  ;  it  appears  that  at  the  poles,  nights  without  an  aurora 
borealis  are  quite  exceptional,  so  that  it  may  be  assumed  that  they  take  place 
every  night,  though  with  varying  intensity.  They  are  visible  at  a  consider- 
able distance  from  the  poles,  and  over  an  immense  area.  Sometimes  the  same 
aurora  borealis  has  been  seen  at  the  same  time  at  Moscow,  Warsaw,  Rome, 
and  Cadiz.  Their  height  is  variously  estimated  at  from  90  to  460  miles. 
Mr.  Newton  found  the  mean  height  of  30  aurorae  to  be  133  miles;  they 
are  most  frequent  at  the  equinoxes,  and  least  so  at  the  solstices.  The 
number  differs  in  different  years,  attaining  a  maximum  every  1 1  years  at 
the  same  time  as  the  sun-spots,  and  like  these  a  minimum  which  is  about  5 
or  6  years  from  the  maximum.  The  years  1844,  1855,  1860,  and  1877  are 
poor  in  the  appearance  of  the  aurora. 

There  is,  moreover,  a  period  of  about  60  years  ;  for  the  years  1728,  1780, 
and  1842  have  been  remarkable  for  the  prevalence  of  the  aurora.  The  last 
two  periods  are  also  remarkable  for  the  occurrence  of  disturbances  in  the 
earth's  magnetism. 

Numerous  hypotheses  have  been  devised  to  account  for  the  auroras 
boreales.  The  constant  direction  of  their  arc  as  regards  the  magnetic  me- 
ridian, and  their  action  on  the  magnetic  needle  (702),  seem  to  show  that  they 
ought  to  be  attributed  to  electric  currents  in  the  higher  regions  of  the  atmo- 
sphere. In  high  latitudes  the  aurora  borealis  acts  powerfully  on  the  wires  of 
the  electric  telegraph ;  the  alarms  are  for  a  long  time  violently  rung,  and 
despatches  frequently  interrupted  by  the  spontaneous  abnormal  working  of 
the  apparatus. 

The  spectrum  of  the  aurora  borealis  has  been  found  by  Vogel  to  consist 
of  five  lines  in  the  green,  and  of  an  indistinct  line  in  the  blue  ;  to  which  must 
be  added  a  red  line  due  to  the  red  protuberances  ;  these  lines  are  the  same 
as  those  of  nitrogen  greatly  rarefied  and  at  a  low  temperature. 

According  to  De  la  Rive  auroras  boreales  are  due  to  electric  discharges 
which  take  place  in  polar  regions  between  the  positive  electricity  of  the 
atmosphere  and  the  negative  electricity  of  the  earth ;  electricities  which 
themselves  are  separated  by  the  action  of  the  sun,  principally  in  the  equa- 
torial regions. 

The  occurrence  of  irregular  currents  of  electricity  which  manifest  them- 
selves by  abnormal  disturbances  of  telegraphic  communications  is  not  in- 
frequent :  such  currents  have  received  the  name  of  earth  currents.  Sabine 
found  that  these  magnetic  disturbances  are  clue  to  a  peculiar  action  of 
the  sun,  and  probably  independently  of  its  radiant  heat  and  light.  It  has 
also  been  ascertained  that  the  aurora  borealis  as  well  as  earth  currents  in- 
variably accompanies  these  magnetic  disturbances.  According  to  Balfour 
Stewart,  auroras  and  earth  currents  are  to  be  regarded  as  secondary  currents 
due  to  small  but  rapid  changes  in  the  earth's  magnetism  :  he  likens  the 
body  of  the  earth  to  the  magnetic  core  of  a  Ruhmkorff's  machine  (905)  ;  the 
lower  strata  of  the  atmosphere  forming  the  insulator,  while  the  upper  and 
rarer,  and  therefore  electrically  conducting  strata,  may  be  considered  as  the 
secondary  coil. 


982  Meteorology.  [1003- 

On  this  analogy  the  sun  may  perhaps  be  likened  to  the  primary  current 
which  performs  the  part  of  producing  changes  in  the  magnetic  state  of  the 
core.  Now  in  RuhmkorfFs  machine  the  energy  of  the  secondary  current  is 
derived  from  that  of  the  primary  current.  Thus,  if  the  analogy  be  correct, 
the  energy  of  the  aurora  borealis  may  in  like  manner  come  from  the  sun  ; 
but  until  we  know  more  of  the  connection  between  the  sun  and  terrestrial 
magnetism,  these  ideas  are  to  be  accepted  with  some  reserve. 

CLIMATOLOGY. 

1004.  Mean  temperature. — -The  mean  daily  temperature,  or  simply  tem- 
perature, is  that  obtained  by  adding  together  24  hourly  observations,  and 
dividing  by  24.     A  very  close  approximation  to  the  mean  temperature   is 
obtained  by  taking  the  mean  of  the  highest  and  lowest  temperatures  of  the 
day  and  of  the  night,  which  are  determined  by  means  of  the  maximum  and 
minimum  thermometers.     These  ought  to  be  protected  from  the  sun's  rays, 
to  be  raised  above  the  ground,  and  far  from  all  objects  which  might  influence 
them  by  their  radiation. 

The  temperature  of  a  month  is  the  mean  of  those  of  30  days,  and  the 
temperature  of  the  year  is  the  mean  of  those  of  12  months.  Finally,  the 
temperature  of  a  place  is  the  mean  of  its  annual  temperature  for  a  great 
series  of  years.  The  mean  temperature  of  London  is  8*28°  C,  or  46-9°  F. 
The  temperatures  in  all  cases  are  those  of  the  air,  and  not  those  of  the 
ground. 

1005.  Causes  which  modify  the  temperature  of  the  air.— The  principal 
causes  which  modify  the  temperature  of  the  air  are  the  latitude  of  a  place, 
its  height,  the  direction  of  the  winds,  and  proximity  of  seas. 

Influence  of  the  latitude. — The  influence  of  the  latitude  arises  from  the 
greater  or  less  obliquity  of  the  solar  rays,  for  as  the  quantity  of  heat  absorbed 
is  greater  the  more  perpendicular  are  the  rays  (414),  the  heat  absorbed  de- 
creases from  the  equator  to  the  poles,  for  the  rays  are  then  more  oblique. 
This  loss  is,  however,  in  summer,  in  the  temperate  and  arctic  zones,  partially 
compensated  by  the  length  of  the  days.  Under  the  equator,  where  the 
length  of  the  days  is  constant,  the  temperature  is  almost  invariable  ;  in  the 
latitude  of  London,  and  in  more  northerly  countries,  where  the  days  are 
very  unequal,  the  temperature  varies  greatly  ;  but  in  summer  it  sometimes 
rises  almost  as  high  as  under  the  equator.  The  lowering  of  the  temperature 
produced  by  the  latitude  is  small:  thus,  in  a  latitude  115  miles  north  of 
France,  the  temperature  is  only  i°  C.  lower. 

Influence  of  height. — The  height  of  a  place  has  a  much  more  consider- 
able influence  on  the  temperature  than  its  latitude.  In  the  temperate 
zone  a  diminution  of  i°  C.  corresponds  in  the  mean  to  an  ascent  of  180 
yards. 

The  cooling  on  ascending  in  the  atmosphere  has  been  observed  in 
balloon  ascents,  and  a  proof  of  it  has  been  seen  in  the  perpetual  snows 
which  cover  the  highest  mountains.  It  is  due  in  part  to  the  greater  rarefac- 
tion of  the  air,  which  necessarily  diminishes  its  absorbing  power  ;  besides 
which  the  air  is  at  a  greater  distance  from  the  ground,  which  heats  it  by 
contact ;  and  finally,  dry  air  is  very  diathermanous. 


-1006]  Isothermal  Lines.  983 

The  law  of  the  diminution  of  temperature  corresponding  to  greater 
heights  in  the  atmosphere  has  not  been  made  out,  in  consequence  of  the 
numerous  disturbing  causes  which  modify  it,  such  as  the  prevalent  winds, 
the  hygrometric  state,  the  time  of  day,  the  season  of  the  year,  &c.  The 
difference  between  the  temperatures  of  two  places  at  unequal  heights  is  not 
proportional  to  the  difference  of  level,  but  for  moderate  heights  an  approxi- 
mation to  the  law  may  be  made.  As  the  mean  of  a  series  of  very  careful 
observations  made  during  balloon  ascents,  a  diminution  of  i°  C.  corresponded 
to  an  increase  in  height  of  232  yaids. 

It  will  thus  be  seen  that  at  a  certain  height  above  the  ground,  there  must 
be  a  surface  or  layer  where  the  temperature  is  uniformly  zero.  The  height 
of  this  isothermal  surface  (1007)  will  vary  materially  with  the  time  of  the  year, 
being  lower  in  the  cold  months ;  it  varies  also  with  the  time  of  day,  rising 
rapidly  about  mid-day.  In  summer  this  height  may  be  taken  at  from  3,400  to 
3,700  metres  above  the  sea-level. 

Direction  of  winds. — As  winds  share  the  temperature  of  the  countries 
which  they  have  traversed,  their  direction  exercises  great  influence  on  the 
air  in  any  place.  In  Paris,  the  hottest  winds  are  the  south  ;  then  come  the 
south-east,  the  south-west,  the  west,  the  east,  the  north-west,  north,  and 
lastly,  the  north-east,  which  is  the  coldest.  The  character  of  the  wind 
changes  with  the  seasons ;  the  east  wind,  which  is  cold  in  winter,  is  warm  in 
summer. 

Proximity  of  the  sea. — The  neighbourhood  of  the  sea  tends  to  raise  the 
temperature  of  the  air,  and  to  render  it  uniform.  The  average  temperature 
of  the  sea  in  equatorial  and  polar  countries  is  always  higher  than  that  of  the 
atmosphere.  With  reference  to  the  uniformity  of  the  temperature,  it  has 
been  found  that  in  temperate  regions — that  is,  from  25°  to  50°  of  latitude — 
the  difference  between  the  highest  and  lowest  temperature  of  a  day  does  not 
exceed,  on  the  sea,  2°  to  3°  ;  while  upon  the  Continent  this  amounts  to  from 
1 2°  to  1 5°.  In  islands  the  uniformity  of  temperature  is  very  perceptible,  even 
during  the  greatest  heats.  In  continents,  on  the  contrary,  the  winters  for 
the  same  latitudes  become  colder,  and  the  difference  between  the  tempera- 
ture of  summer  and  winter  becomes  greater. 

1006.  Gulf  Stream.— A  similar  influence  to  that  of  the  winds  is  exerted 
by  currents  of  warm  water.  To  one  of  these,  the  Gulf  Stream,  the  mildness 
of  the  climate  in  the  north-west  of  Europe  is  mainly  due.  This  great  body 
of  water,  taking  its  origin  in  equatorial  regions,  flows  through  the  Gulf  of 
Mexico,  from  whence  it  derives  its  name  ;  passing  by  the  southern  shores  of 
North  America,  it  makes  its  way  in  a  north-westerly  direction  across  the 
Atlantic,  and  finally  washes  the  coast  of  Ireland  and  the  north-west  of  Europe 
generally.  Its  temperature  in  the  Gulf  is  about  28°  C.  ;  and  it  is  usually  a 
little  more  than  5°  C.  higher  than  the  rest  of  the  ocean  on  which  it  floats, 
owing  to  its  lower  specific  gravity.  To  its  influence  is  due  the  milder  climate 
of  West  Europe  as  compared  with  that  of  the  opposite  coast  of  America  ;  thus 
the  river  Hudson,  in  the  latitude  of  Rome,  is  frozen  over  three  months  in  the 
year.  It  also  causes  the  polar  regions  to  be  separated  from  the  coasts  of 
Europe  by  a  girdle  of  open  sea ;  and  thus  the  harbour  of  Hammerfest  is 
open  the  year  round.  Besides  its  influence  in  thus  moderating  climate,  the 
Gulf  Stream  is  an  important  help  to  navigators. 


984  Meteorology.  [1007- 

1007.  Isothermal  lines.— When  on  a  map  all  the  points  whose  tempera- 
ture is  known  to  be  the  same  are  joined,  curves  are  obtained  which  Hum- 
boldt  first  noticed,  and  which  he  called  isothermal  lines.     If  the  temperature 
of  a  place  only  varied  with  the  obliquity  of  the  sun's  rays— that  is,  with  the 
latitude — isothermal  lines  would  all  be  parallel  to  the  equator ;  but  as  the 
temperature  is  influenced  by  many  local  causes,  especially  by  the  height,  the 
isothermal  lines  are  always  more  or  less  curved.     On  the  sea,  however,  they 
are  almost  parallel.     A  distinction  is  made  between  isothermal  lines,  isotheral 
lines,  and  isochimenal  lines,  where  the  mean  general,  the  mean  summer,  and 
the  mean  winter  temperatures  are  respectively  constant.     An  isothermal 
zone  is  the  space  comprised  between  two  isothermal  lines.     Kupffer  also 
distinguishes  isogcothermic  lines  where  the  mean  temperature  of  the  soil  is 
constant. 

1008.  Climate. — By  the  climate  of  a  place  is  understood  the  whole  of  the 
meteorological  conditions  to  which  a  place  is  subjected ;  its  mean  annual 
temperature,  summer  and  winter  temperatures,  and   the   extremes   within 
which   these   are  comprised.     Some   writers   distinguish    seven   classes   of 
climates,  according  to  their  mean  annual  temperature  :  a  hot  climate  from 
30°  to  25°  C.  ;  a  warm  climate  from  25°  to  20°  C. ;  a  mild  climate  from  20° 
to  15°  C. ;  a  temperate  cJimate  from  15°  to  10°  C.  ;  a  cold  climate  from  10°  to 
5°  C.  ;  a  very  cold  climate  from  5°  to  zero  C. ;  and  an  arctic  climate  where 
the  temperature  is  below  zero. 

Those  climates,  again,  are  classed  as  constant  climates,  where  the  dif- 
ference between  the  mean  and  summer  and  winter  temperature  does  not 
exceed  6°  to  8°  ;  variable  climates,  where  the  difference  amounts  to  from 
1 6°  to  20°  ;  and  extreme  climates,  where  the  difference  is  greater  than  30°. 
The  climates  of  Paris  and  London  are  variable  ;  those  of  Pekin  and  New 
York  are  extreme.  Island  climates  are  generally  little  variable,  as  the 
temperature  of  the  sea  is  constant ;  and  hence  the  distinction  between  land 
and  sea  climates.  Marine  climates  are'  characterised  by  the  fact  that  the 
difference  between  the  temperature  of  summer  and  winter  is  always  less 
than  in  the  case  of  continental  climates.  But  the  temperature  is  by  no 
means  the  only  character  which  influences  climates  ;  there  are,  in  addition, 
the  moisture  of  the  air,  the  quantity  and  frequency  of  the  rains,  the  number 
of  storms,  the  direction  and  intensity  of  the  winds,  and  the  nature  of  the  soil. 

1009.  Distribution  of  temperature  on  the  surface  of  the  globe. — The 
temperature  of  the  air  on  the  surface  of  the  globe  decreases  from  the  equator 
to  the  poles  ;  but  it  is  subject  to  perturbing  causes  so  numerous  and  so 
purely  local,  that  its  decrease  cannot  be  expressed  by  any  law.  It  has 
hitherto  not  been  possible  to  do  more  than  obtain  by  numerous  observations 
the  mean  temperature  of  each  place,  or  the  maximum  and  minimum  tempe- 
ratures. The  following  table  gives  a  general  idea  of  the  distribution  of  heat 
in  the  Northern  Hemisphere  :  — 

Mean  temperature  at  different  latitudes. 

Abyssinia  .   :>.,,*••».•  .  31-0°  C.  Cairo     «#  .    -• .-:. •  ;  '.  .  22-4°  C. 

Calcutta.  . :     .;  ;  .  28-5  Constantino  .  ^?  v '•  .  17-2 

Jamaica.  .  u  26-1  Naples    .  .»• .  ...      v  .  167 

Senegal.  .        .  .  24-6  Mexico  .  -  »        ^  .  16-6 


-1010]  Temperature  of  Lakes •,  Seas,  and  Springs.  985 

Rio  de  Janeiro  .  .23-1  Marseilles       .  .  .14-1 

Constantinople  .  .     137°  C.    London  ....  8-3°  C. 

Pekin     .         .  .  .127  Stockholm*      .  .  .  -  5*6 

Paris       .         .  .  .10-8  Moscow'         .  .  .  3 '6 

Brussels          .  .  .     10-2  St.  Petersburg  .  .  3-5 

Strasburg        .  .  .9-8  St.  Gothard   .  .  —  ro 

Geneva  ....       97  Greenland      .  .  —  77 

Boston  .                                  9'3  Melville  Island  .  .  -187 

These  are  mean  yearly  temperatures.  The  highest  temperature  which  has 
been  observed  on  the  surface  of  the  globe  is  47*4°  at  Esne,  in  Egypt,  and  the 
lowest  is  -  75°  in  the  Arctic  Expedition  of  1876  ;  which  gives  a  difference  of 
122°  between  the  extreme  temperatures  observed  on  the  surface  of  the  globe. 

The  highest  temperature  observed  at  Paris  was  38-4°  on  July  8,  1793, 
and  the  lowest  -23-5°  on  December  26,  1798.  The  highest  observed  at 
Greenwich  was  35°  C.  in  1808,  and  the  lowest  -20°  C.  in  1838. 

No  arctic  voyagers  have  succeeded  in  reaching  the  poles,  in  consequence 
of  these  seas  being  completely  frozen,  and  hence  the  temperature  is  not 
known.  In  our  hemisphere  the  existence  of  a  single  glacial  pole — that  is,  a 
place  where  there  was  the  maximum  cold— has  been  long  assumed.  But  the 
bendings  which  the  isothermal  lines  present  in  the  Northern  Hemisphere  have 
shown  that  in  this  hemisphere  there  are  two  cold  poles — one  in  Asia,  to  the 
north  of  Gulf  Taymour ;  and  the  other  in  America,  north  of  Barrow's  Straits, 
about  1 5°  from  the  earth's  north  pole.  The  mean  temperature  of  the  first  cf 
these  poles  has  been  estimated  at  —17°,  and  that  of  the  second  at  —19°. 
With  respect  to  the  austral  hemispheres,  the  observations  are  not  sufficiently 
numerous  to  tell  whether  there  are  one  or  two  poles  of  greatest  cold,  or  to 
determine  their  position. 

1010.  Temperature  of  lakes,  seas,  and  springs. — In  the  tropics  the 
temperature  of  the  sea  is  generally  the  same  as  that  of  the  air ;  in  polar 
regions  the  sea  is  always  warmer  than  the  atmosphere. 

The  temperature  of  the  sea  under  the  torrid  zone  is  always  about  26°  to 
27°  at  the  surface  :  it  diminishes  as  the  depth  increases,  and  in  temperate 
as  well  as  in  tropical  regions  the  temperature  of  the  sea  at  great  depths  is 
between  2*5°  and  3'5°.  The  temperature  of  the  lower  layers  is  caused  by 
submarine  currents  which  carry  the  cold  water  of  the  polar  seas  towards  the 
equator. 

The  variations  in  the  temperature  of  lakes  are  more  considerable  ;  their 
surface,  which  becomes  frozen  in  winter,  may  become  heated  to  20°  or  25°  in 
summer.  The  temperature  of  the  bottom,  on  the  contrary,  is  virtually  4°, 
which  is  that  of  the  maximum  density  of  water. 

Springs,  which  arise  from  rain  water  which  has  penetrated  into  the  crust 
of  the  globe  to  a  greater  or  less  depth,  necessarily  tend  to  assume  the  tempe- 
rature of  the  terrestrial  layers  which  they  traverse.  Hence,  when  they  reach 
the  surface  their  temperature  depends  on  the  depth  which  they  have  attained. 
If  this  depth  is  that  of  the  layer  of  invariable  temperature,  the  springs  have 
a  temperature  of  10°  or  1 1°  in  this  country,  for  this  is  the  temperature  of  this 
layer,  or  about  the  mean  annual  temperature.  If  the  springs  are  not  very 
copious,  their  temperature  is  raised  in  summer  and  cooled  in  winter  by  that 


986  Meteorology.  [1010 

of  the  layers  which  they  traverse  in  passing  from  the  invariable  layer  to  the 
surface.  But  if  they  come  from  below  the  layer  of  invariable  temperature 
their  temperature  may  considerably  exceed  the  mean  temperature  of  the 
place,  and  they  are  then  called  thermal,  springs.  The  following  list  gives 
the  temperature  of  some  of  them  : — 

Wildbad    .  .'  '          .  .  .  .  37'5°  C. 

Vichy         .  .  .  40 

Bath  .  46 

Ems       "    .  .  .  .         ^  ...  f  r.,  .•    •  46 

Baden-Baden  .  .  .  67-5 

Chaudes-Aigues  .  .  .  .  ... 

Trincheras  ....  * " .  ^  67 

Great  Geyser,  in  Iceland,  at  a  depth  of  66  ft.      .  124 

From  their  high  temperature  they  have  the  property  of  dissolving  many 
mineral  substances  which  they  traverse  in  their  passage,  and  hence  form 
mineral  waters.  The  temperature  of  mineral  waters  is  not  modified  in 
general  by  the  abundance  of  rain  or  of  dryness  ;  but  it  is  by  earthquakes, 
after  which  they  have  sometimes  been  found  to  rise  and  at  others  to  sink. 

101 1.  Distribution  of  land  and  water. — The  distribution  of  water  on  the 
surface  of  the  earth  exercises  great  influence  on  climate.  The  area  covered 
by  water  is  considerably  greater  than  that  of  the  dry  land  ;  and  the  distribu- 
tion is  unequal  in  the  two  hemispheres.  The  entire  surface  of  the  globe 
occupies  about  200  millions  of  square  miles,  nearly  \  of  which  is  covered  by 
water ;  that  is,  the  extent  of  the  water  is  nearly  three  times  as  great  as  that 
of  the  land.  The  surface  of  the  sea  in  the  Southern  Hemisphere  is  to  that  in 
the  Northern  in  about  the  ratio  of  13  to  9. 

The  depth  of  the  open  sea  is  very  variable  ;  the  lead  generally  reaches 
the  bottom  at  about  300  to  450  yards  ;  in  the  ocean  it  is  often  1,300  yards, 
and  instances  are  known  in  which  a  bottom  has  not  been  reached  at  a  depth 
of  4,500.  It  has  been  computed  that  the  total  mass  of  the  water  does  not 
exceed  that  of  a  liquid  layer  surrounding  the  earth  with  a  depth  of  about 
1,100  yards. 


PROBLEMS    AND    EXAMPLES 
IN    PHYSICS. 


I.  EQUILIBRIUM. 

1.  A  body  being  placed  successively  in  the  two  pans  of  a  balance,  requires  180 
grammes  to  hold  it  in  equilibrium  in  one  pan,  and  181  grammes  in  the  other;  required 
the  weight  of  the  body  to  a  milligramme. 

From  the  formula  x  =•  \/pp,  we  have 

x  =    \/i8o  y  181   =   i8o?r,  499. 

2.  What  resistance  does  a  nut  offer  when  placed  in  a  pair  of  nutcrackers  at  a 
distance  of  f  of  an  inch  from  the  joint,  if  a  pressure  of  5  pounds  applied  at  a  distance 
of  4  inches  from  the  joint  is  just  sufficient  to  crack  it  ?  Ans.  26%  pounds. 

3.  What  force   is  required  to  raise  a  cask  weighing  6  cwt.  into  a  cart  o'8  metre 
high  along  a  ladder  275  metres  in  length  ?  Ans.  195^  pounds. 

4.  If  a  horse  can  move  30  cwt.  along  a  level  road,  what  can  it  move  along  a  road 
the  inclination  of  which  is  i  in  80,  the  coefficient  of  friction  on  each  road  being  i  ? 

Ans.  26§  cwt. 

5.  The  piston  of  a  force-pump  has  a  diameter  of  8  centimetres,  and  the  arms  of 
the  lever  by  which  it  is  worked  are  respectively  12  and  96  centimetres  in  length  ;  what 
force  must  be  exerted  at  the  longer  arm  if  a  pressure  of  12  '36  pounds  on  a  square  cen- 
timetre is  to  be  applied?  Ans.  77  "6g  pounds. 

II.  GRAVITATION. 

6.  A  stone  is  thrown  from  a  balloon  with  a  velocity  of  50  metres  in  a  second.   How 
soon  will  the  velocity  amount  to  99  metres  in  a  second,  and  through  what  distance 
will  the  stone  have  fallen  ? 

To  find  the  time  requisite  for  the  body  to  have  acquired  the  velocity  of  99  metres  in 
a  second,  we  have 

v  —   V  +  gt  ; 

in  which  V  is  the  initial  velocity,  g  the  acceleration  of  gravity  which,  with  sufficient 
approximation,  is  equal  to  9*8  metres  in  a  second,  and  t  the  time.  Substituting  these 
values,  we  have 

/   =  99^50  =    49    =  5  seconds. 

9-8  9-8 

ror  the  space  traversed  we  have 


s  =    Vt  +  ?igt'*  —  50  x  5  +  4  '9  x  25  =372  '5  metres. 

7.  A  projectile  was  thrown  vertically  upwards  to  a  height  of  5iom>22.     Disregard- 
ing the  resistance  of  the  air,  what  was  the  initial  velocity  of  the  body  ? 

The  velocity  is  the  same  as  that  which  the  body  would  have  acquired  on  falling 
from  a  height  of  510-22  metres. 

From  the  formula  v  =   \/2gs\\e.  get 

v  =   \/2  x  9'8  x  510-22  =   -s/ioooo  =   100  metres, 

8.  A  stone  is  thrown  vertically  upwards  with  an   initial  velocity  of  100  metres. 
After  what  time  would  it  return  to  its  original  position  ? 


988  Problems  and  Examples  in  Physics. 

The  time  of  rising  and  falling  is  the  same,  but  the  time  of  falling  is  ^  (from  the 

<!> 

formula  v=gt]  or  -°?  =io'2,  which  is  half  the  time  required  ;  therefore  /=2o'4  sec. 
9-8 

9.  A  stone  is  thrown  vertically  upwards  with  an  initial  velocity  of  100  metres  ;  after 
x  seconds  a  second  stone  is  thrown  with  the  same  velocity.     The  second  stone  is  rising 
87  seconds  before  it  meets  the  first.     What  interval  separated  the  throws? 

The  rising  stone  will  have  the  velocity  v  =  Vg-  gt,  whence  v  =  100  —  9-8  x  87. 
On  the  other  hand,  the  falling  stone,  at  the  moment  the  stones  meet,  will  have  the  velocity 
given  by  the  equation  v  =  gt'  in  which  t'  is  the  time  during  which  the  stone  falls 

before  it  meets  the  second  one.    This  time  is  equal  to"87  seconds  +  x  —  I0°.    Hence 

9'8 
its  velocity  is  /  i     \ 

Equating  the  two  values  of  v  and  reducing,  we  obtain  x  =  3  seconds. 

10.  A  body  moving  with  a  uniformly  accelerated  motion  traverses  a  space  of  looj 
metres  in  10  seconds.     What  would  be  the  space  traversed  during  the  eighteenth 
second  if  the  motion  continued  in  the  same  manner  ? 

The  formula  s  =  ^gf*  gives  for  the  accelerating  force  g  =  20  metres  per  second. 
The  space  traversed  during  the  eighteenth  second  will  be  equal  to  the  difference  of 
the  space  traversed  in  18  seconds  and  that  traversed  at  the  end  of  the  seventeenth. 
x  =   20 _^i8«  _  20_x   IT2   =   35ometres< 

11.  A  cannon-ball  has  been  shot  vertically  upwards  with  a  velocity  of  250  metres  in 
a  second.  After  what  interval  of  time  would  its  velocity  have  been  reduced  to  54  metres 
under  the  retarding  influence  of  gravity,  and  what  space  would  have  been  traversed  by 
the  ball  at  the  end  of  this  time  ? 

If  t  be  the  time,  then  at  the  end  of  each  second  the  initial  velocity  would  be  dimi- 
nished by  9m  '8.  Hence  we  shall  have 

54  =  250  —  t  x  9 '8,  whence  t  =  20  seconds  ; 
and  for  the  space  traversed  ,     (J^  % 

Q-8    X    202 

=  250  x  20  —  2L  —  =  3040  metres. 

12.  Required  the  time  in  which  a  body  would  fall  through  a  height  of  2000  metres, 
neglecting  the  resistance  of  the  air. 

From  s  =  £  gfi  and  substituting  the  values,  we  have 

2000  =  9—  ft,  whence  /  =   20 '2  seconds. 
2 

13.  A  body  falls  in  air  from  a  height  of  4000  metres.     Required  the  time  of  its  fall 
and  its  velocity  when  it  strikes  the  ground. 

From  the  formula  s  =  £  gtz  we  have  for  the  time  t  =       /  2~  >    and,  on  the  other 

V    g 

hand,  from  the  formula  for  velocity  v  =  gt  we  have  /  =   t'=200  =  2o-4. 


^— ,  from  which  v  =   -v/2  sg,  and  substituting  the  values  for  s  and 
g,  ~u  =  280  metres. 

14.  A  stone  is  thrown  into  a  pit  150  metres  deep  and  reaches  the  bottom  in  4 
seconds.     With  what  velocity  was  it  thrown,  and  what  velocity  had  it  acquired  on 
reaching  the  ground  ?    Ans.  The  stone  was  thrown  with  a  velocity  of  17-9,  and  on 
reaching  the  ground  had  acquired  the  velocity  57-1. 

15.  A  stone  is  thrown  downwards  from  a  height  of  150  metres  with  a  velocity  of  10 
metres  per  second.     How  long  will  it  require  to  fall  ? 

The  distance  through  which  the  stone  falls  is  equal  to  the  sum  of  the  distances 


Gravitation.  989 

through  which  it  would  fall  in  virtue  of  its  initial  impulse  and  of  that  which  it  would 
traverse  under  the  influence  of  gravity  alone  ;  that  is,  150  =   10  t  +  9'8  -. 
Taking  the  positive  value  only  we  get  t  —  4*61  seconds. 

16.  How  far  will  a  heavy  body  fall  in  vacuo  during  the  time  in  which  its  velocity 
increases  from  40*25  feet  per  second  to  88-55  feet  per  second  ? 

Ans.  Taking  the  value  of  g  at  32*2  feet,  the  body  falls  through  96*6  feet. 

17.  Required  the  time  of  oscillation  of  a  single  pendulum  whose  length  is  0*9938, 
and  in  a  place  where  the  intensity  of  gravity  is  9-81. 

From  the  general  formula  t  =  ir      /   ,   in  which   t  expresses  the  time   of  one 
oscillation,  /  the  length  of  the  pendulum,  and  g  the  intensity  of  "gravity,  we  have 


t  =  3*1416  (Vi      =   i  second. 

18.  What  is  the  intensity  of  gravity  in  a  place  in  which  the  length  of  the  seconds 
pendulum  is  om'99i  ? 

In  this  case  /  =  it     /   ,  ;  and  also  t  =  it    /  _  .  ;  and  therefore         =    -  ,    from 

V  g'  V  g'  g'       g 

which  g'  =    —  .     Substituting  in  this  latter  equation  the  values  of  g',  I  and  F,  we 


19.  In  a  place  at  which  the  length  of  the  seconds  pendulum  is  0*99384,  it  is  required 
to  know  the  length  of  a  pendulum  which  makes  one  oscillation  in  5  seconds. 

In  the  present  case,  as  g  remains  the  same  in  the  general  formula,  and  /  varies,  the 
length  /  must  vary  also.  We  shall  have,  then, 

' 


from  which,  reducing  and  introducing  the  values,  we  have 
/'  =  52  x  0*99384  =  24*846. 

20.  A  pendulum,  the  length  of  which  is  im'95,  makes  61,682  oscillations  in  a  day. 
Required  the  length  of  the  seconds  pendulum.  Ans.  0*99385  metres. 

21.  A  pendulum  clock  loses  5  seconds  in  a  day.     By   how  much  must    it   be 
shortened  to  keep  correct  time  ? 

Let  s  =  the  number  of  seconds  in  one  day,  and  /  the  number  indicated  by  the 
clock,  then  s  :  sf=n  :  n'  =  t'  :  t=  *J  I'  :  >//  .«.  86400  :  86395=  i  :  */xx.-.x=  "9998843. 
Hence  1  —  ^  =  0*0001157  Ans. 

22.  What   is   the  normal  acceleration  of  a  body  which  traverses  a  circle  of  4*2 
metres  diameter  with  a  rectangular  velocity  of  3  metres  ?  Ans.  4*286  metres. 

23.  An  iron  ball  falls  from  a  height  of  68  cm.   on  a  horizontal  iron  plate,   and 
rebounds  to  a  height  of  27  cm.     Required  the  coefficient  of  elasticity  of  the  iron. 

If  an  imperfectly  elastic  ball  with  the  velocity  v  strikes  against  a  plate,  it  rebounds 
with  the  velocity  v,  =   —  k  v,  from  which,  disregarding  the  sign,  k  —    '.     Now  we 


have   the  velocity  f,  =    Vz  gh,  and  v  —   \fzgh,  from  which  k  ——•'    Substitut- 

*Jh 
ing  the  corresponding  values,  we  get  k  —   0*63. 

24.  Two  inelastic  bodies,  weighing  respectively  100  and  200  pounds,  strike  against 
each  other  with  velocities  of  50  and  20  feet  ;  what  is  their  common  velocity,  after  the 
impact  ?  Ans.  30,  or  3*3,  according  as  they  move  in  the  same  or  in  opposite  directions 
before  impact. 


99O  Problems  and  Examples  in  Physics. 


III.     ON  LIQUIDS  AND  GASES. 

25.  The  force  with  which  a  hydraulic  press  is  worked  is  20  pounds  ;  the  arm  of  the 
lever  on  which  this  force  acts  is  5  times  as  long  as  that  of  the  resistance ;  lastly,  the 
area  of  the  large  piston  is  70  times  that  of  the  smaller  cue.     Required  the  pressure 
transmitted  to  the  large  piston. 

If  F  be  the  power,  and  /  the  pressure  transmitted  to  the  smaller  piston,  we  have 
from  the  principle  of  the  lever  p  x  i  =  F  x  5.  Moreover,  from  the  principle  of  the 
equality  of  pressure 

P  x   i   =  p  x  70  =   5  x  20  x  70  =   7000  pounds. 

26.  The  force  with  which  a  hydraulic  press  is  worked  being  30  kilos,  and  the  arm 
of  the  lever  by  which  this  force  is  applied  being  10  times  as  long  as  that  of  the  resist- 
ance, and  the  diameter  of  the  small  piston  being  two  centimetres  ;  find  the  diameter  of 
the  large  piston,  In  order  that  a  pressure  of  2000  kilos,  may  be  produced. 

A  us.  5  -164  centimetres. 

27.  One  of  the  limbs  of  a  U-shaped  glass  tube  contains  mercury  to  a  height  of 
om*i75  ;  the  other  contains  a  different  liquid  to  a  height  of  om*42  ;  the  two  columns 
being  in  equilibrium,  required  the  density  of  the  second  liquid  with  reference  to  mer- 
cury and  to  water. 

If  d  is  the  density  of  the  liquid  as  compared  with  mercury  and  dt  the  density  com- 
pared with  water,  then  i  x  0*175  =  0*42  x  d ;  and  13*6  x  o'i75  =  o'42  x  dt\ 
whence  d  =  0*416  and  dt  =  5 '66. 

28.  What  force  would  be  necessary  to  support  a  cubic  decimetre  of  platinum  in 
mercury  at  zero?     Density  of  mercury  13*6  and  that  of  platinum  21-5. 

From  the  formula  P  —  VD  the  weight  of  a  cubic  decimetre  of  platinum  is 
T  x  2i'5  =  2ik<5  and  that  of  a  cubic  decimetre  of  mercury  is  i  x  13*6  =  i3k'6. 
From  the  principle  of  Archimedes,  the  immersed  platinum  loses  part  of  its  weight 
•equal  to  that  of  the  mercury  which  it  displaces.  Its  weight  in  the  liquid  is  therefore 
21 '5  —  13*6  =.  7*9,  and  this  represents  the  force  required. 

29.  Given  a  body  A  which  weighs  7*55  grammes  in  air,    5-17  gr.  in  water,   and 
6*35  gr.  in  another  liquid,  B  ;  required  from  these  data  the  density  of  the  body  A  and 
that  of  the  liquid  B. 

The  weight  of  the  body  A  loses  in  water  7*55  —  5*17  =  2*38  grammes  ;  this  repre- 
sents the  weight  of  th?  displaced  water.  In  the  liquid  B  it  loses  7*55  —  6*35  =  1*2  gr. ; 
this  is  the  weight  of  the  same  volume  of  the  body  B,  as  that  of  A  and  of  the  displaced 
water.  The  specific  gravity  of  A  is  therefore 

755  =  3.172|  and  that  of  5  I2°  =  0*504. 

30.  A  cube  of  lead,  the  side  of  which  is  4  cm.,  is  to  be  supported  in  water  by 
being  suspended  to  a  sphere  of  cork.    What  must  be  the  diameter  of  the  latter,  the 
specific  gravity  of  cork  being  0*24,  and  that  of  lead  11*35  ? 

The  volume  of  the  lead  is  64  cubic  centimetres  ;  its  weight  in  air  is  therefore 
64  x  11*35,  and  its  weight  in  water  64  x  11*35  —  64  =  662*4  gr. 

If  r  be  the  radius  of  the  sphere  in  centimetres,  its  volume  in  cubic  centimetres  will 

be  4  * — ,  and  its  weight  in  grammes  is  4  n       x  °  24.     Now,  as  the  weight  of  the 

3  3 

displaced  water  is  obviously  -  TT  r5  in  grammes,  there  will  be   an  upward  buoyancy 

represented  by  *  "  ^  _  4jf  r*  x  0*24  =  4  IT  ^  x  076  which  must  be  equal  tQ  the 

weight  of  the  lead;  that  is,  4  ff  ^  x  o 76  =  ^.^  from  which  r  =  s<™-g2S  and  the 
diameter  =  ir85. 


On  Liquids  and  Gases.  991 

31.  A  cylindrical  steel  magnet  15  cm.  in  length  and  1*2  mm.  in  diameter,  is  loaded 
at  one  end  with  a  cylinder  of  platinum  of  the  same  diameter  and  of  such  a  length  that 
when  the  solid  thus  formed  is  in  mercury,  the  free  end  of  the  steel  projects  10  mm. 
above  the  surface.      Required  the  length  of  this  platinum,  specific  gravity  of  steel 
being  7*8  and  of  platinum  21 '5. 

The  weight  of  the  steel  in  grammes  will  be  15  ff  r2  x  7-8  and  of  the  platinum 
x  r*  x  21-5. 

These  are  together  equal  to  the  weight  of  the  displaced  mercury,  which  is 

•n  r-  (14  +  x}  13*6,  from  which  x  =  9*29  cm. 

32.  A  cylindrical  silver  wire  om*ooi5  in  diameter  weighs  3*2875  grammes  ;  it  is  to 
be  covered  with  a  layer  of  gold  om*ooo2  in  thickness.  Required  the  weight  of  the  gold  ; 
the  specific  gravity  of  silver  being  10*47  and  tnat  °f  S°W  19*26. 

If  r  is  the  radius  of  the  silver  wire  and  R  its  radius  when  covered  with  gold,  then 
r  =  oc*075  and  R  —  oc'O95.  The  volume  of  the  silver  wire  will  be  it  r~  /  and  its 
weight  it  r1  /  10*47,  from  which  /  =  I7C768. 

The  volume  of  the  layer  of  gold  is 

n  (fit  _  ,-2)  17768, 

and  its  weight 

*•  (°'°952  —  °'°75")  x  17768  x  19-26  =  3-656  nearly. 

33.  A  kilogramme  of  copper  is  to  be  drawn  into  wire  having  a  diameter  of  o'i6 
centimetre.     What  length  will  it  yield  ?    Specific  gravity  of  copper  8 '88. 

The  wire  produced  represents  a  cylinder  /  cm.  in  length,  the  weight  of  which  is 
«•  r2  /  8'88,  and  this  is  equal  to  1000  grammes.  Hence  /  =  56m>oo85. 

34.  The  specific  gravity  of  cast  copper  being  8*79,  and  that  of  copper  wire  being 
8-88,  what  change  of  volume  does  a  kilogramme  of  cast  copper  undergo  in  being 

drawn  into  wire?  Ans.    *°°  . 

86617 

35.  Determine  the  volumes  of  two  liquids,  the  densities  of  which  are  respectively 
i -3  and  07,  and  which  produce  a  mixture  of  three  volumes  having  the  density  0-9. 

If  x  and  y  be  the  volumes,  then  from  P  —  VD,  1*3  #  +  o'j  y  =  3  x  o'9  and 
x.  +  y  =  3,  from  which  x  =  i  and  y  =  z. 

36.  The  specific  gravity  of  zinc  being  7  and  that  of  copper  9,  what  weight  of  each 
metal  must  be  taken  to  form  50  grammes  of  an  alloy  having  the  specific  gravity  8 '2,  it 
being  assumed  that  the  volume  of  the  alloy  is  exactly  the  sum  of  the  alloyed  metals  ? 

Let  x  =  the  weight  of  the  zinc,  and  y  that  of  the  copper,  then  x  +  y  =  50,  and 

7> 

from  the  formula  P  —   VD,  which  gives  V  =      ,  the  volumes  of  the  two  metals  and  of 

the  alloy  are  respectively  *  +  ^  =  $°  .     From  these  two  equations  we  get  x  =   17*07 
and;)/  =  32-93. 

37.  A  platinum  sphere  3  cm.  in  diameter  is  suspended  to  the  beam  of  a  very  ac- 
curate balance,  and  is  completely  immersed  in  mercury.    It  is  exactly  counterbalanced 
by  a  copper  cylinder  of  the  same  diameter  completely  immersed  in  water.     Required 
the  height  of  the  cylinder.      Specific  gravity  of  mercury  13-6,   of  copper  8*8,  and  of 
platinum  21-5.  Ans.  2*025  centimetres. 

38.  To  balance  an  ingot  of  platinum  27  grammes  of  brass  are  placed  in  the  other 
pan  of  the  balance.     What  weight  would  have  been  necessary  if  the  weighing  had  been 
effected  in  vacuo?    The  density  of  platinum  is  21*5,  that  of  brass  8-3,  and  air  under 

a  pressure  of  760  mm.  and  at  the  temperature  o°  has  —  the  density  of  water. 

770 

The  weight  of  brass  in  air  is  not  27  grammes,  but  this  weight  minus  the  weight  of 
a  volume  of  air  equal  to  its  own. 

Since  P  =    VD  .  * .  V  =   £  and  the  weight  of  the  air  is  — — — -    = ?Z 

D  D  x  770        8*3  x  770 

By  similar  considerations,  if  x  is  the  weight  of  platinum  in  vacuo,  its  weight  in  air 


992  Problems  and  Examples  in  Physics. 

will  be  x  minus  the  weight  of  air  displaced,  that  is  x  —  — ,  and  this  weight 

21-5  x  770 

is  equal  to  that  of  the  true  weight  of  the  brass  ;  and  we  have 

x  —  °L =  27 ?Z ;  from  which  x  =   26-996. 

21-5  x  770  8-3  x  770 

39.  A  body  loses  in  carbonic  acid  1*15  gr.  of  its  weight.     What  would  be  its  loss 
of  weight  in  air  and  in  hydrogen  respectively  ? 

Since  a  litre  of  air  at  o°  and  760  mm.  weighs  1*293  gramme,  the  same  volume  of 
carbonic  acid  weighs  i  '293  x  i  '524  =  i  -97  gramme.  We  shall,  therefore,  obtain  the 
volume  of  carbonic  acid  corresponding  to  i'i5gr.  by  dividing  this  number  by  1*97, 
which  gives  0-5837  litre.  This  being  then  the  volume  of  the  body,  it  displaces  that 
volume  of  air,  and  therefore  its  loss  of  weight  in  air  is  0-5837  x  1*293  —  07547  grammes, 
and  in  hydrogen  0*5837  x  1*293  x  0*069  =  0*052076. 

40.  Calculate  the  ascensional  force  of  a  spherical  balloon  of  oiled  silk  which,  when 
empty,  weighs  62*5  kilos,  and  which  is  filled  with  impure  hydrogen,  the  density  of 

which  is   *  that  of  air.     The  oiled  silk  weighs  0*250  kilo,  the  square  metre. 
13 

The  surface  of  the  balloon  is      2^   _  250  square  metres.  This  surface  being  that  of 
0*25 

r>J 

a  sphere,  is  equal  to  4  ?r  R*,  whence  4  rr  R"2  =  250  and  R  =  4*459  ;  therefore  V  =  4_ 

=  37*' S2  cubic  metres. 

The  weight  of  air  displaced  is  371*52  x  1*293  kilo  =  480*375  kilos  ;  the  weight  of 
the  hydrogen  is  36*88  kilos,  and  therefore  the  ascensional  force  is 
480*375  -  (36'88  +  62*5)   =  380*995. 

41.  A  balloon  4  metres  in  diameter  is  made  of  the  same  material  and  filled  with 
the  same  hydrogen  as  above.     How  much  hydroge     is  required  to  fill  it,  and  what 
weight  can  it  support  ? 

The  volume  is  4.  „  R5  =  33*51  cubic  metres,  and  the  surface  4  vRz  =  50-265  square 

metres.  The  weight  of  the  air  displaced  is  33*51  x  1*293  =  43 '328  kilos,  and  that  of 
the  hydrogen  is  from  the  above  data  3*333  kilos,  while  the  weight  of  the  material  is  12-566 
kilos.  Hence  the  weight  which  the  balloon  can  support  is 

43*328  -  (12-566  +  3-333)   =  27-429  kil. 

42.  Under  the  receiver  of  an  air-pump  is  placed  a  balance,  to  which  are  suspended 
two  cubes;  one  of  these  is  3  centimetres  in  the  side, and  weighs  26'324gr.  ;  and  the  other 
is  5  centimetres  in  the  side,  and  weighs  26*2597  grammes.     When  a  partial  vacuum  is 
made  these  cubes  just  balance  each  other.     What  is  the  pressure?          Ans.  om*374. 

43.  A  soap-bubble  8  centimetres  in  diameter  was  filled  with  a  mixture  of  one 
volume  of  hydrogen  gas  and  15  volumes  air.     The  bubble  just  floated  in  the  air  ;  re- 
quired the  thickness  of  the  film. 

The  weight  of  the  volume  of  air  displaced  is  ^  it  r5  x  0*001293  gramme,  and  that 

of  the  mixture  of  gases    4  *  r5  x  0*001293  x  T.5  +  oo  93  .  ancj  tne  difference   of 

3  ID 

these  will  equal  the  weight  of  the  soap-bubble. 

This  weight  is  that  of  a  spherical  shell,  which,  since  its  thickness  /  is  very 
small,  is  with  sufficient  accuracy  4  TT  r2  t  s  in  grammes,  where  s  is  the  specific  gravity 
=  1*1.  Hence 

4  TT  i*  (-001293  -  -001293  x    Il^?3^   =  4  v  rv  t  ri 
Dividing  each  side  by  4  «•  r2,  and  putting  r  =  4,  we  get 
4  x   -001293  (i 


On  Liquids  and  Gases.  993 

or 

•001293  x  -i 
4 


•001293  x    93°7  _  3-3  /: 


whence  /  =   •00009116629  cm. 

44.  In  a  vessel  whose  capacity  is  3  litres,  there  are  introduced  2  litres  of  hydrogen 
under  the  pressure  of  5  atmospheres  ;  3  litres  of  nitrogen  under  the  pressure  of  half  an 
atmosphere,  and  4  litres  of  carbonic  acid  under  the  pressure  of  4  atmospheres.     What 
is  the  final  pressure  of  the  gas,  the  temperature  being  supposed  constant  during  the 
experiment  ? 

The  pressure  of  the  hydrogen,  from  Dalton's  law,  will  be  2  x  5,  that  of  the  nitro- 
gen will  remain  unchanged,  and  that  of  the  carbonic  acid  will  be  — -.  Hence  the 

total  pressure  will  be 

—  +  -  +  —  =  9&  atmospheres. 

45.  A  vessel  containing  10  litres  of  water  is  first  exposed  in  contact  with  oxygen 
under  a  pressure  of  78  cm.  until  the  water  is  completely  saturated.     It  is  then  placed 
in  a  confined  space  containing  100  litres  of  carbonic  acid  under  a  pressure  of  72  cm. 
Required  the  volumes  of  the  two  gases  when  equilibrium  is  established.    The  coeffi- 
cient of  absorption  of  oxygen  is  0-042,  and  that  of  carbonic  acid  unity. 

The  volume  of  oxygen  dissolved  is  0-42.  Being  placed  in  carbonic  acid  it  will 
act  as  if  it  alone  occupied  the  space  of  the  carbonic  acid,  and  its  pressure  will  be 

78   x     °'42     =  0-326  cm. 

I00'42 

Similarly  the  10  Jitres  of  water  will  dissolve  10  litres  of  carbonic  acid  gas,  the  total 
volume  of  which  will  be  no,  of  which  100  are  in  the  gaseous  state  and  10  are  dissolved. 
Its  pressure  is  therefore  72  x  ——  =  65*454  cm. 

Hence  the  total  pressure  when  equilibrium  is  established  is 

0^326  +  65-454  =  65-78  cm.  ; 
and  the  volume  of  the  oxygen  dissolved  reduced  to  the  pressure  6578  is 

ollt>42  x  — ? —  =  olit'oo2o8,  and  that  of  the  carbonic  acid  10  x  _Al54  _  g-gt- 
6578  6578 

46.  In  a  barometer  which  is  immersed  in  a  deep  bath  the  mercury  stands  743 
mm.  above  the  level  of  the  bath.     The  tube  is  lowered  until  the  barometric  space, 
which  contains  air,  is  reduced  to  one-third,  and  the  mercury  is  then  at  a  height  of  701 
mm.    Required  the  atmospheric  pressure  at  the  time  of  observation.    Ans.  s=  764mm. 

47.  What  is  the  pressure  on  the  piston  of  a  steam  boiler  of  8  decimetres  diameter 
if  the  pressure  in  the  boiler  is  3  atmospheres  ?  Ans.  10385.85  kilos. 

48.  What  is  the  pressure  of  the  atmosphere  at  that  height  at  which  an  ascent  of  21 
metres  corresponds  to  a  diminution  of  imm  in  the  barometric  height?  Ans.  yjZ'gmm. 

49.  What  would  be  the  height  of  the  atmosphere  if  its  density  were  everywhere 
uniform?  Ans.  7954*1  metres,  or  nearly  5  miles. 

50.  How  high  must  we  ascend  at  the  sea-level  to  produce  a  depression  of  i  mm. 
in  the  height  of  the  barometer  ? 

Ans.  Taking  mercury  as  10,500  times  as  heavy  as  air,  the  height  will  be  10-5  metres. 

51.  Mercury  is  poured  into  a  barometer  tube  so  that  it  contains  15  cc.  of  air  under 
the  ordinary  atmospheric  pressure.     The  tube  is  then  inverted  in  a  mercury  bath  and 
the  air  then  occupies  a  space  of  25  cc.  ;  the  mercury  occupying  a  height  of  302  mm. 
What  is  the  pressure  of  the  atmosphere  ? 

Let  x  be  the  amount  of  this  pressure,  the  air  in  the  upper  part  of  the  tube  will  have 
a  pressure  represented  by  i^fl,  and  this,  together  with  the  height  of  the  mercurial 
column  302,  will  be  the  pressure  exerted  in  the  interior  of  the  tube  on  the  level  of  the 

3S 


994 


Problems  and  Examples  in  Physics. 


+  302 


mercury  in  the  bath,  which  is  equal  to  the  atmospheric  pressure  ;  that  is  ^5^ 

25 
=  x,  from  which  x  =  755  mm. 

52.  What  effort  is  necessary  to  support  a  cylindrical  bell-jar  full  of  mercury 
immersed  in  mercury  ;  its  internal  diameter  being  6  centimetres,  its  height  ob  above 
the  surface  of  the  mercury  (fig.  i)  18  centimetres,  and  the  pressure  of  the  atmosphere 
0*77  centimetre? 

The  bell-jar  supports  on  the  outside  a  pressure  equal  to  that  of  a  column  of  mercuiy 
the  section  of  whose  base  is  cd,  and  the  height  that  of  the  barometer.  This  pressure  is 
equal  to 

irT?2  x  0*77  x  13-6. 

The  pressure  on  the  inside  is  that  of  the  atmosphere  less  the  weight  of  a  column 
of  mercury  whose  base  island  height^.  This  is  equal  torr  J?*  x  (0*77-0*18)  x  13*6; 
and  the  effort  necessary  is  the  difference  of  these  two  pres- 
sures.    Making  R  =  3  cm.,  this  is  found  to  be  69*216  kilo- 
grammes. 

53.  A  barometer  is  placed  within  a  tube  which  is  after- 
wards hermetically  closed.  At  the  moment  of  closing,  the 
temperature  is  15°  and  the  pressure  750  mm.  The  ex- 
ternal space  is  then  heated  to  30°.  What  will  be  the  height 
of  the  barometer  ? 

The  effect  of  the  increase  of  temperature  would  be  to 

raise  the  mercury  in  the  tube  in  the  ratio  i  +    -^°-    to  i  + 

5550 

*5  ,  and  the  height  h  would  therefore  be 
5550 


Fig.  i. 

5SSO 

and  since  in   the  closed  space,   the  elastic  force  of  the  air  increases  in  the  ratio 
i  +  30  a  :  i    +   15  a  we  shall  have  finally  h  =  301*74  mm. 

54.  The  heights  of  two  barometers  A  and  B  have  been  observed  at  —  10°  and 
+  15°,  respectively,  to  be  A   =  737  and  B  =  763.     Required  their  corrected  heights 

at  o°.  Ans.  A   =   738*33.     B  =  760*94. 

55.  A  voltaic  current  gives  in  an  hour  840  cubic  centimetres  of  detonating  gas 
under  a  pressure  of  760  and  at  the  temperature  12° '5  ;  a  second  voltaic  current  gives 
in  the  same  time  960  cubic  centimetres  under  a  pressure  of  755  and  at  the  temperature 
I5°'S-     Compare  the  quantities  of  gas  given  by  the  two  currents.     Ans.  i  :  1*129. 

56.  The  volume  of  air  in  the  pressure  gauge  of  an 
apparatus  for  compressing  gases  is  equal  to  152  parts. 
By  the  working  of  the  machine  this  is  reduced  to 
7  parts,   and  the  mercury  is  raised   through  0*48 
metre.     What  is  the  pressure  of  the  gas  ? 

Here  AB  =  152,  AC  =  37 parts,  and  BC  =  om'48. 
The  pressure  of  air  therefore  in  AC  is,  from  Boyle's 
law, 

37    =  4*  m  Z°     =  3m  I22' 
The  pressure  in  the  receiver  is  therefore 

3*122  +  0*48  =  3m>6o2, 
which  is  equal  to  4*74  atmospheres. 

57.  An  airtight    bladder    holding    two  litres  of 
air  at   the   standard  pressure    and   temperature   is 
immersed  in  sea- water  to  a  depth  of   100  metres, 
where  the  temperature  is  4°.     Required  the  volume 
of  the  gas. 


Fig.  a. 


Air  Pump.  995 

The  specific  gravity  of  sea-water  being  i  '026,  the  depth  of  too  metres  will  repre- 
sent a  column  of  pure  water  102  '6  metre's  in  height.  As  the  pressure  of  an  atmo- 
sphere is  equal  to  a  pressure  of  10-33  metres  of  pure  water,  the  pressure  of  this  column 


=  =  9-94  atm. 

10-33 
Hence,  adding  the  atmospheric  pressure,  the  bladder  is  now  under  a  pressure  of  10*94 

atmospheres,  and  its  volume  being  inversely  as  the  pressure  will  be  —  —  =  0*183  litre, 

10-94 

if  the  temperature  be  unaltered.    But  the  temperature  is  increased  by  4°,  and  therefore 
the  volume  is  increased  in  the  ratio  277  to  273,  and  becomes 

0-183  x  277  =  0-18568  litre. 

58.  To  what  height  will  water  be  raised  in  the  tube  of  a  pump  by  the  first  stroke  of  the 
piston,  the  length  of  stroke  of  which  is  0-5111.,  the  height  of  the  tube  6  metres,  and  its  section 
rii  that  of  the  piston  ?    At  starting  the  air  in  the  tube  is  under  a  pressure  of  10  metres. 

If  we  take  the  section  of  the  tube  as  unity,  that  of  the  body  of  the  pump  is  10  ;  and 
the  volumes  of  the  tube  and  of  the  body  of  the  pump  are  in  the  ratio  of  6  to  5.  Then 
if  x  is  the  height  to  which  the  water  is  raised  in  the  pipe,  the  volumes  of  air  in  the 
pump  before  and  after  the  working  of  the  pump  are  6  at  the  pressure  10,  and  5  -t-  6  -  x 
at  the  pressure  10  —  x. 

Forming  an  equation  from  these  terms,  and  solving,  we  have  two  values,  x'  =  18™  26 
and  x"  =  2-74.  The  first  of  these  must  be  rejected  as  being  physically  impossible  ; 
and  the  true  height  is  x  =  2-75  metres. 

59.  A  receiver  with  a  capacity  of  10  litres  contains  air  under  the  pressure  76  cm. 
It  is  closed  by  a  valve,  the  section  of  which  is  32  square  centimetres,  and  is  weighted 
with  25  kilogrammes.     The  temperature  of  the  air  is  30°  ;  its  density  at  o°  and  76  cm. 
pressure  is  -i-  that  of  water.     The  coefficient  of  the  expansion  of  gases  is  0-00366. 

Required  the  weight  of  air  which  must  be  admitted  to  raise  the  valve. 

The  air  already  present  need  not  be  taken  into  account  as  it  is  under  the  pressure 
of  the  atmosphere.  Let  x  be  the  pressure  in  centimetres  of  mercury  of  that  which  is 
admitted,  x  x  *3  will  represent  in  kilogrammes  its  pressure  on  a  square  centi- 

1000 

metre  ;  and  therefore  the  internal  pressure  on  the  valve,  and  which  is  equal  to  the  ex- 
ternal pressure  of  25  kilogrammes,  is  x  x  I3~     x  32  =  25  k.    From  which  x  =  57*44. 
For  the  weight  we  shall  have 


P  =  _       __  x  55,44  =  8.8  mes 

i  +  0*00366  x  30       76-00 
6O.  A  bell-jar  contains  3-17  litres  of  air  ;  a  pressure  gauge  connected  with  it  marks 
zero  when  in  contact  with  the  air  (fig.  3).     The  jar  is 
closed  and  the  machine  worked  ;  the  mercury  rises 
to  65  cm.      A  second  barometer  stands  at  76  cm. 
during  the  experiment.     Required  the  weight  of  air 
withdrawn  from  the  bell-jar  and  the  weight  of  that 
which  remains. 

At  o°  and  76  cm.  the  weight  of  air  in  the  bell-jar  is 

1-293  x  3'1?  =  4*09881. 

At  o°  and  under  the  pressure  76  —  65  the  weight 
of  the  residual  air  is 


_ 

76 

and  therefore  the  weight  of  that  which  is  withdrawn  is 

4-0988  -  0-5932  =  3*5056  gr. 
61.  The  capacity  of  the  receiver  of  an  air-pump 


3S2 


996  Problems  and  Examples  in  Physics. 

is  7*53  ;  it  is  full  of  air  under  the  ordinary  atmospheric  pressure  and  at  o°.  Re- 
quired the  weight  of  air  when  the  pressure  is  reduced  to  o'2i ;  the  weight  with- 
drawn by  the  piston  ;  and  the  weight  which  would  be  left  at  15°. 

The  weight  of  7*53  litres  of  air  under  the  ordinary  conditions  is  9736  grammes. 

Under  a  pressure  of  0*21  it  will  be  2*69  grammes,  and  at  the  temperature  15°  it  will 

be ^2 r  =  0-255  gramme. 

i  +  o '00366  x   1 5 

62.  In  a  theoretically  perfect  air-pump,  how  great  is  the  rarefaction  after  10  strokes, 
if  the  volumes  of  the  barrel  and  the  receiver  are  respectively  2  and  3  ? 

Ans.   =  4'59mm  ;  or  about of  an  atmosphere. 

1 66 

63.  What  must"  be  the  capacity  of  the  barrel  of  an  air-pump  if  the  air  in  a  re- 
ceiver of  4  litres  is  to  be  reduced  to  J  the  density  in  two  strokes?  Ans.  2*9. 

64.  The  reservoir  of  an  air-gun,  the  capacity  of  which  is  40  cubic  inches,  contains 
air  whose  density  is  8  times  that  of  the  mean  atmospheric  pressure.     A  shot  is  fired 
when  the  atmospheric  pressure  is  741  mm.  and  the  gas  which  escapes  occupies  a  volume  of 
80  cubic  inches.  What  is  the  elastic  force  of  the  residual  air?  Ans.  6 '05 atmospheres. 

65.  Suppose  that  at  the  limit  of  the  atmosphere  the  pressure  of  the  attenuated 
air  is  the   -^—  of  a  millimetre  of  mercury  and  the  temperature  —  135°,  and  that  in  a 

IOOO 

place  at  the  sea-level,  in  latitude  45°,  the  pressure  of  the  atmosphere  is  760™™  and  its 
temperature  15°  C.  Determine  from  these  data  the  height  of  the  atmosphere. 

From  the  formula  18400  j  i  +  o-oo2 {  T  +  /}  j-  log  --,  we  get  for  the  height  in  metres 
82237,  which  is  equal  to  51*1  miles. 

66.  If  water  is  continually  flowing  through  an  aperture  of  3  square  inches  with  a 
velocity  of  10  feet,  how  many  cubic  feet  will  flow  out  in  an  hour?  Ans.  750  cubic  feet. 

67.  With  what  velocity  does  water  issue  from  an  aperture  of  3  square  inches,  if 
37-5  cubic  feet  flow  out  every  minute?  Ans.  30  feet. 

68.  What  is  the  ratio  of  the  pressure  in  the  above  two  cases?  Ans.  i  :  9. 

69.  What  is  the  theoretical  velocity  of  water  from  an  aperture  which  is  9  feet 
below  the  surface  of  water?  Ans.  24  feet. 

70.  In  a  cylinder,  water  stands  2  feet  above  the  aperture  and  is  loaded  by  a  piston 
which  presses  with  a  force  of  6  pounds  on  the  square  inch.     Required  the  velocity  of 
the  effluent  water.  Ans.  32  feet. 

71.  How  deep  must  the  aperture  of  the  longer  leg  of  a  syphon,  which  has  a  sec- 
tion of  4  square  centimetres,  be  below  the  surface  of  the  water  in  order  that  25  litres 
may  flow  out  in  a  minute ?  Ans.  5*535  cm. 

72.  Through  a  circular  aperture  having  an  area  of  0-196  square  cm.  in  the  bottom 
of  a  reservoir  of  water  which  was  kept  at  a  constant  level,  55  cm.  above  the  bottom, 
it  was  found  that  98-5  grammes  of  water  flowed  in  22  seconds.     Required  the  coeffi- 
cient of  efflux. 

Since  the  velocity  of  efflux  through  an  aperture  in  the  bottom  of  a  vessel  is  given  by 
the  formula  v  =  \/2gh,  it  will  readily  be  seen  that  the  weight  in  grammes  of  water 
which  flows  in  a  given  time,  /,  will  be  given  by  the  formula  iv  =  a  «  t*J^gh,  where  a  is 
the  area  in  square  centimetres,  a.  the  coefficient  of  efflux,  /  the  time  in  seconds,  and  h 
the  height  in  centimetres.  Hence  in  this  case  a  =  0*699. 

73.  Similarly  through  a  square  aperture,  the  area  of  which  was  almost  exactly  the 
same  as  the  above,  and  at  the  same  depth,  104-4  grammes  flowed  out  in  21 '6  seconds. 
In  this  case  «  =  073. 


Sound.  997 


IV.    ON  SOUND. 

74.  A  stone  is  dropped  into  a  well,   and  4  seconds  afterwards  the  report  of  its 
striking  the  water  is  heard.     Required  the  depth,  knowing  that  the  temperature  of  the 
air  in  the  pit  was  io°74. 

From  the  formula  v  =  333  \/i  +  at  we  get  for  the  velocity  of  sound  at  the  tem- 
perature in  question  339 '05  metres. 

Let  t  be  the  time  which  the  stone  occupies  in  falling ;  then  \  gfi  =  x  will  represent 
the  depth  of  the  well ;  on  the  other  hand,  the  time  occupied  by  the  report  will  be  4  —  /, 
and  the  distance  will  be  (4  -  /)  v  =  x  (i)  ;  thus  (4  —  t)  v  =  \g&  (ii),  from  which, 
substituting  the  values, 

(4  -  0  339'5  =  4'9  & 

I  =  3793  seconds,  and  substituting  this  value  in  either  of  the  equations  (i)  or  (ii), 
we  have  the  depth  =  72-6  metres  nearly. 

75.  A  bullet  is  fired  from  a  rifle  with  a  velocity  of  414  metres,  and  is  heard  to  strike 
a  target  4  seconds  afterwards.     Required  the  distance  of  the  target  from  the  marks- 
man, the  temperature  being  assumed  to  be  zero. 

-?-  +    ~    =  4;  x  =  738-2. 
4H       333 

76.  At  what  distance  is  an  observer  from  an  echo  which  repeats  a  sound  after  3 
seconds,  the  temperature  of  the  air  being  10°  ? 

In  these  3  seconds  the  sound  traverses  a  distance  of  3  x  339  =  1017  metres  ;  this 
distance  is  twice  that  between  the  observer  and  the  reflecting  surface  ;  hence  the  dis- 
tance is 

iESiZ  =  508-5  metres. 

2 

77.  Between  a  flash  of  lightning  and  the  moment    at  which   the  corresponding 
thunder  is  first  heard,  the  interval  is  the  same  as  that  between  two  beats  of  the  pulse. 
Knowing  that  the  pulse  makes  80  beats  in  a  minute,  and  assuming  the  temperature 
of  the  air  to  be  15°  C.,  what  is  the  distance  of  the  discharge?       Ans.  454'!  metres. 

78.  A'stone  is  thrown  into  a  well  with  a  velocity  of  12  metres,  and  is  heard  to 
strike  the  water  4  seconds  afterwards.  Required  the  depth  of  the  well. 

Ans.  About  no  metres. 

79.  What  is  the  velocity  of  sound  in  coal  gas  at  o°,  the  density  being  0*5? 

Ans.  470*9  metres. 

SO.  What  must  be  the  temperature  of  air  in  order  that  sound  may  travel  in  it  with 
the  same  velocity  as  in  hydrogen  at  o°  ?  Ans.  About  3680°  C. 

81.  What  must  be  the  temperature  of  air  in  order  that  the  velocity  of  sound  may 
be  the  same  as  in  carbonic  acid  at  o°  ?  Ans.  —  io5°5  C. 

82.  Kendall,  in  a  North  Pole  Expedition,  found  the  velocity  of  sound  at  —40° 
was  314  m.     How  closely  does  this  agree  with  that  calculated  from  the  value  we  have 
assumed  for  o°  ?  A  ns.  6  '64  metres  too  much. 

83.  The  report  of  a  cannon  is  heard  15  seconds  after  the  flash  is  seen.     Required 
the  distance  of  the  cannon,  the  temperature  of  the  air  being  22°. 

From  the  formula  for  the  velocity  of  sound  we  have 

*5  x  333  \/i  +  0-003665  x  22  =  5190  metres. 

84.  If  a  bell  is  struck  immediately  at  the  level  of  the  sea,  and  its  sound,  reflected 
from  the  bottom,  is  heard  3  seconds  after,  what  is  the  depth  of  the  sea  ? 

Ans.  7140  feet. 


998  Problems  and  Examples  in  Physics. 

85.  A  person  stands  150  feet  on  one  side  of  the  line  of  fire  of  a  rifle  range  450  feet 
in  length  and  at  right  angles  to  a  point  150  feet  in  front  of  the  target.     What  is  the 

velocity  of  the  bullet  if  the  person  hears  it  strike  the  target  x  of  a  second  later  than 

the  report  of  the  gun?    The  temperature  is  assumed  to  be  i60>5.       Ans.  2038  feet. 

86.  An  echo  repeats  five  syllables,  each  of  which  requires  a  quarter  of  a  second  to 
pronounce,  and  half  a  second  elapses  between  the  time  the  last  syllable  is  heard  and 
the  first  syllable  is  repeated.     What  is  the  distance  of  the  echo,  the  temperature  of 
the  air  being  10°  C.  ?  Ans.  297-47  metres. 

87.  The  note  given  by  a  silver  wire  a  millimetre  in  diameter  and  a  metre  in 
length  being  the  middle  C,  what  is  the  tension  of  the  wire  ?     Density  of  silver  10-47. 

Ans.  22-67  kilogrammes. 

88.  The  density  of  iron  being  7*8  and  that  of  copper  8 -8,   what  must  be  the 
thickness  of  wires  of  these  materials,  of  the  same  length  and  equally  stretched,  so  that 
they  may  give  the  same  note  ? 

From  the  formula  for  the  transverse  vibration  of  strings  we  have  for  the  number  of 

vibrations  n  =  -       / As  in  the  present  case,  the  tensions,  the  length  of  the 

rl  V    IT  d 
strings,  and  the  number  of  vibrations  are  the  same,  we  have 

1      /Z  =  -1-     /Z",  from  which  -1-     /\  =    I      /I  ; 
rl  V    «•  d        r,l  V    *  d]  r  V    d        rt  V    d, 

whence  r-   =  d>    =  8^ ;  hence  '  =,       /81   =   *•** 
r?         d         7-8  r,        \/  7-8 

89.  A  wire  stretched  by  a  weight  of  13  kilos,  sounds  a  certain  note.     What  must 
be  the  stretching  weight  to  produce  the  major  third  ? 

The  major  third  having  ^  the  number  of  vibrations  of  the  fundamental  note,  and  as, 

all  other  things  being  the  same,  the  numbers  of  vibrations  are  direc.tly  as  the  square 
roots  of  the  stretching  weight,  we  shall  have  x  =  20-312  kilos. 

90.  The  diameters  of  two  wires  of  the  same  length  and  material  are  0-0015  and 
0*0038  m.  ;  and  their  stretching  weights  400 and  1600 grammes  respectively.     Required 
the  ratio  of  the  numbers  of  their  vibrations.  Ans.  n  :  n,  =   1-266  :  i. 

91.  A  brass  wire  i  metre  in  length  stretched  by  a  weight  of  2  kilogrammes,  and  a 
silver  wire  of  the  same  diameter,  but  3*165  metres  in  length,  give  the  same  number  of 
vibrations.     What  is  the  stretching  weight  in  the  latter  case  ? 

Since  the  number  of  vibrations  is  equal,  we  shall  have 

L     /"?  =   J      /* 

rl  V    v  d        rl,  V    JT  d, ' 
from  which,  replacing  the  numbers,  we  get  x  =  25  kilos. 

92.  A  brass  and  a  silver  wire  of  the  same  diameter  are  stretched  by  the  weights  of  2 
and  25  kilogrammes  respectively,  and  produce  the  same  note.  What  are  their  lengths, 
knowing  that  the  density  of  brass  is  8-39,  and  of  silver  10-47? 

Ans.  The  length  of  the  silver  wire  is  3-16  times  that  of  the  brass. 

93.  A  copper  wire  1*25  mm.   in  diameter  and  a  platinum  one  of  0-75  mm.  are 
stretched  by  equal  weights.     What  is  the  ratio  of  their  lengths,  if,  when  the  copper 
wire  gives  the  note  C  the  platinum  gives  F  on  the  diatonic  scale  ? 

Ans.  The  length  of  the  copper  is  to  the  length  of  the  platinum   =   1*264  :  i. 

94.  An  organ  pipe  gives  the  note  C  at  a  temperature  o°  ;  at  what  temperature 
will  it  yield  the  major  third  of  this  note?  Ans.   153°  C. 

95.  A  brass  wire  a  metre  in  length,  and  stretched  by  a  weight  of  a  kilogramme, 
yields  the  same  note  as  a  silver  wire  of  the  same  diameter  but  2-5  metres  in  length  and 
stretched  by  a  weight  of  7-5  kilogrammes.    Required  the  specific  gravity  of  the  silver. 

Ans.  io"o68. 

96.  How  many  beats  are  produced  in  a  second  by  two  notes,  whose  rates  of  vibra- 
tion are  respectively  340  and  354  ?  Ans.   14. 


Heat. 


999 


V.    ON  HEAT. 

97.  Two  mercurial  thermometers  are  constructed  of  the  same  glass  ;  the  internal 
diameter  of  one  of  the  bulbs  is  7mm'S  and  of  its  tube  2-5  ;  the  bulb  of  the  other  is 
6 '2  in  diameter  and  its  tube  1*5.     What  is  the  ratio  of  the  length  of  a  degree  of  the 
first  thermometer  to  a  degree  of  the  second  ? 

Let  A  and  B  be  the  two  thermometers,  D  and  D  the  diameters  of  the  bulbs,  and 
d  and  d'  the  diameters  of  the  tubes.  Let  us  imagine  a  third  thermometer  C  with  the 
same  bulb  as  B  and  the  same  tube  as  A,  and  let  /,  /',  and  /"  denote  the  length  of  a 
degree  in  each  of  the  thermometers  respectively.  Since  the  stems  of  A  and  C 
have  the  equal  diameters,  the  lengths  /  and  /"  are  directly  as  the  volumes  of  the 
tubes,  or  what  is  the  same,  as  the  cubes  of  their  diameters  ;  and  as  B  and  C  have 
the  same  bulk,  the  lengths  /'  and  /"  are  inversely  proportionate  to  the  sections  of 
the  stems,  or  what  amounts  to  the  same,  to  the  squares  of  their  diameters.  We 
have  then 

/    _  Z>3  /"  _  d'* . 

introducing  the  values  and  solving,  we  have 
'-  =  0-638. 

98.  At  what  temperature  is  the  number  on  the 
Centigrade  and  Fahrenheit  thermometers  the  same  ? 

Ans.  -  40°. 

99.  The  same  question  for  the  Fahrenheit  and 
Rdaumur  scales.  Ans.  —  25-6. 

100.  A  capillary  tube   is  divided  into  180  parts 
of  equal  capacity,   25  of  which   weigh  1*2  gramme. 
What  must  be  the  radius  of  a  spherical  bulb  to  be 
blown  to  it  so  that  180  divisions  correspond  to  150 
degrees  Centigrade? 

Since    25    divisions    of    the   tube    contain    1*2 

gramme,  180  divisions  contain  L±L*       \   =   8-64. 

And  since  these  180  divisions  are  to  represent  150  degrees,  the  weight  of  mercury 

corresponding  to  a  single  degree  is     -      . 


But  as   the  expansion   corresponding    to 
one  degree  is  only  the  apparent  expansion  of  mercury  in  glass,  the  weight       ^  is 


1*8755  centimetre. 


of  the  mercury  in  the  reservoir,  which  is  4  *R~0.    From  this  R 

101.  By  how  much  is  the  circumference  of  an  iron  wheel,  whose  diameter  is  6  feet, 
increased  when  its  temperature  is  raised  400  degrees?    Coefficient  of  expansion  cf 
iron  =  o'ooooi22.  Ans.  By  0-092  foot. 

102.  What  must  be  the  length  of  a  wire  of  this  metal  which  for  a  temperature  of 
i°  expands  by  one  foot  ?  Ans.  81967  feet. 

103.  A  pendulum  consists  of  a  platinum  rod,  on  a  flattening  at  the  end  of  which 
rests  a  spherical  zinc  bob.     The  length  of  the  platinum  is  /  at  o°.     What  must  be  the 
diameter  of  the  bob,  so  that  its  centre  is  always  at  the  same  distance  from  the  point  of 
suspension  whatever  be   the  temperature  ?     Coefficient   of  expansion   of    platinum 
o  "0000088  and  of  zinc  o  '0000294. 

Ans.  The  diameter  of  the  bob  must  be  5  of  the  length  of  the  platinum. 

104.  Two  walls,  which  when  perpendicular   are  30  feet  apart,  have  bulged   out- 
wards to  the  extent  of  2*4  inches.     They  are  to  be  made  perpendicular  by  the  contrac- 


I'ooo  Problems  and  Examples  in  Physics. 

tion  of  an  iron  bar.    By  how  much  must  its  temperature  be  raised  above  that  of  the  air, 
which  is  taken  at  o°?  Ans.  532°. 

105.  An  iron  wire  4  sq.  mm.  in  cross  section  is  stretched of  its  length  by  a 

81200 

weight  of  i  kilogramme.     What  weight  must  be  applied  to  a  bar  9  sq.  mm.  in  cross 
section,  when  it  is  heated  from  o°  to  20°,  in  order  to  prevent  it  from  expanding  ? 

Ans.  44 -5  kilo. 

106.  At  the  temperature  zero  a  solid  is  immersed  0*975  of  its  total  volume  in 
alcohol.     At  the  temperature  25°  the  solid  is  wholly  immersed.     The  coefficient  of 
expansion  of  the  solid  being  o '000026,  required  the  coefficient  of  expansion  of  the 
alcohol.  Ans.  o-ooio52. 

107.  Into  a  glass  globe,  the  capacity  of  which  at  o°  is  250  cc.,  are  introduced 
25  cc.  of  air  measured  at  o°  and  76  cm.     The  flask  being  closed  and  heated  to  100°, 

required  the  internal  pressure.     Coefficient  of  cubical  expansion  of  glass 

At  100°  the  capacity  of  the  flask  is  250  (  i  +     IO°    )  ;  again  at  100°  the  volume  of 

\         38700/ 

the  free  air  under  the  pressure  76  is  25  (i  +  100  x  o "00366).     But  its  real  volume  is 
250  x  ^ —  under  a  pressure  x.     Hence 

387  88 

76    :  x  =  250  x  ?--   :  25  x  1*366,  from  which  x  =   10-3548  cm. 

387 

108.  The  specific  gravity  of  mercury  at  o°  being  13*6,  required  the  volume  of  3 

kilogrammes  at  85°.     Coefficient  of  expansion  — L_ . 

5550 

The  volume  at  o°  will  be  -?—  and  at  85°  _3£.    x  ( i  +  J3U  J  =  2-239  litres. 
13 '6  13 '6      V         5550' 

109.  A  hollow  copper  sphere  20  cm.  in  diameter  is  filled  with  air  at  o°  under  a 
pressure  of  i£  atmosphere  ;  what  is  the  total  pressure  on  the  interior  surface  when  the 
enclosed  air  is  heated  to  a  temperature  of  600°  ?  Ans.  6226-5  kilogrammes. 

110.  Between  the  limits  of  pressure  700  to  780 mm.  the  boiling-point  of  water  varies 
°°'°375  C.  for  each  mm.  of  pressure.     Between  what  limits  of  temperature  does  the 
boiling  point  vary,  when  the  height  of  the  barometer  is  between  735  and  755  mm.  ? 

Ans.  Between  99°  '0625  and  99°  '8125. 

111.  Liquid  phosphorus  cooled  down  to  30°,  is  made  to  solidify  at  this  tempera- 
ture.    Required  to  know  if  the  solidification  will  be  complete,  and  if  not,  what  weight 
will  remain  melted  ?  The  melting  point  of  phosphorus  is  44-2  ;  its  latent  heat  of  fusion 
5-4,  and  its  specific  heat  0*2. 

Let  x  be  the  weight  of  phosphorus  which  solidifies ;  in  so  doing  it  will  give  out  a 
quantity  of  heat  =  5-4  x  ;  this  is  expended  in  raising  the  whole  weight  of  the  phos- 
phorus from  30  to  44-2.  Hence  we  have  5*4  #  =  i  x  (44*2  —  30)  o'2,  from  which 

x  —  ^—^  =  0*526,  so  that  0-474  °f  phosphorus  will  remain  liquid. 

112.  A  pound  of  ice  at  o°  is  placed  in  two  pounds  of  water  at  o°  ;  required  the 
weight  of  steam  at  100°  which  will  melt  the  ice  and  raise  the  temperature  of  the  mix- 
ture to  30°.   The  latent  heat  of  the  liquefaction  of  ice  is  79-2,  and  that  of  the  vaporisa- 
tion of  water  536.  Ans.   -279  pound. 

113.  65-5  grammes  of  ice  at  —  20°  having  been  placed  in  x  grammes  of  oil  of 
turpentine  at  3-3°,  the  final  temperature   is  found  to  be  3-1°.     The  specific  heat  of 
turpentine  is  0-4,  and  it  is  contained  in  a  vessel  weighing  25  grammes,  whose  specific 
heat  is  o'i.     The  specific  heat  of  ice  is  0-5.     Required  the  value  of  x. 

Ans.  x  —  382-0  grammes. 

114.  In  what   proportion  must  water  at  a  temperature  of  30°  and  linseed  oil 
(sp.  heat  =  0-5)  at  a  temperature  of  50°  be  mixed  so  that  there  are  20  kilogrammes  of 
the  mixture  at  40°?  Ans.  Water  =  6 -66  kilos,  and  linseed  oil  =   13-34. 


Heat.  1001 

115.  By  how  much  will  mercury  at  o°  be  raised  by  an  equal  volume  of  water  at 
iooj?  Ans.  68°'9  C. 

116.  The  specific  heat  of  gold  being  0-03244,  what  weight  of  it  at  45°  will  raise  a 
kilogramme  of  water  from  12° '3  to  15°  7? 

Let  x  be  the  weight  sought ;  then  x  kilogrammes  of  gold  in  sinking  from  45°  tc 
1 5° 7  will  give  out  a  quantity  of  heat  represented  by  x  (45°  —  is°7)  0-0324,  and  this  is 
equal  to  the  heat  gained  by  the  water,  that  is  to  i  (15-7  —  12-3)  =  3-4,  that  is  x  =  3-58. 

117.  The  specific  heat  of  sulphide  of  copper  is  0-1212,  and  that  of  sulphide  of  silver 
0-0746.    5  kilos,  of  a  mixture  of  these  two  bodies  at  40°,  when  immersed  in  6 kilos,  of 
water  at  7-669  degrees,  raises  its  temperature  to  10°.    How  much  of  each  sulphuret  did 
the  mixture  contain  ? 

The  weight  of  the  copper  sulphuret  =  2,  and  that  of  the  silver  sulphuret  3. 

118.  Into  a  mass  of  water  at  o°,  100  grammes  of  ice  at  —  12°  are  introduced  ;  a 
weight  of  7 '2  grammes  of  water  at  o°  freezes  about  the  lump  immersed,  while  its 
temperature  rises  to  zero.     Required  the  specific  heat  of  ice.     Latent  heat  of  water 
79-2.  Ans.  0-4752. 

119.  Four  pounds  of  copper  filings  at  130°  are  placed  in  20  pounds  of  water  at  20°, 
the  temperature  of  which  is  thereby  raised  2  degrees.     What  is  the  specific  heat,  c,  of 
copper?  Ans.  c  =  0*0926. 

120.  Two  pieces  of  metal  weighing  300  and  350  grammes,  heated  to  a  temperature 
x,  have  been  immersed,  the  former  in  940*8  grammes  of  water  at  10°,  and  the  latter  in 
546  grammes  at  the  same  temperature.    The  temperature  in  the  first  case  rises  to  20°, 
and  in  the  second  to  30°.     Required  the  original  temperature  and  the  specific  heat  of 
the  metal.  Ans.  x  the  temperature  =•  1980° ;  c  the  specific  heat  =    "1038. 

121.  In  what  proportions  must  a  kilogramme  of  water  at  50°  be  divided  in  order  that 
the  heat  which  one  portion  gives  out  in  cooling  to  ice  at  zero  may  be  sufficient  to  change 
the  other  into  steam  at  100°  ?  Ans.  x  =  0-830. 

122.  Three  mixtures  are  formed  by  mixing  two  and  two  together,  equal  quantities 
of  ice,  salt,  and  water  at  o°.     Which  of  these  mixtures  will  have  the  highest  and  which 
the  lowest  temperature  ?    Ans.  The  mixture  of  ice  and  salt  will  produce  the  lowest 
temperature,  while  that  of  ice  and  water  will  produce  no  lowering  of  temperature. 

123.  In  25-45  kilogrammes  of  water  at  i2°'5  are  placed  6*17  kilos,  of  a  body  at  a 
temperature  of  80°  ;  the  mixture  acquires  the  temperature  14° "i.    Required  the  specific 
heat  of  the  body. 

If  c  is  the  specific  heat  required,  then  me  (f  —  6)  represents  the  heat  lost  by  the  body 
in  cooling  from  80°  to  14°'!  ;  and  that  absorbed  by  the  water  in  rising  from  i2°'5  to 
14°'!  ism'  (9  —  t).  These  two  values  are  equal.  Substituting  the  numbers,  we  have 

C    =    0*1011. 

124.  Equal  lengths  of  the  same  thin  wire  traversed  by  the  same  electrical  current  are 
placed  respectively  in  i  kilogramme  of  water  and  in  3  kilogrammes  of  mercury.     The 
water  is  raised  10°  in  temperature,  by  how  much  will  the  mercury  be  raised  ? 

Ans.  100° -04. 

125.  How  many  cubic  feet  of  air  under  constant  pressure  are  heated  through  i°  C. 
by  one  thermal  unit  ?  Ans.  5105  cubic  feet. 

126.  Given  two  pieces  of  metal,  one  x  weighing  2  kilos,  heated  to  80°,  and  the  othei 
y  weighing  3  kilos,  and  at  the  temperature  50°.     To  determine  their  specific  heats 
they  are  immersed  in  a  kilogramme  of  water  at  10°,  which  is  thereby  raised  to  26°'3. 

The  experiment  is  repeated,  the  two  metals  being  at  the  temperature  100°  and  40° 
respectively,  and,  as  before,  they  are  placed  in  a  kilogramme  of  water  at  10°,  which 
this  time  is  raised  to  28° -4.  Required  the  specific  heats  of  the  two  metals. 

Ans.  x  =  0-115  ;  y  =  0*0555. 

127.  For  high  temperatures  the  specific  heat  of  iron  is  0*1053  +  0*000071  /.  What 
is  the  temperature  of  a  red-hot  iron  ball  weighing  a  kilogramme,  which,  plunged  in  16 


IOO2  Problems  arid  Examples  in  Physics. 

kilogrammes  of  water,  raises  its  temperature  from  12°  to  24°  ?    What  was  the  tempe- 
rature of  the  iron  ? 

(0*1053  +  0-000017*)  (t  —  24)   =   16  (24  —  12), 
or  '000017  fl  +  '1048892  t  —  2-5272  =   192  ; 

transposing  and  dividing  by  the  coefficient  of  /2,  we  get 

t"1  +  6170  t  =   11442776, 
tz  +  6170  t  +  (3085)2  =  20960001  ; 
hence  /  +  3085  =  4578  -3  nearly  ;    .'.  t  =   1493-3. 

128.  A  kilogramme  of  the  vapour  of  alcohol  at  80°  passes  through  a  copper  worm 
placed  in  10*8  kilogrammes  of  water  at  12°,  the  temperature  of  which  is  thereby  raised 
to  36°.     The  copper  worm  and  copper  vessel  in  which  the  water  is  contained  weigh 
together  3  kilogrammes.     Required  the  latent  heat  of  alcohol  vapour.    Ans,  238-77. 

129.  Determine  the  temperature  of  combustion  of  charcoal  in  burning  to  form  car- 
bonic acid. 

We  know  from  chemistry  that  one  part  by  weight  of  carbon  in  burning  unites 
with  2§  parts  by  weight  of  oxygen  to  form  3§  parts  by  weight  of  carbonic  acid. 
Again  the  number  of  thermal  units  produced  by  the  combustion  of  a  pound  of  charcoal 
is  8080  ;  the  whole  of  this  heat  is  contained  in  the  3  §  parts  of  carbonic  acid  produced, 
and  if  its  specific  heat  were  the  same  as  that  of  water,  its  temperature  would  be 

2204°  C.  ;  but  since  the  specific  heat  of  carbonic  acid  is  0*2163  that  of  an  equal 


° 


weight  of  water,  the  temperature  will  be  22O4.   «=  10180°  C. 

0-2163 

ISO.  A  glass  globe  measuring  60  cubic  centimetres  is  found  to  weigh  19-515 
grammes  when  filled  with  air  under  a  pressure  of  752  '3mm  and  at  a  temperature  of  10°  C. 
Some  ether  is  introduced  and  vaporised  at  a  temperature  of  60°,  whereupon  the  flask 
is  sealed  while  quite  full  of  vapour,  the  pressure  being  753  "4mm.  Its  weight  is  now 
found  to  be  19-6786  grammes.  Required  the  density  of  the  ether  vapour  compared 
with  that  of  hydrogen.  Ans.  54-4. 

131.  Calculate  the  density  of  alcohol  vapour  as  compared  with  air  by  Gay-Lussac's 
method  from  the  following  data  :  — 

Weight  of  alcohol  0-1047  grm.;  vol.  of  vapour  at  110°  C.  =  82-55  c.c.  >  height  of 
mercury  above  the  level  in  the  bath,  98  mm.  ;  barometric  height,  752-3  mm.  ;  tempera- 
ture of  the  room,  15°  C.  Ans.  i'6. 

132.  In  a  determination  of  the  vapour  density  by  Gay-Lussac's  method,  0*1163 
gramme  of  substance  was  employed.     The  volume  observed  was  50*79  cc,  the  height 
of  the  mercury  above  the  level  of  that  in  the  bath  was  8o'omin,  the  height  of  the  oil 
column  reduced  to  millimetres  of  mercury  16-9;   the  temperature  215°  C.,  and  the 
height  of  the  barometer  at  the  time  of  observation  755  '5mm.     Required  the  specific 
gravity  of  the  vapour  as  compared  with  that  of  hydrogen.  Ans.  50-1. 

133.  Through  a  U-tube  containing  pumice  saturated  with  sulphuric  acid  a  cubic 
metre  of  air  at  15°  is  passed,  and  the  tube  is  found  to  weigh  3-95  grammes   more. 
Required  the  hygrometric  state  of  the  air. 

The  pressure  of  aqueous  vapour  at  15°  is  12-699;  hence  the  weight  of  a  cubic 
metre  of  aqueous  vapour  saturated  at  15°  is  I293  x  12*699  x  5  _  I2.^g  o-rammes, 


and  the  hygrometric  state  is  3  95    _  o-qoq. 
1279 

134.  The  quantity  of  water  given  out  by  the  lungs  and  skin  may  be  taken  at 
30  ounces  in  24  hours.  How  many  cubic  inches  of  air  already  half  saturated  at  10°  will 
be  fully  saturated  by  the  moisture  exhaled  from  the  above  two  sources  by  one  man  ? 
Tension  of  aqueous  vapour  in  inches  =  0*532..  Pressure  of  the  atmosphere  =  30  inches. 

Ans.  328782-5  c.i.  =  a  cube  5752  feet  in  the  side. 


Heat.  1003 

135.  A  mass  of  air  extending  over  an  area  of  60,000  square  metres  to  a  height  of 
300  metres  has  the  dew  point  at  15°,  its  temperature  being  20°.     How  much  rain  will 
fall  if  the  temperature  sinks  to  io°? 

The  weight  of  vapour  condensed  from  one  cubic  metre  under  these  circumstances 
will  be  3*1435  grammes,  and  therefore  from  18,000,000  cubic  metres  it  will  be  56,583 
kilogrammes,  which  is  equal  to  a  rainfall  0*0943  mm.  in  depth. 

136.  When  3  cubic  metres  of  air  at  10°  and  5  cubic  metres  at  18°,  each  saturated 
with  aqueous  vapour  at  those  temperatures,  are  mixed  together,  is  any  water  precipi- 
tated ?    And  if  so,  how  much  ? 

The  weight  of  water  contained  in  the  two  masses  under  the  given  conditions  are 
respectively  28*i8and  76*59  grammes  ;the  weight  required  to  saturate  the  mixture  at  the 
temperatureof  15°  is  102-39  grammes,  and  therefore  2*38  grammes  will  be  precipitated. 

137.  The  temperature  of  the  air  at  sunset  being  10°,  what  must  be  the  lowest  hygro- 
metric  state,  in  order  that  dew  may  be  deposited,  it  being  assumed  that  in  conse- 
quence of  nocturnal  radiation  the  temperature  of  the  ground  is  7°  below  that  of  the  air  ? 

Ans.  The  hygrometric  state  must  be  at  least  0*608  of  total  saturation. 

138.  It  is  stated  as  a  practical  rule  that  when  the  tension  of  aqueous  vapour  present 
in  the  atmosphere,  as  indicated  by  the  dew  point,  is  equal  to  x  mm.  of  mercury,  the 
weight  of  water  present  in  a  cubic  metre  of  that  air  is  x  grammes.     What  is  the  error 
in  this  statement  for  a  pressure  of  10  mm.  and  the  temperature  15°  C.  ? 

Ans.  0*172  gr. 

139.  A  raindrop  falls  to  the  ground  from  a  height  of  a  mile  ;  by  how  much  would 
its  temperature  be  raised,  assuming  that   it  imparts  no  heat   to  the  air  or  to  the 
ground?  Ans.  3°'8  C. 

140.  A  lead  bullet  falls  through  a  height  of  10  metres  ;  by  what  amount  will  its 
temperature  have  been  raised  when  it  reaches  the  ground,  if  all  the  heat  is  expended  in 
raising  the  temperature  of  the  bullet  ?  Ans.  0*7515°  C. 

141.  From  what  height  must  a  lead  bullet  fall  in  order  that  its  temperature  may 
be  raised  n  degrees  ? — and  what  velocity  will  it  have  acquired  ?    It  is  assumed  that  all  the 
heat  is  expended  in  raising  the  temperature  of  the  bullet ;  the  specific  heat  of  lead  is 
taken  at  0*0314,  and  Joule's  equivalent  in  metres  at  424. 

Ans.  13*31  x  n  metres  ;  v  =  28*8  Vn. 

142.  How  much  heat  is  disengaged  if  a  bullet  weighing  50  grammes  and  having 
a  velocity  of  50  metres  strikes  a  target  ? 

Ans.  Sufficient  to  raise  one  gramme  of  water  through  15°  C. 

143.  How  much  heat  is  produced  in  the  room  of  a  manufactory  in  which  i  *2  horse- 
power of  the  motor  is  consumed  each  second  in  overcoming  the  resistance  of  friction  ? 

Ans.  A  quantity  sufficient  to  raise  41024  pounds  of  water  one  degree  Centigrade. 

144.  What  is  the  ratio  between  the  quantities  of  heat  which  are  respectively  pro- 
duced, when  a  bullet  weighing  50  grammes  and    having  a  velocity  of  500  metres, 
and  a  cannon-ball  weighing  40  kilogrammes  with  a  velocity  of  400  metres,  strike  a 
target?  Ans.   i  :  512. 

145.  The  specific  heat  of  lead  is  0*031,  and  its  latent  heat  5*37.     What  is  the 
mechanical  equivalent  of  the  heat  necessary  to  raise  5  pounds  of  lead  from  a  tempera- 
ture of  270°  C.  to  its  melting-point  335°  C.,  and  then  to  melt  it  ? 

Ans.  51326  foot-pounds. 

146.  Assuming  that  the  temperature  at  which  heat  leaves  a  perfect  engine  is  16°  C., 
at  what  temperature  must  it  be  taken  in  in  order  to  obtain  a  theoretical  useful  effect  of  J  ? 

Ans.  160*5°  C. 

147.  Assuming  that  in  a  perfect  engine  heat  is  taken  in  at  a  temperature  of  144°, 
and  is  given  out  at  a  temperature  of  36°  :  what  is  the  greatest  theoretical  useful  effect  ? 

Ans.  0*261. 


IOO4  Problems  and  Examples  in  Physics. 


VI.    LIGHT. 

148.  How  many  candles  are  required  to  produce  at  a  distance  of  2*5  metres,  the 
same  illuminating  effect  as  one  candle  at  a  distance  of  0-45  m.  ?  Ans.  31. 

149.  Two  sources  of  light  whose  intensities  are  as  i  :  2  are  two  metres  apart.     At 
what  position  is  a  space  between  them  equally  illuminated  ? 

Ans.  o'828  metre  from  the  less  intense  light. 

150.  A  candle  sends  its  rays  vertically  against  a  plane  surface.  When  the  candle  is 
removed  to  thrice  the  distance  and  the  surface  makes  an  angle  of  60°  with  the  original 

position,  what  is  the  ratio  of  the  illuminations  in  the  two  cases  ?  Ans.  i  :  —  . 

lo 

151.  An  observer,  whose  eye  is  6  feet  above  the  ground,  stands  at  a  distance  of  18 
feet  from  the  near  edge  of  a  still  pond,  and  sees  there  the  image  of  the  top  of  a  tree, 
the  base  of  which  is  at  a  distance  of  100  yards  from  the  place  at  which  the  image  is 
formed.     Required  the  height  of  the  tree.  Ans.  100  feet. 

152.  What  is  the  height  of  a  tower  which  casts  a  shadow  56  '4  m.  in  length  when  a 
vertical  rod  0*95  m.  in  height  produces  a  shadow  i'38  m.  in  length?          Ans.  38*8. 

153.  A  minute  hole  is  made  in  the  shutter  of  a  dark  room,  and  at  a  distance  of 
2 -5  metres  a  screen  is  held.     What  is  the  size  of  the  image  of  a  tree  which  is  15 '3 
metres  high  and  is  at  a  distance  of  40  metres?  Ans.  ©'95625  metre. 

154.  What  is  the  length  of  the  shadow  of  a  tree  50  feet  high  when  the  sun  is  30° 
above  the  horizon?  What  when  it  is  45°,  and  60° ?    Ans.  86'6  ;  50,  and  28-867  feet- 

155.  Under  what  visual  angle  does  a  line  of  30  feet  appear  at  a  distance  of  18  feet  ? 

Ans.  79°'36. 

156.  The  apparent  diameter  of  the  moon  amounts  to  31'  3".     What  is  its  real  dia- 
meter if  its  distance  from  the  earth  is  taken  at  239000  geographical  miles  ? 

Ans.  2166  geographical  miles. 

157.  For  an  ordinary  eye  an  object  is  visible  with  a  moderate  illumination  and  pure 
air  under  a  visual  angle  of  40  seconds.     At  what  distance,  therefore,  can  a  black  circle 
(6  inches  in  diameter)  be  seen  on  a  white  ground  ?  Ans.  2578  feet. 

158.  At  what  distance  from  a  circle  with  a  diameter  of  one  foot  is  the  visual  angle  a 
second?  Ans.  206265  feet. 

159.  At  what  distance  would  a  circular  disc  i  inch  in  diameter,  of  the  same  bright- 
ness as  the  sun's  surface,  illuminate  a  given  object  to  the  same  extent  as  a  vertical  sun 
in  the  tropics,  the  light  absorbed  by  the  air  being  neglected  ? 

Ans.  Taking  the  sun's  angular  diameter  at  30',  x  =  38  inches. 

160.  What  is  the  minimum  deviation  for  a  glass  prism  (n  =  i'53),  whose  refracting 
angle  is  60°  ?  Ans.  39°  50'. 

161.  What  is  the  minimum  deviation  for  a  prism  of  the  same  substance  when  the 
refracting  angle  is  45°  ?  Ans.  63°  38'. 

162.  The  refracting  angle  of  a  prism  of  silicate  of  lead  has  been  found  by  measure- 
ment to  be  21° '12,  and  the  minimum  deviation  to  be  24° -46.     Required  the  refractive 
index  of  the  substance.  Ans.  2-i22. 

163.  Construct  the  path  of  a  ray  which  falls  on  an  equiangular  crown-glass  prism 
at  an  angle  of  30°  ;  and  find  its  deviation.  Ans.  70° '45. 

164.  What  are  the  angles  of  refraction  upon  a  ray  which  passes  from  air  into  glass 
at  an  angle  of  40°  ;  from  air  into  water  at  an  angle  of  65°  ;  and  from  air  into  diamond 
at  an  angle  of  80° ?  Ans.  25° '20  ;  44° '5  ;  23° '12. 

165.  The  focal  distance  of  a  concave  mirror  is  8  metres.     What  is  the  distance  of 
the  image  from  the  mirror  when  the  object  is  at  a  distance  of  12,  5,  and  7  metres 
respectively?  Ans.  24;  —  13-3  and  —  56. 


Light.  1005 

166.  An  object  at  a  distance  of  10  feet  produces  a  distinct  image  at  a  distance  of  3 
feet.     What  is  the  focal  distance  of  the  mirror?  Ans.  2*3077  feet. 

167.  Required  the  focal  distance  of  a  crown-glass  meniscus,  the  radius  of  curvature 
of  the  concave  face  being  45  mm.,  and  that  of  the  convex  face  30  mm.  ;  the  index  of 
refraction  being  1*5.  Ans.  f  =   180  mm. 

168.  What  is  the  principal  focal  distance  of  a  double-convex  lens  of  diamond,  the 
radius  of  curvature  of  each  of  whose  faces  is  4  mm.,  and  the  refractive  index  of  dia- 
mond 2-487?  Ans.   i'34mm. 

169.  A  watch-glass  with  ground  edges,  the  curvature  of  which  was  4-5  cm.,  was 
filled  with  water  and  a  glass  plate  slid  over  it.     The  focus  of  the  plano-convex  lens 
thus  formed  was  found  to  be  13-5  cm..    Required  the  refractive  index  of  the  water. 

Ans.  n   =   1-33. 

170.  What  is  the  focal  distance  of  a  double-convex  lens  when  the  distances  of  the 
image  and  object  are  respectively  5  and  36  centimetres?  Ans.  4*4  centimetres. 

171.  The  radii  of  curvature  of  a  double-convex  lens  of  crown  glass  are  six  and 
eight  inches.     What  is  the  focal  distance  ?  Ans.  6-85  inches. 

172.  The  focal  distance  of  a  double-convex  lens  is  4  inches  ;  the  radius  of  cur- 
vature of  one  of  its  faces  is  3  inches.     What  is  that  of  the  second?   Ans.  6  inches. 

173.  The  radius  of  curvature  of  a  plano-convex  lens  is  12  inches.     Required  its 
focal  distance.  Ans.  24  inches. 

174.  If  the  focal  distance  of  a  double-convex  lens  is  i  centimetre,  at  what  distance 
must  a  luminous  object  be  placed  so  that  its  image  is  formed  at  2  centimetres  dis- 
tance from  the  lens  ?  Ans.  2  centimetres. 

175.  A  candle  at  a  distance  of  120  centimetres  from  a  lens  forms  an  image  on  the 
other  side  of  the  lens  at  a  distance  of  200  feet.     Required  the  nature  of  the  lens  and 
its  focal  distance.  Ans.  It  is  a  convex  lens,  and  its  focal  distance  is  75  cm. 

176.  A  plano-convex  lens  was  found  to  produce  at  a  distance  of  62  cm.  a  sharp 
image  of  an  infinitely  distant  object.     In  front  of  the  same  lens,  at  a  distance  of  84  cm., 
a  millimetre  scale  was  placed,  and  a  sharp  image  was  formed  at  a  distance  of  250  cm. 
It  was  thus  found  that  10  millimetres  in  the  object  corresponded  to  29  in  the  image. 
From  these  observations  determine  the  focal  distance. of  the  lens.     Ans.    The  mean 
of  the  results  is  62*4. 

177.  The  image  of  a  distant  tree  was  sharply  formed  at  a  distance  of  31  cm.  from 
the  centre  of  a  concave  mirror. 

In  another  case  the  image  of  an  object  18  mm.  in  length  at  a  distance  of  405  mm. 
from  the  mirror  was  formed  at  1350  mm.  from  the  mirror  and  had  a  length  of  61  mm. 
In  another  experiment  the  distances  of  object  and  image  and  the  size  of  the  image  were 
respectively  2200,  355,  and  3  mm. 

Deduce  from  these  several  data  the  focal  distance  of  the  mirror.     Ans.  31*2  ;  30-5. 

178.  What  must  be  the  radii  of  curvature  of  the  faces  of  a  lens  of  best  form  made 
of  glass  (»  =  i'5)  if  its  focal  distance  is  to  be  6  inches?    Ans.  3*5  inches  and  21  inches. 

179.  A  diffraction  grating,  with  lines  0*05  mm.  apart,  is  held  in  front  of  a  Bunsen's 
burner  in  which  common  salt  is  volatilised,  and  when  viewed  through  a  telescope  it  is 
found  that  the  angular  distances  of  the  first,  second,  fourth,  and  sixth  bright  bands  from 
the  central  one  are  respectively  o°  41',   i°  21',  2°  42',  and  4°  3'.     Required  the  wave- 
length of  sodium  light. 

The  formula  X  =  -    sm — ',  where  X  is  the  wave-length,  </>  the  angular  distance  of 

any  bright  line  of  order  n  from  the  central  one,  gives  as  the  mean  of  the  4  observa- 
tions :  Ans.  0*00059088  mm. 


1 006  Problems  and  Examples  in  Physics. 


VII.     MAGNETISM  AND  FRICTIONAL  ELECTRICITY. 

ISO.  A  compass  needle  at  the  magnetic  equator  makes  15  oscillations  in  a  minute  ; 
how  many  will  it  make  in  a  place  where  the  horizontal  force  of  the  earth's  magnetism  is 

—  as  great?  Ans.  12. 

25 

181.  A  compass  needle  makes  9  oscillations  a  minute  under  the  influence  of  the 
•earth's  magnetism  alone  ;  how  many  will  it  make  when  re-magnetised  so  as  to  be 
half  as  strong  again  as  before?  Ans.  n. 

182.  A  small  magnetic  needle  makes  100  oscillations  in  7  min.  42  sees,  under  the 
influence  of  the  earth's  force  only ;  when  the  south  pole  of  a  long  bar  magnet  A  is 
placed  10  inches  north  of  it,  it  makes  100  oscillations  in  4  min.  3  sees.  ;  and  with  the 
^outh  pole  of  another  magnet  B  in  the  same  place,  it  makes  100  oscillations  in  4  min. 
48  sees.     What  are  the  relative  strengths  of  the  magnets  A  and  B  ? 

Ans.  A  =  1*404  B. 

183.  On  a  table  where  the  earth's  magnetism  is  counteracted,  the  north  pole  of  a 
compass  needle  makes  20  oscillations  in  a  minute  under  the  attraction  of  a  south  pole 
4  inches  distant ;  how  many  will  it  make  when  the  south  pole  is  3  inches  distant  ? 

Ans.  26 '6. 

184.  If  the  oscillating  magnet  be  re-magnetised  so  as  to  be  twice  as  strong  as 
'before,  how  many  oscillations  in  a  minute  will  it  make  in  the  two  positions  respectively  ? 

Ans.  28 '28  and  SQ'27' 

185.  At  one  end  of  a  light  glass  thread,  carefully  balanced  so  as  to  oscillate  in  a 
vertical  plane,  is  a  pith  ball.     Over  this  and  in  contact  with  it  is  a  fixed  pith  ball  of  the 
same  dimensions.     Both  balls  being  charged  with  the  same  electricity  it  is  found  that 
to  keep  them  1*4  inch  apart,  a  weight  of  '9  mgr.  must  be  placed  at  the  free  end  of  the 
glass  thread.     What  weight  must  be  placed  there  to  keep  the  balls  i  '05  inch  apart  ? 

Ans.  i  '6  mgr. 

186.  A  small  insulated  sphere  A  charged  with  the  quantity  of  +  electricity  2  is 
at  a  distance  of  25  mm.  from  a  second  similar  sphere  B  charged  with  the  quantity  5  ; 
the  latter  is  momentarily  touched  with  an  unelectrified  sphere  B,  of  the  same  size,  and 
the  distance  altered  to  20  mm.     What  is  the  ratio  of  the  repulsive  forces  in   the  two 

•cases?  Ans.  32  :  25. 

187.  Two  insulated  spheres  A  and  B,  whose  diameters  are  respectively  as  7  :  10, 
have  equal  quantities  of  electricity  imparted  to  them.    In  what  ratio  are  their  electrical 
densities?  Ans.  100  :  49. 

188.  Two  such  spheres  whose   diameters   are  as  3  :  5   contain  respectively  the 
quantities  of  electricity  7  and  10,     In  what  ratio  are  their  densities  ?      Ans.  35  :  18. 

189.  Three  insulated  conducting  spheres,  A,  B,  and  C,  whose  radii  are  respectively 
i,  2,  and  3,  are  charged  with  electricity,  so  that  their  respective  potentials  are  as  3  :  2  :  i, 
and  are  then  connected  by  wires,  whose  capacity  may  be  neglected.     What  is  the  total 
quantity  and  potential  of  the  system  ?  Ans.  Q  =  io  ;  V  =  i'66. 

190.  Supposing  each  of  the  spheres  discharged  separately,  what  would  be  the  total 
work  they  would  produce,  as  compared  with  that  produced  by  the   discharge  of  the 
-whole  system  ?  .  Ans.  30 : 25. 


Voltaic  Electricity.  1007 


VIII.     VOLTAIC  ELECTRICITY. 

191.  A  galvanometer  offering  no  appreciable  resistance  is  connected  by  short  thick 
wires  with  the  poles  of  a  cell,  and  deflects  20°.  By  how  much  will  it  be  deflected  if  two 
exactly  similar  cells  are  connected  with  the  first  side  by  side  ?  Ans.  47° -30. 

192.  By  how  much  if  the  three  cells  are  connected  in  series  ?  Ans.  20^. 

193.  Two  cells  each  of  i  ohm  resistance  are  connected  in  series  by  a  wire  the 
resistance  of  which  is  also  i  ohm.     If  each  of  these  when  connected  singly  by  short 
thick  wires  to  a  galvanometer  of  no  appreciable  resistance  deflects  it  25°,  how  much 
will  the  combination  deflect  it,  the  connections  being  made  by  short  thick  wires  ? 

Ans.  i7°-i6. 

A  Siemens  unit  is  equal  to  the  resistance  of  a  column  of  pure  mercury  a  metre  in 
length  and  a  square  mm.  in  cross  section.  It  is  equal  to  0-9536  of  an  ohm  or  BA 
unit;  or  a  BA  unit  equals  1-0485  Siemens  unit,  or  equals  a  column  of  mercury  1-0485 
metre  in  length  and  a  square  mm.  in  cross  section. 

194.  A  single  thermo-electric  couple  deflects  a  galvanometer  of  100  ohms  resist- 
ance o°  30';  how  much  will  a  series  of  30  such  couples  deflect  it,  the  connections  being 
made  by  short  thick  wires  ?  Ans.  14° -40. 

195.  Suppose  a  sine  galvanometer  had  been  used  in  the -last  question,   and  the 
first  reading  had  beeno°-3o',  what  would  the  second  be?  Ans.  i5°'io. 

196.  The  internal  resistance  of  a  cell  is  half  an  ohm  ;  when  a  tangent  galvano- 
meter of  i  ohm  resistance  is  connected  with  it  by  short  thick  wires  it  is  deflected  15°  ; 
by  how  much  will  it  be  deflected  if  for  one  of  the  thick  wires  a  thin  wire  of  i£  ohm 
resistance  is  substituted?  Ans.  7°'37. 

197.  What  will  be  the  deflection  if  each  of  the  wires  is  replaced  by  a  thin  wire  of 
i£  ohm  resistance  ?  Ans.  6°  10'. 

198.  A  cell  of  one-third  of  an  ohm  resistance  deflects  a  tangent  galvanometer  of 
unknown  resistance  45°,  the  connection  being  made  by  two  short  thick  wires.  If  a  wire 
of  3  ohms  resistance  be  substituted  for  one  of  the  short  wires  the  deflection  is  30°.  What 
is  the  resistance  of  the  galvanometer?  Ans.  375  ohms. 

199.  What  would  be  the  deflection  if  for  the  cell  in  the  last  question  three  exactly 
similar  cells  in  series  were  substituted  (a)  when  the  galvanometer  alone  is  in  circuit  ; 
U)  when  both  the  galvanometer  and  the  thin  wire  are  in  circuit  ? 

Ans.  a  67° -48.  b  =  57° -41. 

200.  A  galvanometer  offering  no   sensible  resistance  is  deflected  50°  by  a  cell 
connected  with  it  by  short  thick  wires.     If  a  resistance  of  3  ohms  be  put  in  the  circuit, 
>the  deflection  is  20°.     Find  the  internal  resistance  of  the  cell.  Ans.  1-32. 

201.  Suppose  the  results  in  the  last  question  were  produced  by  two  exactly  similar 
•cells  in  series,  find  the  internal  resistance  of  each.  Ans.  0*659. 

202.  Suppose  they  were  produced  by  two  exactly  similar  cells  placed  side  by  side., 
'find  the  internal  resistance  of  each.  Ans.  2*639. 

203.  If  the  resistance  of  130  yards  of  a  particular  copper  wire  -1-  of  an  inch  in 

16 

diameter  is  an  ohm,  express  in  that  unit  the  resistance  of  8242  yards  of  copper  wire  — 
of  an  inch  in  diameter.  Ans.  35*66. 

204.  One  form  of  fuse  for  firing  mines  by  voltaic  electricity  consists  of  a  platinum 
wire  f  of  an  inch  long,  of  which  a  yard  weighs  2  grains.     Required  its  resistance  in 
terms  of  a  Siemens  unit.     Specific  gravity  of  platinum  22,  and  its  conducting  power 
1 1  '25  that  of  mercury.  Ans.  0*131. 

205.  Express  in  ohms  the  resistance  of  one  mile  of  copper  wire  i  of  an  inch  in 
•diameter  of  the  same  quality  as  that  referred  to  in  203.  Ans.  0-8461. 


ioo8  Problems  and  Examples  in  Physics. 

206.  The  whole  resistance  of  a  copper  wire  going  round  the  earth  (24800  miles)  is 
221650  ohms.     Find  its  diameter  in  inches.  Ans  0*0738. 

207.  What  length  of  platinum  wire  0^05  of  an  inch  in  diameter  must  be  taken  to 
get  a  resistance  equal  to  i  ohm,  the  specific  resistance  of  platinum  being  taken  at  5-55 
that  of  copper  ?  Ans.  14-25  metres. 

208.  660  yards  of  iron  wire  0-0625  of  an  inch  in  diameter  have  the  same  electrical 
resistance  as  a  mile  of  copper  wire  0*0416  of  an  inch  in  diameter.     Find  the  specific 
resistance  of  iron,  that  of  copper  being  unity.  Ans.  6-15. 

209.  Ten  exactly  similar  cells  in  series  produce  a  deflection  of  45°  in  a  tangent 
galvanometer,  the  external  resistance  of  the  circuit  being  10  ohms.     If  arranged  so 
that  there  is  a  series  of  5  cells,  of  two  abreast,  a  deflection  of  33° '42  is  produced  ; 
find  the  internal  resistance  of  the  cell.  Ans.  %  ohm. 

210.  On  the  bobbins  of  the  new  Post  Office  pattern  of  a  single  needle  instrument 
are  coiled  225  yards  of  No.  35  copper  wire  0*0087  inch  in  diameter,  the  resistance  of 
which  is  about  92  ohms.     Required  the  conducting  power  of  the  wire    in  terms  of 
mercury.  Ans.  46. 

211.  Ten  exactly  similar  cells  each  of  §  of  an  ohm  resistance  give,  when  arranged 
in  five  series  of  2  each,  a  deflection  of  230*57  ;  but  when  arranged  in  2  series  of  5  each 
a  deflection  of  33° '42.     Required  the  external  resistance  of  the  circuit  including  that 
of  the  galvanometer.  Ans.  ^. 

212.  A  cell  in  a  certain  circuit  deflects  a  tangent  galvanometer  18°  26' ;  two  such 
cells  abreast  in  the  same  circuit  deflect  it  23°  57' ;  two  such  cells  in  series  in  the  same 
circuit  diminished  by  i  ohm  deflect  it  29° '2.    Find  the  internal  resistance  of  one  cell 
and  that  of  the  circuit.  Ans.  R  =  r  =  i'66. 

213.  What  is  the  best  arrangement  of  6  cells,   each  of  §  of  an  ohm  resistance, 
against  an  external  resistance  of  2  ohms  ? 

Ans.  Indifferent  whether  in  6  cells  of  i  each  or  in  3  cells  of  2  each. 

214.  What  is  the  best  arrangement  of  20  cells,  each  of  o'8  ohm  resistance,  against 
an  external  resistance  of  4  ohms  ?  Ans.  10  cells  of  2  each. 

215.  In  a  circuit  containing  a  galvanometer  and  a  voltameter,  the  current  which 
deflects  the  galvanometer  45°  produces  10*32  cubic  centimetres  of  mixed  gas  in  a 
minute.     The  electrodes  are  put  farther  apart,   and  the  deflection  is  now  20°  ;  find 
how  much  gas  is  now  produced  per  minute.  Ans.  3*757  cc. 

216.  100  inches  of  copperwire  weighing  100  grains  has  a  resistance  of  0*1516  ohm. 
Required  the  resistance  of  50  inches  weighing  200  grains.  Ans.  0*01895. 

217.  A  knot  of -nearly  pure  copper  wire  weighing  one  pound  has  a  resistance  of 
1200  ohms  at  i5°*5  C. ;  what  is  the  resistance  at  the  same  temperature  of  a  knot  of  the 
same  quality  of  wire  weighing  125  pounds?  Ans.  9*6  ohms, 

218.  Find  the  length  in  yards  of  a  wire  of  the  same  diameter  and  quality  as  the 
knot  pound  in  217,  having  a  resistance  of  2  ohms.  Ans.  3*38  yards. 

219.  Find  the  length  in  yards  of  a  wire  of  the  same  quality  and  total  resistance  as 
the  knot  pound  in  217,  but  of  three  times  the  diameter.  Ans.  18261  yards. 

220.  The  specific  gravity  of  platinum  is  2^  times  that  of  copper  ;  its  resistance  5f 
as  great.     What  length  of  platinum  wire  weighing  100  grains  has  the  same  resistance 
as  loo  inches  of  copper  wire  also  weighing  TOO  grains?  Ans.  27. 

221.  A  cell  with  a  resistance  of  an  ohm  is  connected  by  very  short  thick  wires  with  the 
binding  screws  of  a  tangent  galvanometer,  the  resistance  of  which  is  half  an  ohm,  and 
the  deflection  is  45°  ;  if  the  screws  of  the  galvanometer  be  also  connected  at  the  same 
time  by  a  wire  of  i  ohm  resistance,  find  the  deflection.  «  Ans.  36°  52'. 

222.  The  resistance  of  a  galvanometer  is  half  an  ohm,  and  the  deflection  when 


Voltaic  Electricity.  1009 

the  current  of  a  cell  is  passed  through  it  is  30°.     When  a  wire  of  2  ohms  resistance  is 
introduced  into  the  circuit  the  deflection  is  15°  ;  find  the  internal  resistance  of  the  cell. 

Ans.  1-23. 

223.  When  the  current  of  a  cell,  the  resistance  of  which  is  f  of  an  ohm,  is  passed 
through  a  galvanometer  connected  with  it  by  very  short  thick  wires,  the  deflection  is 
45° ;  when  the  binding  screws  are  also  connected  by  a  shunt  having  a  resistance  of  i 
the  deflection  is  33° '42.     Find  the  resistance  of  the  galvanometer.  Ans.  2. 

224.  A  cell  whose  internal  resistance  is  2  ohms  has  its  copper  pole  connected  with 
the  binding  screw  A  of  a  galvanometer  formed  of  a  thick  band  of  copper.     From 
the  other  screw  B  a  wire  of  20  ohms  resistance  passes  to  the  zinc  pole,  and  the  deflection 
read  off  is  7° '8.     Find  the  deflection  when  B  is  at  the  same  time  connected  with  the 
zinc  pole  by  a  second  wire  of  30  ohms  resistance.  Ans.  n°-&'. 

225.  What  would  be  the  deflection  in  212  if  the  second  wire  instead  of  passing 
from  B  to  the  zinc  pole  passed  directly  from  the  zinc  pole  to  the  copper  pole  ? 

Ans.  2-437. 

226.  A  Leclanche"  cell  deflects  a  galvanometer  30°  when  200  ohms  resistance  are 
introduced  into  the  circuit,    15°  when  570  ohms  are  introduced ;  a  standard  Daniell 
cell  deflects  it  30°   when  100  ohms  are  in  circuit  and  15°  when  250  additional  ohms  are 
introduced.     Required  the  electromotive  force  of  the  Leclanche"  in  terms  of  that  of  the 
Daniell.  Ans.  1-48. 

227.  A  Bunsen  and  a  Daniell  cell  are  placed  in  the  same  circuit  in  the  first  case 
so  that  the  carbon  of  the  first  is  united  to  the  ziric  of  the  Daniell ;  and  in  the  second 
case  so  that  their  currents  oppose  each  other.     The  currents  are  respectively  30° '2, 
and  in  the  second  io°'6.     Required  the  electromotive  force  of  the  Bunsen  in  terms  of 
the  Daniell.  Ans.  i'8g. 

228.  A  telegraph  line  constructed  of  copper  wire,  a  kilometre  of  which  weighs  30*5 
kilogrammes,  is  to  be  replaced  by  iron  wire  a  kilometre  of  which  weighs  135 '6  kilo- 
grammes.    In  what  ratio  does  the  resistance  alter?     Ans.  The  resistance  of  the  iron 
wire  will  be  i'i8  times  that  of  the  copper  wire  for  which  it  is  substituted. 

229.  A  telegraph  line  which  has  previously  consisted  of  copper  wire  weighing  30-5 
kilogrammes  to  the  kilometre  is  to  be  replaced  by  an  iron  wire  of  the  same. diameter 
which  shall  offer  the  same  resistance.     What  must  be  the  section  of  the  latter,  and 
what  its'  weight  per  kilometre  ? 

Ans.  The  section  of  the  copper  wire  is  3^4357  sq.  mm.,  that  of  the  iron  by  which 
it  is  replaced  is  2o'6  sq.  mm.,  and  its  weight  per  kilometre  is  i6o'4  kilogrammes. 

230.  When  the  poles  of  a  voltaic  cell  are  connected  by  a  conductor  of  resist- 
ance i,  a  current  of  strength  1*32  is  produced  ;  and  when  they  are  connected  by  a 
conductor  of  resistance  5  the  strength  of  the  current  is  o'33.     Find  from  these  data 
the  internal  resistance  and  the  electromotive  force  of  the  cell.     Ans.  J?  =  ^  E  =  i'j6. 

231.  A  silver  wire  is  joined  end  to  end  to  an  iron  wire  of  the  same  length,  but  of 
double  the  diameter,  and  six  times  the  specific  resistance  ;  the  other  ends  are  joined 
to  the  battery,  the  current  of  which  is  transmitted  for  five  minutes,  during  which  time 
a  total  quantity  of  45  units  of  heat  is  generated  in  the  two  wires.     How  is  it  shared 
between  them  ?  Ans.  Ag  :  Fe  — 18  :  27. 

232.  A  window  casement  of  iron  faces  the  south,  and  the  hinges  which  support  it 
are  on  the  east.     What  electrical  phenomena  are  observed  (a]  when  the  window  is 
opened,  and  (b]  when  it  is  closed  ? 

233.  Two  points  135°  apart  in  a  uniform  circular  conducting  ring  are  connected 
with  the  opposite  poles  of  a  voltaic  battery.     Compare  the  strength  of  the  current  in 
the  two  portions  of  the  ring. 

234.  A  mile  of  cable  with  a  resistance  of  3*59  ohms  was  put  in  water,  with  the 
end  B  insulated  ;  its  core  having  been  pricked  with  a  needle  the  resistance  tested  from 
the  end  A  was  found  to  be  2*81  ohms.     A  being  insulated,  a  test  from  B  showed  the 
resistance  to  be  276.     Required  the  distance  from  A  to  the  injured  spot. 

Ans.  867  yards. 
3T 


/ 


INDEX. 


(THE  NUMBERS  REFER  TO  THE  ARTICLES.) 


ABE 

ABEL'S  electric  fuse,  794 
Aberration,        chromatic,        583  ; 
spherical,  533 

Absolute  electrical  units,  963 

Absolute  expansion  of  mercury,  322 

Absolute  measure  of  electrical  resistance, 
954  ;  temperature,  496 

Absorbent  power  of  aqueous  vapour,  985 

Absorbing  power,  424 

Absorption,  electrical,  748  ;  of  gases  by 
solids,  193  ;  of  gases  by  liquids,  189  ; 
of  heat  by  liquids,  434  ;  by  vapours, 
435  ;  heat  produced  by,  482 

Acceleration  of  a  force,  27,  77 

Accidental  haloes,  627  ;  images,  626  ; 
magnetic  variations,  694 

Accommodation  (of  the  eye),  620 

Accumulator,  hydraulic,  151 

Accumulators,  765 

Achromatism,  584  ;  of  the  microscope,  592 

Achromatopsy,  632 

Acidometer,  126 

Acierage.  857 

Aclinic  lines,  698 

Acoustics,  220-287 

Acoustic  foci,  237  ;  attraction  and  repul- 
sion, 290 

Actinic  rays,  433,  573 

Action  and  reaction,  39 

Adhesion,  86 

Aerial  meteors,  975  ;  perspective,  618 

Aerolites,  480 

yKsculine,  582 

Affinity,  85 

After  action,  elastic,  91 

Agents,  6 

Agonic  line,  692 

Air,  aspirating  action  of  currents  of,  207  ; 
causes  which  modify  temperature  of, 
974,  1006;  heating  by,  491  ;  thermo- 
meter, 334 ;  resistance  of,  48  ;  trap,  167 

Air-balloons,  196  ;  chamber,  217 

Air-pump,    200,    467  ;    Bianchi's,    203 ; 


ANT 

condensing,     209  ;      Deleuil's,     204  ; 

gauges,  20 1  ;  rarefaction  in,  200  ;  re- 
ceiver of,  200  ;  Sprengel's,  205  j  uses 

of,  210 
Ajutage,  146 
Alarum,  electric,  897 
Alcarrazas,  373 
Alcoholic  value  of  wines,  378 
Alcoholometer,  128;  Gay-Lussac's,  128; 

centesimal,  128 
Alcohol  thermometer,  306 
Alloys,  340 

Alternate  currents,  914 
Amalgam,  754 
Amalgamated  zinc,  816 
Amber,  723 

Amici's  camera  lucida,  603 
Ampere,  814 
Ampere's  memoria  technica^  820  ;  theory 

of  magnetism,  879  ; 
Amplitude  of  vibration,  55 
Analogous  pole,  732 
Analyser,  656 

Analysis,  spectral,  575 ;  of  solar  light,  430 
Anamorphoses,  534 
Anelectrics,  724,  748 
Anelectrotonus,  828 
Anemometer,  974,  975 
Aneroid  barometer,  187 
Angle  of  deviation,  544,  1002  ;    critical. 

540;  optic,  617;  of  polarisation,  654; 

of  reflection  and  incidence,  511,  536; 

of    repose,    39 ;    of    refraction,    536  ; 

visual,  617 
Angular  currents,  laws  of,  860  ;  velocity, 

53 

Animal  heat,  485 
Anione,  842 
Annealing,  90 
Annual  variations,  693 
Anode,  842 
Anticyclone,  980 
Antilogous  pole,  732 

3T2 


1012 


Index. 


ANY 

Anvil,  922 

Aperiodic  galvanometer,  821 

Aperture  of  a  lens,  558 

Aplanatic  lenses,  558 

Aqueous  humour,  612 

Aqueous  vapour,  its  influence  on  climate, 
985  ;  tension  of,  355-361 

Arago's  experiment,  181 

Arbor  Dianre,  853  ;  Saturni,  853 

Arc  lamps,  838 

Arc  of  vibration,  55  ;  voltaic,  833 

Archimedes'  principle,  113;  applied  to 
gases,  195 

Area,  unit  of,  22 

Armatures,  718;  drums,  918;  Siemens', 
914 

Arms  of  levers,  40 

Armstrong's  hydro-electric  machine,  758 

Artesian  wells,  1 1 1 

Artificial  magnets,  680 

Ascent  of  liquids  in  capillary  tubes,  132  ; 
between  surfaces,  133 

Aspirating  action  of  air  currents,  207 

Astatic  currents,  873  ;  needle  and  system, 
700  ;  circuits,  873 

Astronomical  telescope,  595 

Athermancy,  434 

Atmolysis,  190 

Atmosphere,  its  composition,  157;  crush- 
ing force  of,  159  ;  amount  of,  determi- 
nation of,  163  ;  electricity  in  the,  993, 

994  ;  moisture  of,  400 
Atmospheric   electricity,  causes  of,  994, 

995  ;  pressure.  158,  163,  972 
Atomic  heat,  458  ;  weight  deduced  from 

specific  heat,  458 

Atoms,  3 

Attraction,  capillary,  134;  and  repulsion 
produced  by  capillarity,  134;  mole- 
cular, 83  ;  universal,  66 

Attractions,  magnetic,  laws  of,  703 ; 
electrical,  laws  of,  734 

Atwood's  machine,  77 

Audiometer,  932 

Aura,  764 

Aurora  borealis,  694,  1002 

Aurum  musivum,  754 

Austral  pole,  689 

Avoirdupois,  23 

Axis  of  crystal,  640  ;  electric,  732  ; 
lenses,  551  ;  optic,  617  ;  of  a  magnet, 
68 1  ;  of  oscillation,  79 

Azimuthal  circle,  695 

~O  AD  conductors,  404 
_D     Bain's  electro-chemical  telegraph, 
895 


BIA 

Balance,  71  ;  beam  of,  72  ;  compensat- 
ing, 320  ;  delicacy  of,  73  ;  hydrostatic, 
1 20  ;  induction,  932  ;  knife-edge  of, 
71  ;  pendulum,  320 ;  physical  and 
chemical,  74 ;  spring,  88  ;  torsion,  89, 
704,  733 

Ballistic  galvanometer,  821  ;  pendulum, 
81 

Balloons,  195— *99  j  construction  and 
management  of,  197  ;  CoxwelPs,  96  ; 
Montgolfier,  196;  weight  raised  by,  199 

Bands  of  spectrum,  576 

Barker's  mill,  149 

Barometers,  164;  aneroid,  187;  Bun- 
ten's,  167  ;  cistern,  165  ;  corrections 
in,  170  ;  determination  of  heights  by, 
178  ;  differential,  186  ;  fixed,  175  ; 
Fortin's,  166  ;  Gay-Lussac's,  167  ; 
glycerine,  176;  precautions  with,  1 68; 
wheel,  174;  variations  of  height  of,  171 

Barometric  formula,  Laplace's,  178  ; 
gradients,  979 ;  height  of,  corrected 
for  heat,  327;  manometer,  186  ;  va- 
riations, 172 

Baroscope,  195 

Battery,  Bunsen's,  810  ;  Callan's,  810  ; 
chemical  effects  of,  841  ;  Daniell's, 
808  ;  electric,  774 ;  floating,  865  ; 
gas,  850;  gravity,  812;  Grove's,  809; 
Leclanche's,  844 ;  Leyden,  constant, 
807  ;  charged  by  coil,  923  ;  local, 
877  ;  luminous  effects,  833  ;  magnetic, 
717  ;  measurement  of  charge,  777  ; 
mechanical  effects  of,  839  ;  Menotti's, 
812  ;  Marie  Davy's,  812  ;  postal,  877  ; 
secondary,  849  ;  Smee's,  811  ;  sulphate 
of  mercury,  8 12  ;  tension  of,  815  ; 
thermo-electric,  944  ;  voltaic,  804, 
805  ;  Walker's,  8ii;  Wollaston's,  805 

Beam  of  a  balance,  72  ;  of  a  steam- 
engine,  467 

Beats,  262 

Beaume's  hydrometer,  127 

Becquerel's  pyrometer,  949  ;  thermo- 
electric battery,  944 ;  electrical  ther- 
mometer, 948 

Bell  of  a  trumpet,  237 

Bell's  telephone,  930  ;  photophone,  936 

Bellows,  243  ;  hydrostatic,  101 ;  water, 
207 

Bennett's  electroscope,  751 

Berthollet's  experiment,  188 

Berlin's  commutator,  870 

Bianchi's  air-pump,  203 

Biaxial  crystals,  double  refraction  in, 
644 ;  optic  axis  of,  644 ;  rings  in, 
667 


Index. 


1013 


BIF 

Bifurcation,  639 

Binnacle,  697 

Binocular  vision,  621 

Blot's  apparatus,  676 

Black's  experiments  on  latent  heat,  461 

Bladder,  swimming,  118 

Block  and  tackle,  45 

Blood-globules,  15 

Blue  cloud,  986 

Bodies,  properties  of,  7,  122 

Bohnenberger's  electroscope,  818 

Boiler,  466 

Boiling,  350 ;  by  cooling,  367  ;  laws  of, 

363 

Boiling-point,  influence  of  dissolved  sub- 
stances on,  365  ;  of  nature  of  vessel, 
366  ;  of  pressure  on,  367  ;  in  a  ther- 
mometer, 302 ;  measurement  of  heights 
by,  369 

Bolometer,  960 

Borda's  method,  75 

Boreal  pole,  689 

Bottomley's  experiment,  990 

Boutigny's  experiments,  385 

Boyle's  law,  180-182 

Brake,  473  ;  air,  209 

Bramah's  hydraulic  press,  108 

Branch  currents,  961 

Breaking  weight,  91 

Breezes,  land  and  sea,  977 

Breguet's  thermometer,  309  ;  magneto- 
electrical  machine,  912 

Bridge,  Wheatstone's,  956 

British  imperial  yard,  22  ;  and  French 
system  of  weights  and  measures,  125 

Browning's  regulator,  836 

Brush  discharge,  787  ;  dynamo-electrical 
machine,  919 

Bull's  eye,  591 

Bunsen's  filter-pump,  206  ;  battery,  810; 
burner,  576 ;  ice  calorimeter,  452 ; 
photometer,  509 

Bunsen  and  Kirchhoffs  researches,  578 

Bunten's  barometer,  167 

Buoyancy  of  liquids,  100 

Burning  mirrors,  420 


telegraph,  886 
\^,     Caesium,  578 

Cagniard-Latour's    syren,    242  ;    experi- 
ments on  formation  of  vapour,  370 
Cailletet's  and  Pictet's  researches,  382 
Calibration,  298 
Callan's  battery,  8n 
Calorescence,  433 
Caloric,  448 


CHL 

Calorific  effects  of  electrical  discharge* 
790  ;  of  current  electricity,  829,  830  ; 
of  Ruhmkorffs  coil,  923  j  of  the  spec- 
trum, 573 

Calorimeter,  450  ;  Bunsen's  ice,  451  ; 
Black's,  451;  Favre  and  Silbermann's, 
463  ;  Lavoisier  and  Laplace's,  45 1 

Calorimetry,  447 

Camera  lucida,  594;  Amici's,  603  ;  ob- 
scura,  602;  Porta's  obscura,  514; 
Wollaston's,  603 

Campani's  eyepiece,  592 

Capacity,  error  of,  165  ;  electrical,  739  ; 
specific  inductive,  748 

Capillarity,  131 ;  attraction  and  repulsion 
produced  by,  134  ;  correction  for,  169 

Capillary  phenomena,  131-138;  electro- 
meter, 840;  tubes,  132;  ascent  and 
depression  in,  132  ;  between  parallel 
or  inclined  surfaces,  133 

Capsule,  of  the  eye,  612 

Carcel  lamp,  849 

Cardan's  suspension,  166 

Carre's  mode  of  freezing,  374  ;  dielectri- 
cal  machine,  760 

Carriage  lamps,  535 

Cartesian  diver,  116 

Cascade,  charging  by,  776 

Cathetometer,  88 

Catoptric  telescopes,  598 

Caustics,  533,  534 

Celsius'  scale,  303 

Centesimal  alcoholometer,  128 

Centigrade  scale,  303 

Centimetre,  125 

Centre,  optical,  555  ;  of  gravity,  68  ;  of 
parallel  forces,  37  ;  of  pressure,  102 

Centrifugal  force,  53 

Charge  of  a  Leyden  jar,  penetration  of, 
773  ;  measurement  of,  787  ;  laws  of, 
778  ;  residual,  773 

Charging  by  cascade,  776 

Chatterton's  compound,  886 

Chemical  affinity,  85  ;  combination,  483  ; 
effects  of  the  battery,  793  ;  decomposi- 
tion, 841  ;  of  electrical  discharge,  793  ; 
of  voltaic  currents,  821  ;  of  RuhmkorfPs 
coil,  923  ;  harmonicon,  278  ;  hygro- 
meter, 394  ;  properties  of  the  spectrum, 

573 

Chemistry,  i 

Chevallier's  microscope,  591 
Cheval-vapeur,  473 
Children's  experiment,  830 
Chimes,  electrical,  763 
Chimney,  487 
Chladni's  experiments,  284 


ioi4 


Index. 


CHL 

Chlorophane,  635 

Chlorophylle,  580 

Chords,  major  and  minor,  247  ;  physical 
constitution  of,  264  ;  tones  dominant 
and  subdominant,  248  ;  vocal,  259 

Choroid,  612 

Chromatic  scale,  250  ;  aberration,  583 

Chromium,  magnetic  limit  of,  720 

Ciliary  processes,  612 

Circle,  azimuthal,  695 

Circular  polarisation,  669 

Cirrocumulus,  981 

Cirrostratus,  981 

Cirrus,  981 

Cistern  barometer,  165 

Clamond's  thermo-electric  battery,  945 

Clarke's  magneto-electrical  machine,  911 

Cleavage,  electricity  produced  by,  731 

Clement  and  Desorme's  experiment,  207 

Climate,  1008;  constant,  1008;  influence 
of  aqueous  vapour  on,  985 

Climatology,  1004-1011 

Clocks,  81  ;  crutch  of,  81  ;  electrical,  898 

Clouds,  981  ;  electricity  of,  996;  forma- 
tion of,  982 

Coatings,  769  ;  Leyden  jar  with  movable, 
771 

Cobalt,  720 

Coercive  force,  687 

Coefficients  of  linear  expansion,  313, 
315,  316;  conductivity,  404,  405 

Cohesion,  84 

Coil,  primary,  879  ;  Ruhmkorffs,  914  ; 
effects  produced  by,  914  ;  secondary, 

879 

Cold,  apparent  reflection  of,  422  ;  pro- 
duced by  evaporation,  373  ;  expansion 
of  gases,  494 ;  by  nocturnal  radiation, 
495  ;  sources  of,  493 

Colladon  and  Sturm's  experiments,  234 

Collecting  plate,  779  »,  ; 

Collimation,  595 

Collision  of  bodks,  58 

Colloids,  140 

Coloration  produced  by  rotatory  polari- 
sation, 675 

Colour.  7  ;  of  bodies,  592  ;  of  heat,  436; 
of  thin  plates,  650 

Colour  discs,  570 

Colour  disease,  632 

Colours,  contrast  of,  627  ;  mixed,  570  ; 
simple,  566  ;  complementary,  570  ; 
produced  by  polarised  light,  662-668  ; 
by  compressed  glass,  668 

Combustion,  ^83  ;  heat  disengaged  dur- 
ing, 484 

Comma,  musical,  248 


COR 

Common  reservoir,  726 

Communicator,  886 

Commutator,  887.  889,  912,  922  ;  Ber- 
tin's,  870 

Compass,  correction  of  errors,  696  ;  de- 
clination, 695  ;  mariner's,  697  ;  incli- 
nation, 698  ;  sine,  824  ;  tangent,  823 

Compensating  cube,  438 

Compensation,  method  of  magnets,  719  ; 
pendulum,  320  ;  balance,  320 ;  grid- 
iron, 320;  strips,  320 

Complementary  colours,  570 

Component  forces,  32 

Composition  of  velocities,  52 

Compound  microscope,  591 

Compressed  glass,  colours  produced  by, 
668 

Compressibility,  7,  16  ;  of  gases,  154, 
180  ;  of  liquids,  97 

Concave  mirrors,  419,  528 

Concert  pitch,  251 

Concordant  tones,  247 

Condensation  of  vapours,  375 

Condensed  gas,  193,  209  ;  wave,  225 

Condenser,  467,  759,  765  ;  limits  to 
charge  of,  768  ;  of  Ruhmkorft's  coil, 
922  ;  Liebig's,  377 

Condensing  engine,  471  ;  air-pump,  209  ; 
force,  .calculation  of,  767  ;  electro- 
scope, 779;  plate,  799  ;  hygrometers, 

395 

Conduction  of  heat,  403  ;  of  electricity, 
725  ;  lightning,  1001 

Conductivity  of  bodies  for  heat,  404  ;  co- 
efficient of,  404,  405  ;  of  gases,  409 ; 
of  liquids,  407  ;  for  electricity,  955,  958 

Conductors,  725  ;  equivalent,  956  ;  good 
and  bad,  404;  lightning,  looi ;  prime, 
753;  resistance  of,  952 

Congelation,  343 

Conjugate  mirrors,  420 ;  focus,  525>  552 

Connecting  rod,  467 

Conservation  of  energy,  65 

Constant  currents,  807 

Contact  theory  of  electricity,  799 

Contractile  force,  319 

Convection,  408  ;  electrolytic,  832 

Convex   meniscus,    131  ;    mirrors,    526, 

529 

Cooling,  method  of,  455  ;  Newton's  law 

of,  416 

Corliss  engine,  47  I 
Cornea,  612 
Cornish  engine,  467 
Corona,  981 
Corpuscular  theory,  499 
Corti's  fibres,  260 


Index. 


1015 


cos 

Cosine,  law  of  the,  414,  508 

Coulomb,  964 

Coulomb's  law,  703 

Couple,  36  ;  terrestrial  magnetic,  690 ; 
voltaic,  So i  ;  thermo-electric,  942 

Couronne  des  tasses,  805 

Cowper's  writing  telegraph,  890 

Cox  well's  balloon,  196 

Crab,  42 

Critical  angle,  540  ;  current,  920  ;  tem- 
perature, 370 

Crookes's  radiometer,  445 ;  vacuum,  446  ; 
experiments,  927 

Cross-wire,  595 

Crutch  of  a  clock,  81 

Cryohydrate,  348 

Cryophorus,  373 

Crystal,  hemihedral,  732 

Crystalline,  612 

Crystallisation,  344 

Crystalloids,  140 

Crystals,  343;  expansion  of,  315  ;  doubly 
refracting,  639,  652,  663  ;  uniaxial, 
642  ;  positive  and  negative,  643 

Cube,  Leslie's,  423 

Cumulostratus,  980 

Cumulus,  980 

Current  electricity,  800 

Currents,  action  on  currents,  862,  863  ; 
action  of  magnets,  866  ;  action  of 
earth  on,  872,  873  ;  action  on  sole- 
noids, 874,  879 ;  constant,  807  ;  di- 
vided, 961  ;  detection  and  measure- 
ment of  voltaic,  819;  diaphragm,  839; 
direct  and  inverse,  900,  901,  908; 
effects  of  enfeeblement  of,  806  ;  energy 
of,  920  ;  extra,  907,  908  ;  of  inclina- 
tion, 967  ;  intensity  of,  825  ;  induc- 
tion by,  900  ;  laws  of  angular,  860  ; 
laws  of  sinuous,  86 1  ;  local,  816  ; 
magnetisation  by,  871  ;  motion  and 
sounds  produced  by,  884  ;  muscular, 
966  ;  in  active  muscle,  969  ;  in  nerve, 
970 ;  rotation  of  magnets  by,  856 ; 
secondary,  806;  terrestrial,  880;  ther- 
mal effects  of,  830,  831;  transmissions 
by,  844 

Curvature  of  liquid  surfaces,  135  ;  in- 
fluence of,  on  capillary  phenomena,  136 

Curves,  magnetic,  704 

Cushions,  753 

Cyanogen  gas,  380 

Cyclones,  979 

Cylinder,  467  ;  electrical  machine,  757 

T-\AGUERREOTYPE,  608 
1  J     Daltonism,  632 


DIE 

Dalton's  laws  on  gases  and  vapours,  383; 
method  of  determining  the  tension  of 
aqueous  vapour,  356 

Damper,  279,  905 

DanielFs  battery,  808  ;  hygrometer,  396; 
pyrometer,  311 

Dark  lines  of  the  spectrum,  574 ;  of 
solar  spectrum,  579 

Davy's  battery,  812 

Davy's  experiment,  421 

Day,  apparent,  21 

Deadbeat  galvanometer,  821 

Decimetre,  24,  125 

Declination  compass,  695  ;  errors  of, 
696  ;  magnetic,  691  ;  of  needle,  691  ; 
variations  in,  691  ;  of  a  star,  600 

Decomposition,  chemical,  841  ;  of  white 
light,  564  ;  of  salts,  843 

Deflagrator,  Hare's,  805,  829 

Degrees  of  a  thermometer,  303 

De  la  Rive's  floating  battery,  867 ;  ex- 
periments, 928 

De  la  Rue  and  Muller's  experiments,  926 

Deleuil's  air-pump,  204 

Delezenne's  circle,  906 

Delicacy  of  balance,  73  ;  of  thermo- 
meter, 307 

Densimeter,  130 

Density,  24  ;  of  the  earth,  67  ;  electric, 
736,  gravimetrical,  185  ;  of  gases,  335- 
337;  maximum  of  water,  330 ;  of 
vapours,  Gay-Lus?ac's  method,  386  ; 
Dumas's,  388  ;  Deville  and  Troost's, 
388  ;  Hofmann's,  387 

Depolarisation,  665 

Depolarising  plate,  663 

Depression  of  liquids  in  capillary  tube, 
132  ;  between  surfaces,  133 

Derived  currents,  961 

Descartes'  laws  of  refraction,  537 

Despretz's  experiment,  404 

Developer,  609 

Deviation,  angle  of,  544 

Deville  and  Troost's  method,  388 

Dew,  987 ;  point,  395 

Diabetic  urine,  analysis  of,  678 

Dial  telegraphs,  888 

Dialyser,  140 

Dialysis,  140 

Diamagnetism,  938 

Diapason,  257 

Diaphanous  bodies,  $00 

Diaphragm,  591  ;  currents,  839 

Diathermancy,  434 

Diatonic  scale,  248 

Dielectrical  machine,  Carre's,  760 

Dielectric  polarisation,  747 


ioi6 


Index. 


DIE 

Dielectrics,  748 
Differential  barometer,  186 
Differential  galvanometer,  821  ;  thermo- 
meter,   Leslie's,    308  ;    Matthiessen's, 
308 ;  tone,  263 
Diffraction,  503  ;    spectra,  648  ;  fringes, 

646 

Diffusion  of  heat,  437;  of  liquids,  140 
Digester,  Papin's,  371 
Dionoea  muscipula,  827 
Dioptric  telescopes,  598 
Diplopy,  631 
Dip,  magnetic,  698 
Dipping  needle,  698 
Direct  Vision  Spectroscope,  511 
Disc,  Newton's,   567  ;  Maxwell's  colour, 

570 

Discharge,  electrical,  766  ;  effects  of  the, 
783  ;  lateral,  1001  ;  silent,   793,   slow 
and  instantaneous,  766  ;  universal,  775 
Discharging  rod,  766 
Dispersion,  544  ;  abnormal,  581 
Dispersive  power,  564 
Displacement,  46 
Dissipation  of  energy,  498 
Dissociation,  389 

Distance,  estimation  of,  618;  adaptation 

of  eye  to,  620 
Distillation,  376 

Distribution  of  free  electricity,  735  ;  of 
magnetism,  722 ;  of  temperature, 
1009  ;  of  land  and  water,  ion 

Diurnal  variations,  693 

Diver,  Cartesian,  116 

Divided  currents,  961 

Dividing  machine,  1 1 

Divisibility,  7,  12 

Dobereiner's  lamp,  482 

Dominant  chords,  248 

Doppler's  principle,  233 

Double-action  steam-engine,  467,  468 

Double  refraction,  652 

Double-weighing,  75 

Doublet,  Wollaston,  586 

Dove's  law  of  storms,  978 

Draught  of  fire-places,  488 

Dredging  machines,  150 

Driving  wheels,  470 

Drum  armature,  918 

Drummond's  light,  606 

Dry  piles,  817 

Duboscq's  microscope,   606  ;    regulator, 

835 

Ductility,  7,  92 

Duhamel's  graphic  method,  245 
Dulong    and    Arago's    experiments    on 

Boyle's  law,    181  ;    method   of  deter- 


ELE 

mining  the  tension  of  aqueous  vapour, 
357 

Dulong  and  Petit's  determination  of  ab- 
solute   expansion    of    mercury,    322  ; 
method  of  cooling,  455  ;  law,  458 
Dumas's    method    for    vapour    density, 

388 

Duplex  telegraphy,  893 
Duration  of  electric  spark,  795 
Dutroche's  endosmometer,  139 
Dynamical  theory  of  heat,  429 
Dynamic  radiation  and  absorption,  442 
Dynamo-electrical  machine,  916-918 
Dynamo-magnetic  machine,  916 
Dynamometer,  90 


EAR,  the,  7,  260 
Ear  trumpet,  239 

Earnshaw  on  velocity  of  sound,  230 

Earth,  density  of,  67  ;  its  action  on 
currents,  871-873;  action  of  solenoids, 
878;  current,  894;  flattening  of,  by 
rotation,  82  ;  magnetic  poles  of  the, 
698  ;  magnetisation  by,  714 

Earth's  magnetism,  701 

Ebullition,  350  ;  laws  of,  363 

Eccentric,  467,  468 

Echelon  lenses,  607 

Echoes,  237  ;  monosyllabic,  trisyllabic, 
multiple,  237 

Edelmann's  hygrometer,  394 

Edison's  lamp,  838  ;  phonograph,  291  ; 
tasimeter,  933  ;  telephone,  934 

Effluvium  electrical,  793 

Efflux,  velocity  of,  142  ;  quantity  of, 
145  ;  influence  of  tubes  on,  146 

Effusion  of  gases,  191 

Elastic  bodies,  58  ;  after  action,  91 

Elastic  force,  152;  of  vapours,  351 

Elasticity,  7,  17  ;  limit  of,  17,  88;  of 
traction,  88  ;  modulus  of,  88  ;  of  tor- 
sion, 89  ;  of  flexure,  90 

Electric  alarum,  897  ;  axis;  732  ;  batter- 
ies, 774,  789 ;  candles,  838  ;  charge, 
778  ;  chimes,  763  ;  clocks,  898  ;  den- 
sity, 736  ;  discharge,  783  ;  egg,  788  ; 
fish,  971  ;  fuse,  794;  glow,  787  ;  lamp, 
838  ;  light,  831-833  ;  stratification  of 
the,  924  ;  lighting,  838 ;  pendulum, 
724;  pistol,  793;  poles,  732  ;  residue, 
773  ;  shock,  770,  785  ;  spark,  762  ; 
telegraphs,  886-899  >  tension,  736  ; 
whirl,  764;  tube,  789 

Electrical  attractions  and  repulsions, 
734  ;  endosmose,  839 ;  potential,  738  ; 
capacity,  739  ;  measurement  of,  740  ; 


Index. 


1017 


ELE 

resistance,  unit  of,  954 ;  conductivity, 
958  ;  quantity,  733  ;  units,  963 

Electrical  machines,  752-761  ;  precau- 
tions in,  754 

Electricity,  6,  723 ;  application  of,  to 
medicine,  972  ;  atmospheric,  992- 
1001  ;  contact  theory,  799  ;  current, 
800 ;  communication  of,  749  ;  de- 
velopment of,  by  friction,  724  ;  by 
pressure  and  cleavage,  731  ;  distribu- 
tion of,  735  ;  dynamical,  797-9° !  j 
disengagement  of,  in  chemical  actions, 
793-799  >  frictional,  730 ;  loss  of, 
743  ;  mechanical  effects,  792  ;  power 
of  points,  742  ;  produced  by  induction, 
744 ;  velocity  of,  796 ;  theories  of, 
728  ;  work  required  for  production  of, 
761 

Electrified  bodies,  motion  of,  729,  750 

Electro-capillary  phenomena,  840 

Electrochemical  equivalent,  844 ;  tele- 
graph, 895  ;  series,  842 

Electrodes,  803  ;  polarisation  of,  806 

Electrodynamics,  858 

Electrodynamometer,  962 

Electro^ilding,  855 

Electrolysis,  842  ;  laws  of,  846 

Electrolyte,  842 

Electrolytic  convection,  832 

Electromagnetic  force,  883 ;  machines, 
899  ;  units,  963 

Electromagnets,  880,  884 

Electrometallurgy,  854,  855 

Electrometer,  751  ;  Lane's,  777  ;  quad- 
rant, 756  ;  Thomson's,  780 

Electromotive  series,  801  ;  force,  802, 
814,  825,  959  ;  determination  of,  959  ; 
force  of  elements,  814 

Electromotor,  886 

Electrophorus,  752 

Electropyrometer,  949 

Electroscope,  724  ;  Bohnenberger's,  818  ; 
Volta's  condensing,  779  ;  gold  leaf,  751 

Electrosilvering,  856 

Electrostatic  units,  963 

Electrotonus,  828 

Elements,  electronegative  and  electro- 
positive, 842 

Elliptical  polarisation,  672 

Emergent  rays,  542 

Emission  theory,  499 

Emissive  power,  425 

Endosmometer,  135 

Endosmose,  139 ;  electrical,  839 ;  of 
gases,  190 

Endosmotic  equivalent,  139 

Energy,  62  ;  conservation  of,  65  ;  dissi- 


FAL 

pation  of,  498  ;  transformations  of,  64  ; 
varieties  of,  63 

Engines,  gas,  476  ;  steam,  465  ;  double- 
action,  467  ;  low  and  high  pressure, 
471  ;  single  action,  469  ;  locomotive, 
470  ;  fire,  219  •  transformation  of,  64; 
Cornish,  467  ;  horizontal,  468  ;  work 
of,  472  ;  heat,  474  ;  hot  air,  475 

Equator,  68 1  ;  magnetic,  698 

Equilibrium  of  forces,  35  ;  of  floating 
bodies,  115  ;  of  heavy  bodies,  69  ;  of 
liquids,  106,  107  ;  mobile  of  tempera- 
ture, 414  ;  neutral,  70  ;  stable,  70  ; 
unstable,  70 

Equivalent,  electrochemical,  846  ;  en- 
dosmotic,  139  ;  conductor?,  955 

Escapement,  81  ;  wheel.  Si 

Ether,  429  ;  luminiferous,  499 

Eustachian  tube,  260 

Evaporation,  350  ;  causes  which  accele- 
rate it,  362  ;  cold  due  to,  373  ;  latent 
heat  of,  372 

Evaporation  and  ebullition,  364 

Exchanges,  theory  of,  415 

Exhaustion,  produced  by  air-pump,  203  ; 
by  Sprengel's  pump,  205 

Exosmose,  139 

Expanded  wave,  225 

Expansibility  of  gases,  147 

Expansion,  296  ;  apparent  and  real,  321  ; 
absolute,  of  mercury,  322  ;  apparent, 
of  mercury,  323  ;  of  liquids,  326  ;  of 
solids,  313  ;  of  gases,  331-333  ;  linear 
and  cubical,  coefficients  of,  313  ; 
measurement  of  linear,  314  ;  of  crystals, 
318;  applications  of,  319;  force  of, 

329 

Expansion  of  gases,  cold  produced  by, 
494  ;  problems  on,  332 

Expansive  force  of  ice,  346 

Experiment,  Berthollet's,  1 88  ;  Frank- 
lin's, 368  ;  Florentine,  97  ;  Pascal's, 
162  ;  Torricellian,  161 

Extension,  7,  9 

Extra  current,  907,  908  ;  direct,  908 ; 
inverse,  908 

Eye,  612  ;  accommodation  of,  620;  not 
achromatic,  628  ;  refractive  indices  of 
media  of,  613;  path  of  rays  in,  615; 
dimensions  of  various  parts  of,  614 

Eye-glass,  544,  630  ;  lens,  592  ;  piece, 
583>  590,  592  5  Campani's,  592 


TTAHRENHEIT'S  hydrometer,  123; 
Jr       scale,  303 
Falling  bodies,  laws  of,  76 


loiS 


Index. 


FAR 

Farad,  964 

Faraday's  experiments,  745  ;  wheel,  625  ; 
theory  of  induction,  747  ;  voltameter, 
846 

Favre  and  Silbermann's  calorimeter, 
463  ;  determination  of  heat  of  com- 
bustion, 483 

Fibres,  Corti's,  260 

Field  lens  and  glass,  592 

Field  magnets,  915 

Field  of  a  microscope,  591  ;  of  view, 
593  ;  magnetic,  707 

Figures,  Lichtenberg's,  772 

Filter-pump,  206 

Finder,  595 

Fire-engine,  219  ;  -places,  487  ;  -works, 
149 

Fish,  electrical,  971 

Fishes,  swimming  bladder  of,  117 

Fizeau's  experiments,  316,  507 

Flag  signals,  887 

Flame,  483 

Flask,  specific  gravity,  121 

Flattening  of  the  earth,  82 

Flexure,  elasticity  of,  90 

Float,  466 

Floating  bodies,  115 

Florentine  experiment,  13,  97 

Fluid,  4  ;  imponderable,  6  ;  elastic,  152  ; 
magnetic,  683 

Fluidity,  7 

Fluorescence,  582 

Flute,  280 

Fluxes,  340 

Fly-wheel,  467 

Focal  distance,  419 

Foci,  acoustic,  237  ;  magnetic,  701  ;  of 
convex  mirrors,  526  ;  in  double  convex 
lenses,  552 

Focus,  419,  525  ;  conjugate,  determina- 
tion of  the  principle,  527  ;  of  a  sphe- 
rical concave  mirror,  525,  552 

Focussing  the  microscope,  587,  591 

Fogs,  980 

Foot,  22 

Foot-pound,  59,  473 

Force,  26  ;  acceleration  of,  77  ;  centri- 
fugal, 53  ;  conservation  of,  65  ;  coer- 
cive, 687 ;  direction  of,  30 ;  elastic, 
of  gases,  152  ;  lines  of  magnetic,  707  ; 
of  expansion  and  contraction,  319; 
electromotive,  802,  814  ;  representation 
of,  30  ;  parallelogram  of,  33  ;  of  liquids, 
329  ;  portative,  719 

Foices,  6;  along  the  same  line,  31; 
equilibrium  of,  38  ;  impulsive,  60  ; 
magnetic,  708  ;  molecular,  83  ;  mo- 


GAS 
ments  of,  38  ;  polygon  of,  35  ;  triangle 

of,  35 

Formulae  for  expansion,  318  ;  barome- 
tric, 178  ;  for  sound,  231  ;  for  spheri- 
cal mirrors,  530,  531  ;  for  lenses,  559 

Fortin's  barometer,  166 

Foucault's  currents,  929  ;  determination 
of  velocity  of  light,  506  ;  experiment, 

834,  929 

Fountain  in  vacuo,  2IO  ;  at  Giggleswick, 
214  ;  intermittent,  212  ;  Hero's,  211 

Fovea  centralis,  612 

Franklin's  experiment,  368,  992;  plale, 
769  ;  theory  of  electricity,  728 

Fraunhofer's  lines,  574,  575 

Freezing,  apparatus  for,  374 

Freezing  mixtures,  347,  348  ;  point  in  a 
thermometer,  302 

French  weights  and  measures,  123 ; 
boiler,  466 

Fresnel's  experimentum  crucis,  645 ; 
rhomb,  671 

Friction,  26,  47  ;  heat  of,  477  ;  hydrau- 
lic, 146  ;  internal,  of  gases,  446  ;  de- 
velopment of  electricity  by,  720 

Friction  wheels,  77 

Frigorific  rays,  422 

Fringes,  646 

Frog,  rheoscopic,  968 

Frost,  987 

Frozen  mercury,  373,  380,  384 

Fulcrum,  44 

Fulgurites,  999 

Fulminating  pane,  769 

Furnace,  electrical,  821 

Fuse,  Abel's,  794 ;  Chatham,  829,  830 

Fusing  point,  338 

Fusion,  laws    of,    338  ;    vitreous,    338 
latent  heat  of,  461  ;  of  ice,  450 


ALILEAN  telescope,  597 
Galleries,  whispering,  237 

Gallium,  578 

Gallon,  125 

Galvani's  experiment,  797 

Galvanometer,  821  ;  differential,  821  ; 
Sir  W.  Thomson's,  822 

Galvanoscope,  821 

Galvano-thermometer,  830 

Gas  battery,  850  ;  engines,  476 

Gases,  absorption  of,  by  liquids,  189 ; 
by  solids,  193  ;  by  vapours,  435  ; 
application  of  Archimedes'  principle 
to,  195  ;  cold  produced  by  expansion 
of,  494;  compressibility  of,  154,  180; 
condensed,  193,  209  ;  conductivity  of, 


Index. 


1019 


GAS 

409 ;  diamagnetism  of,  937 ;  density 
of,  335-337  ;  dynamical  theory  of, 
293;  expansion  of,  153,  33 1- 334  ; 
endosmose  of,  190  ;  effusion,  191  ; 
transpiration  of,  192  ;  Gay-Lussac's 
method,  331  ;  index  of  refraction  of, 
550  ;  laws  of  mixture  of,  188 ;  and 
vapours,  mixtures  of,  383  ;  permanent, 
380 ;  problems  in,  332,  383 ;  lique- 
faction of,  380  ;  physical  properties  of, 
152  ;  pressure  exerted  by,  156  ;  radia- 
tion of,  441  ;  Regnault's  method,  336  ; 
specific  heat  of,  460 ;  velocity  of  sound 
in,  230,  231,  232  ;  viscosity  of,  446  ; 
weight  of,  155 

Gaseous  state,  4 

Gassiott's  battery,  815 

Gauge,  air-pump,  201  ;  rain,  983 

Gay-Lussac's  alcoholometer,  128  ;  baro- 
meter, 167  ;  determination  and  expan- 
sion of  gases,  331  ;  of  vapour-density, 
385  ;  stopcock,  382 

Geissler's  tubes,  205,  578,  925 

Generating  plate,  80 1 

Geographical  meridian,  691 

Geometrical  shadows,  503 

Giffard's  injector,  207 

Gilding  metal,  855 

Gimbals,  697 

Glacial  pole,  1009 

Glaciers,  991 

Glashiers  balloon  ascents,  196  ;  factors, 
398 

Glass,  compressed,  668  ;  expansion  of, 
325  ;  magnifying,  583  ;  object,  590 ; 
opera,  597  ;  unannealed,  668 

Glasses,  periscopic,  629  ;  weather,  174 

Globe  lightning,  997 

Glow,  electrical,  787  ;  worm,  635 

Glycerine  barometer,  176 

Gold-leaf  electroscope,  75 1 

Goldschmid's  aneroid,  182 

Goniometers,  534 

Good  conductors,  404 

Governor,  468 

Gradient,  barometric,  978 

Gramme,  24,  125 

Gramme's  magneto-electrical  machine, 
917 

Graphic  method,  DuhamePs,  245  ;  Fos- 
ter's, 831 

Graphite,  810 

Gratings,  647 

.Gravesand's  ring,  295 

Gravimetrical  density,  185 

Gravitation,  6,  82  ;  terrestrial,  67  ;  ac- 
celerative  effect  of,  27 


HEM 

Gravity,  battery,  812 
Gravity,  centre  of,  68 
Gregorian  telescope,  599 
Gridiron  pendulum,  320 
Grimaldi's  experiment,  645 
Grotthiiss'  hypothesis,  845 
Grove's  battery,  809  ;  gas,  850 
Guericke's  air-pump,  200 
Gulf  Stream,  1006 
Guthrie's  researches,  348 


HADLEY'S  reflecting  sextant,  521 
Hail,  989, 

Hair  hygrometer,  399 

Haldat's  apparatus,  101 

Hall's  experiment,  88 1 

Hallstrom's  experiments,  329 

Haloes,  627,  981 

Hammer,  279,  922 

Hardening,  90 

Hardness,  7  ;  scale  of,  93 

Hare's  deflagrator,  805,  829,   830 

Harmonicon,  chemical,  278 

Harmonics^  254,  273 

Harmonic  triad,  247  ;  grave,  263 

Harp,  281 

Harris's  unit  jar,  778 

Heat,  292  ;  animal,  485  ;  absorption  of, 
by  vapours,  &c.,  435,  439;  atomic, 
458  ;  conduction  of,  403  ;  diffusion  of, 
437 ;  developed  by  induction,  929  ; 
dynamical  theory  of,  429  ;  hypothesis 
on,  292  ;  influence  of  the  nature  of, 
435  ;  latent,  341  ;  mechanical  equi- 
valent of,  497  ;  polarisation  of,  679  ; 
produced  by  absorption  and  imbibi- 
tion, 482  ;  radiated,  403 ;  radiant, 
411,  44612;  reflection  of,  ^.18;  scat- 
tered, 424;  sources  of,  477-496; 
specific,  448,  454-460;  transmission 
of,  403  ;  terrestrial,  481 

Heaters,  466 

Heating,  486  ;  by  steam,  490 ;  by  hot 
air,  491  ;  by  hot  water,  492 

Height  of  barometer,  165  ;  variations 
in,  171 

Heights  of  places,  determination  of,  by 
barometer,  178,  179;  by  boiling  point, 

369 

Heliogiaph,  523 

Heliostat,  534 

Helix,  45,  882 

Helmholtz's  analysis  of  sound,  255  ;  re- 
searches, 258 

Hemihedral  crystal,  732 

Hemispheres,  Magdeburg,  160 


1020 


Index. 


HEN 

Henley's  electrometer,  756  ;  discharger, 
792 

Henry's  experiment,  909 

Herepath's  salt,  656 

Hero's  fountain,  21 1 

Herschelian  rays,  430  ;  telescope,  601 

Hirn's  experiments,  474 

Hoar-frost,  987 

Hofmann's  density  of  vapours,  387 

Holmes's  magneto-electrical  machine,  913 

Holtz's  electrical  machine,  759 

Homogeneous  light,  572  ;  medium,  502 

Hope's  experiments,  330 

Horizontal  line,  67  ;  plane,  67 

Horse-power,  472 

Hot-air  engines,  475,  491 

HotnesSj  297 

Hot- water,  heating  by,  492 

Hour,  21 

Howard's  nomenclature  of  clouds,  981 

Hughes's  microphone,  931  ;  induction 
balance,  932 

Humour,  aqueous,  612 

Huyghen's  barometer,  177 

Hyaloid  membrane,  612 

Hydraulic  press,  108  ;  engine,  151  ;  fric- 
tion, 146;  ram,  150;  tourniquet,  149 

Hydraulics,  95 

Hydrodynamics  141 

Hydro-electric  machine,  758  ;   currents, 

939 

Hydrometers,  119;  Nicholson's,  120; 
Fahrenheit's,  123  ;  with  variable 
volume,  126;  Beaume's,  127;  of  con- 
stant volume,  126  ;  specific  gravities, 
1 19  ;  uses  of  tabler,  of,  125 

Hydrostatic  bellows,  101 ;  paradox,  103  ; 
balance,  120 

Hydrostatics,  95-98 

Hygrometers,  393  ;  of  absorption,  399  ; 
chemical,  394 ;  condensing,  395  ; 
DanielPs,  396  ;  wet-bulb,  398;  Mason's, 
398  ;  Regnault's,  397 

Hygrometric  stale,  392  ;  substances,  391 

Hygrometry,  391  ;  problem  on,  401 

Hygroscope,  399 

Hypothesis,  5 

Hypsometer,  369 


ICE,  990  ;  method  of  fusion  of,  450 
Ice    calorimeter,    450  ;     Bunsen's, 
451  ;  expansive   force    of,    346 ;    ma- 
chine, 494 
Iceland  spar,  659 
Idioelectrics,  724 
Image  and  object,  magnitudes  of,  561 


INT 

Images,  accidental,  626  ;  condition  of 
distinctness  of,  587  ;  formation  of,  in 
concave  mirrors,  528  ;  in  convex  mir- 
rors, 529  ;  in  plane  mirrors,  513  ;  of 
multiple,  516;  magnitude  of,  532; 
produced  by  small  apertures,  504 ; 
virtual  and  real,  514  ;  inversion  of,  616 

Imbibition,  193  ;  heat  produced  by,  482 

Impenetrability,  7 

Imperial  British  yard,  22 

Imponderable  matter,  6 

Impulsive  forces,  57 

Incandescent  lamps,  838 

Inch,  125 

Incident  ray,  536 

Inclination,  708  ;  compass,  698 

Inclined  plane,  43  ;  motion  on,  50 

Index  of  refraction,  538  ;  measurement 
of,  in  solids,  548  ;  in  liquids,  549 ;  in 
gases,  550 

Indicator,  473,  886,  888,  889 

Indices,  refractive,  table  of,  550 

Indium,  57'^ 

Induced  currents,  900-911 

Induction,  apparatus  founded  on,  911  ; 
balance,  932  ;  by  the  earth,  905  ;  by 
currents,  900  ;  of  a  current  on  itself, 
907  ;  electrical.  744 ;  in  telegraph 
cables,  891  ;  limit  to,  746;  Faraday's 
theory  of,  747  ;  heat  developed  by, 
929;  by  magnets,  904;  magnetic,  686; 
vertical,  715 

Inductive  capacity,  specific,  748 

Inductori  um,  921 

Inelastic  bodies,  58 

Inertia,  19  ;  applications  of,  20 

Influence,  magnetic,  686 ;  electrical,  744 

Ingenhaus's  experiment,  404 

Injector,  Giffard's,  207 

Insects,  sounds  produced  by,  242 

Insolation,  635,  636 

Instruments,  optical,  585 ;  polarising, 
656;  mouth,  271;  reed,  272; 
stringed,  279  ;  wind,  270,  280 

Insulating  bodies,  726  ;  stool,  762 

Insulators,  725 

Intensity  of  the  current,  825  ;  of  the 
electric  light,  837  ;  illumination,  508  ; 
of  reflected  light,  519;  of  a  musical 
tone,  246  ;  of  radiant  heat,  414  ;  of 
sound,  causes  which  influence,  226  ; 
of  terrestrial  magnetism,  701  ;  of  ter- 
restrial gravity,  82 

Interference  of  light,  645;  of  sound,  261 
Intermittent  fountain,  212;  springs,  214  ; 

syphon,  214 
Interpolar,  825 


Index. 


1 02 1 


INT 

Intervals,  musical,  247 

Intrapolar  region,  828 

Inversion  of  images,  616 

lones,  842 

Iris,  612 

Iron,    passive   state   of,    851  ;    electrical 

deposition  of,  857 
Iron  ships,  magnetism  of,  7J5 
Irradiation,  627 
Irregular  reflection,  518 
Isobars,  979 
Isochimenal  line,  1007 
Isoclinic  lines,  698 
Isodynamic  lines,  701 
Isogeothermic  lines,  1007 
Isogonic  lines,  692 
Isotheral  lines,  1007 
Isothermal  lines,  1007  ;  zone,  1007 


JABLOCHKOFF  candle,  838 
Jacobi's  unit,  846,  952 
Jar,  Leyden,  770-780 
Jar,  luminous,  785  ;  Harris's  unit,  778 
Jet,  lateral,   143  ;  height  of,   144 ;  form 

of,  148 

Jolly's  spring  balance,  88 
Jordan's  barometer,  176 
Joule's  experiment  on  heat   and    work, 

497  ;  equivalent,  497 
Jupiter,  505 
Jurin's  laws  of  capillarity,  132 


r^ALEIDOPHONE,  625 

|N^      Ka'eidoscope,  516 
Kamsin,  977 
Kater's  pendulum,  82 
Kathelectrotonus,  828 
Kathode,  842 
Katione,  842 
Keepers,  718 

Kerr's  electro-optical  experiments,  937 
Key,  887,  906,  912,  922  ;  note,  249 
Kienmayer's  amalgam,  754 
Kilogramme,  24,  125 
Kilogrammetre,  473 
Kinetic  energy,  62 
Kinnersley's  thermometer,  792 
Kirk's  ice  machine,  494 
Knife-edge,  71 
Konig's    apparatus,    256 ;     manometric 

flames,  288 

Kravogl's  machine,  899 
Kiilp's  method  of  compensation,  719 
Kundt's  velocity  of  sound,  277 


LIG 

LABYRINTH  of  the  ear,  260 
Lactometer,  129 

Ladd's  dynamo-electrical  machine,  916 

Lambert's  method,  570 

Lamps,  incandescent,  836 

Land  and  water,  101 1 

Lane's  electrometer,  777 

Lantern,  magic,  604 

Laplace's  barometric  formula,  178 

Laryngoscope,  563 

Larynx,  259 

Latent  heat,  341  ;  of  fusion,  461  ;  of 
vapours,  372,  462 

Lateral  jet,  143 

Latitude,  influence  on  the  air,  1005  ; 
parallel  of,  82 

Lavoisier  and  Laplace's  calorimeter,  450  ; 
method  of  determining  linear  expan- 
sion, 314 

Law,  5  • 

Laws  of  mixture  of  gases  and  liquids,  383 

Lead  tree,  853 

Leclanche's  elements,  813,  814 

Ledger  lines,  252 

Leidenfrost's  phenomenon,  385 

Lemniscate,  667 

Length,  unit  of,  22  ;  of  undulation,  225 

Lens,  axis  of,  551 

Lenses,  551-559  ;  achromatic,  582  ; 
aplanatic,  558  ;  centres  of  curvature, 
551  ;  combination  of,  560  ;  echelon, 
607  ;  foci  in  double  convex,  552  ;  in 
double  concave,  553  ;  formation  of 
images  in  double  convex,  556  ;  in 
double  concave,  557  ;  formulae  relat- 
ing to,  559  ;  lighthouse,  607  ;  optical 
centre,  secondary  axis  of,  555 

Lenz's  law,  901 

Leslie's  cube,  423 ;  experiment,  373  ; 
thermometer,  308 

Level,  water,  109;  spirit,  no 

Level  surface,  67 

Levelling  staff,  109 

Lever,  40 

Leyden  discharge,  inductive  action  of,  903 

Leyden  jars,  770-780  ;  charged  by 
Ruhmkorffs  coil,  923  ;  potential  of, 
782  ;  work  by,  784 

Lichtenberg's  figures,  772 

Liebig's  condenser,  377 

Ligament,  suspensory,- 612 

Light,  499  ;  diffraction  of,  646  ;  homo- 
geneous, 569,  572  ;  intensity  of,  508  ; 
interference  of,  645  ;  laws  of  reflection 
of,  511  ;  medium,  502  ;  oxyhydrogen, 
606  ;  polarisation  of,  652  ;  relative 
intensities  of,  510;  sources  of,  634; 


1022 


Index. 


LIG 

theory   of  polarised    light,    66 1  ;    un- 
dulatory  theory  of,  499,  637  ;  velocity 

of,  5°5-5°7 
Lighthouse  lenses,  607 
Lighting,  electric,  838 
Lightning,  999  ;  ascending,  997  ;  effects 

of,  997  ;  conductor,  1001  ;  globe,  999 ; 

heat,  997  ;  brush,  997  j  flashes,  997  ; 

zigzag,  997 
Limit,  magnetic,  720;  to  induction,  746; 

of  perceptible  sounds,  244 
Line,  aclinic,  698  ;  of  collimation,  595  ; 

isoclinic,  698  ;  agonic,  692  ;  isogonic, 

692 ;     isodynamic,      701  ;     of    sight, 

595 
Linear    expansion,    coefficients    of,    313, 

315 

Lines  of  magnetic  force,  707 

Lippmann's  capillary  electrometer, 
840 

Liquefaction  of  gases,  380,  381  ;  of 
vapours,  375 

Liquids,  99  ;  active  and  inactive,  667  ; 
buoyancy  of,  100  ;  compressibility  of, 
97  ;  conductivity  of,  407  ;  calculation 
of  density  of,  107  ;  diffusion  of,  140  ; 
diamagnetism  of,  938  ;  expansion  of, 
321  ;  equilibrium  of,  104  ;  manner  in 
which  they  are  heated,  408  ;  pressure 
on  sides  ot  vessel,  102  ;  refraction  of, 
549  ;  rotatory  power  of,  676  ;  sphe- 
roidal form  of,  84  ;  spheroidal  state  of, 
385  ;  specific  heat  of,  456  ;  volatile 
and  fixed,  349;  tensions  of  vapours  of, 
359  ;  of  mixed  liquids,  360 

Lissajous's  experiments,  284-286 

Lithium,  578 

Litre,  24,  125 

Local  action,  806  ;  attraction,  7155  bat- 
tery, 889  ;  currents,  816 

Locatelli's  lamp,  428 

Locomotives,  470,  471 

Lodestone,  680 

Long  sight,  629 

Loops  and  nodes,  269 

Loss  of  electricity,  743  ;  of  weight  in  air, 
correction  for,  402 

Loud  ness  of  a  musical  tone,  246 

Luminiferous  ether,  499 

Luminous  bodies,  500 ;  effects  of  the 
electric  discharge,  773,  833  ;  of  the 
electric  current,  923  ;  of  Ruhmkorff's 
coil,  923  ;  jar,  790  ;  meteors,  993  ; 
paint,  636  ;  pane,  789  ;  pencil,  501  ; 
ray,  501  ;  tube,  789 ;  square,  and 
bottle,  789 

Luminous  radiation,  432 ;  heat,  434 


MAN 

MACHINE,  Atwood's,  77  ;  elec- 
trical, 752-760;  Von  Ebner's, 
794  ;  electro-magnetic,  886 

Mackerel-sky,  981 

Magazine,  717 

Magdeburg  hemispheres,  1 60 

Magic  lantern,  604 

Magnetic  attractions  and  repulsions,  702  ; 
battery,  717;  couple,  690;  curves, 
706 ;  declination,  691  ;  dip,  698 ; 
effects  of  the  electrical  discharge,  791  ; 
equator,  698  ;  field,  707,  963  ;  fluids, 
683  ;  induction,  686  ;  influence,  686  ; 
limit,  720;  meridian,  691;  needle, 
691,  692  ;  oscillations  of,  705  ;  obser- 
vatories, 702  ;  poles,  698  ;  saturation, 
716  ;  storms,  694 

Magnetisation,  710  ;  by  the  action  of  the 
earth,  714;  by  currents,  882;  single 
touch,  711 

Magnetism,  6,  700  ;  determination  of, 
in  absolute  pressure,  709  ;  earth's,  701  ; 
of  iron  ships,  715  ;  Ampere's  theory 
of,  879  ;  remanent,  883  ;  theory  of, 
683  ;  terrestrial  distribution  of  free, 
721 

Magneto  and  dynamo-electrical  machines, 
918-920 

Magneto-electrical  apparatus,  911  ; 
Gramme's,  917  ;  machines,  913-916 

Magnetometer,  949 

Magnets,  artificial  and  natural,  680 ; 
broken,  685  ;  action  of  earth  on,  689  ; 
equator  of,  68 1 ;  floating,  722  ;  heat 
developed  by,  929  ;  meter,  949  ;  north 
and  south  poles  of,  682  ;  portative  force 
of,  719  ;  saturation  of,  716  ;  influence 
of  heat,  720  ;  induction  by,  904  ;  in- 
ductive action  on  moving  bodies,  905  ; 
action  on  currents,  867  ;  on  solenoids, 
877  ;  rotation  of  induced  currents  by, 
928 ;  optical  effects  of,  935  ;  total  action 
of  two,  708 

Magnification,  linear  and  superficial,  88  ; 
measure  of,  589  ;  of  a  telescope,  55,  64 

Magnifying  power,  594 

Magnitude,  9  ;  apparent,  of  an  object, 
588  ;  of  images  in  mirrors,  587 

Major  chord,  247  ;  triads,  248 

Malleability,  859 

Mance's  heliograph,  523  ;  method,  957 

Manganese,  magnetic  limit  of,  720 

Manhole,  466 

Manipulator,  888 

Manometer,  97,  183  ;  open-air,  183  ; 
with  compressed  air,  184  ;  Regnault's 
barometric,  186 


Index. 


1023 


MAN 

Manometric  flames,  288 

Mares'  tails,  981 

Marie-Davy  battery,  812 

Marine  barometer,    165 ;    galvanometer, 

822 

Mariner's  card,  975  ;  compass,  697 
Mariotte  and  Boyle's  law,  1 80 
Mariotte's  tube,  180 
Marloye's  harp,  281 
Maskelyne's  experiment,  67 
Mason's  hygrometer,  398 
Mass,  measure  of,  23  ;  unit  of,  23 
Matter,  2 

Matteucci's  experiment,  903 
Matthiessen's  thermometer,  308  ;  table  of 

electromotive   forces,    940 ;    electrical 

conductivity,  958 
Maxim's  lamp,  838 
Maximum  current,  conditions  of,  826 
Maximum  and  minimum  thermometers, 

310  ;  of  tension,  755 
Maxwell's  electromagnetic  theory  of  light, 

748,  965  ;  colour  discs,  570 
Mayer's  floating  magnets,  722 
Mean  temperature,  1004 
Measure  of  force,  29  ;  of  work,  60 
Measure  of  magnification,   589,  594  ;  of 

mass,  23  ;  of  space,  22  ;  of  time,  21  ; 

of  velocity,  25 

Measurement  of  small  angles  by  reflec- 
tion, 522 
Mechanical    equivalent    of    heat,    497 ; 

effects    of    electrical   discharge,    792 ; 

battery,  839 
Melloni's   researches,    429 ;    thermomul- 

tiplier,  412,  946 
Melting  point,  influence  of  pressure  on, 

339 

Membranes,  vibrations  of,  283 

Memoria  technica,  820 

Meniscus,  132  ;  convex,  131  ;  in  baro- 
meter, 169  ;  Sagitta  of,  169 

Menotti's  battery,  812 

Mercury,  frozen,  373,  381,  384  ;  pendu- 
lum, 320 ;  coefficient  of  expansion, 
323  ;  expansion  of,  322  ;  pump,  208 

Meridian.  21  ;  geographical  and  mag- 
netic, 691 

Metacentre,  115 

Metal,  Rose's  and  Wood's  fusible,  340 

Metals,  conductivity  of,  955 

Meteoric  stones,  480 

Meteorograph,  974 

Meteorology,  973 

Meteors,  aerial,  964 

Metre,  22,  125 

Mica,  664 


MOU 

Microfarad,  964 

Micrometre  lines,  594  ;  screw,  1 1 

Microphone,  931 

Microscope,  12  ;  achromatism  of,  592  ; 
Duboscq's,  606  ;  compound,  591  ;  field 
of,  591  ;  focussing,  587  ;  magnifying 
powers  of,  594  ;  photo-electric,  606  ; 
simple,  586  ;  solar,  605 

Microspectroscope,  580 

Mill,  Barker's,  194 

Milliampere,  964 

Millimetre,  125 

Mineral  waters,  1000 

Mines,  firing  by  electricity,  795,  829 

Minimum  thermometer,  310  ;  deviation, 
547 

Minor  chord,  247 

Minotto's  battery,  812 

Minute,  21 

Mirage,  541 

Mirrors,  512  ;  applications  of,  534;  burn- 
ing, 420;  concave,  419,  528;  conju- 
gate, 420;  convex,  526-529;  glass, 
515;  parabolic,  535;  rotating,  520, 
795  ;  spherical,  524 

Mists,  980 

Mixture  of  gases,  188;  of  gases  and 
liquids,  189  ;  laws  of,  383 

Mixtures,  freezing,  347  ;  method  of,  452 

Mobile  equilibrium,  415 

Mobility,  7,  18 

Modulus  of  elasticity,  88 

Moisture  of  the  atmosphere,  400 

Molecular  forces,  3  ;  attraction,  83  ; 
state  of  bodies,  4;  velocity,  294 

Molecular  state,  relation  of  absorption  to, 

443 

Molecules,  3 

Moments  of  forces,  38 

Momentum,  28 

Monochord,  266 

Monochromatic  light,  569 

Monosyllabic  echo,  237 

Montgolfier's  balloon,  196;  ram,  150    • 

Moon,  510 

Morgagni's  humour,  610 

Morin's  apparatus,  78 

Morren's  mercury  pump,  208 

Morse's  telegraph,  889 

Moser's  images,  193 

Motion,  18;  on  an  inclined  plane,  50; 
curvilinear,  25  ;  in  a  circle,  53,  54 ; 
rectilinear,  25 ;  resistance  to,  in  a 
fluid,  48  ;  uniformly  accelerated  rec- 
tilinear, 48 ;  quantity  of,  29 ;  of  a 
pendulum,  55;  of  projectile,  51 

Mouth  instrument,  271 


IO24 


Index. 


MUL 

Multiple  battery,  826 

Multiple  echoes,  237  ;  images  formed  by 
mirrors,  515,  516,  517 

Multiplier,  821 

Muscular  currents,  966,  967,  968 

Music,  220;  physical  theory  of,  246- 
264 

Musical  boxes,  279  ;  comma,  248  ; 
intervals,  247  ;  scale,  248  ;  tempera- 
ment, 250  ;  tones,  properties  of,  246  , 
intensity,  notation,  252 ;  pitch  and 
timbre,  246  ;  sound,  223 ;  range,  252 

Myopy,  619,  629 

~\  I  AIRNE'S  electrical  machine,  757 

1\      Nascent  state,  85 

Natterer's  apparatus,  381 

Natural  magnets,  680 

Naumann's  law,  458 

Needle,    declination   of,    691  ;    dipping, 

698  ;  astatic,  700 ;  magnetic,  691 
Negative  plate,  80 1 
Negatives  on  glass,  609 
Nerve-currents,  970 
Neutral     line,     744 ;     equilibrium,     70 ; 

point,  744  ;  temperature,  940 
Newtonian  telescope,  600 
Newton's  disc,  567  ;  law  of  cooling,  416 

rings,  650,  651  ;  theory  of  light,  568 
Niaudet's  element,  812 
Nicholson's  hydrometer,  120 
Nickel,    electrical    deposition    of,    857 ; 

magnetic  limit  of,  720 
Nicol's  prism,  660 
Nimbus,  981 
Nobili's  battery,  943  ;  rings,   852  ;  ther- 

momultipliers,     945  ;    thermo-electric 

pile,  428,  431,  943 
Nocturnal  radiation,  495 
Nodal  points,  271,  645 
Nodes  and  loops,  269  ;  of  an  organ  pipe, 

274  ;  explanation  ot,  276 
Noises,  221 
Nonconductors,  725 
Norremberg's  apparatus,  657 
Northern  light,  1003 
Norwegian  stove,  410 
Notation,  musical,  252 
Notes  in  music,  247  ;  musical,  of  women 

and  boys,  259  ;  wave-length  of,  253 
Nut  of  a  screw,  45 


OBJECT-glass,  590 
Objective,  590 
Obscure     radiation,     432 ; 
transmutation  of,  433 


rays,    433; 


PEN 

I    Observatories,   magnetic,  702 

Occlusion  of  gases^  194 
1    Occultation,  505 

Octave,  249 

•    Oersted's  experiment,  820 
j    Ohms,  987 

Ohm's  law,  825 

Opaque  bodies,  500 

Opera-glasses,  597 

Ophthalmoscope,  633 

Optic  axis,  617  ;  axis  of  biaxial  crystals, 
644;  angle,  607;  nerve,  612 

Optical  centre,  555  ;  effects  of  magnets, 
926  ;  instruments,  585  ;  electrical  ex- 
periments, 937 

Optics,  499 

Optometer,  619 

Organ  pipes,  274 ;  nodes  and  loops  of,  274 

Orrery,  electrical,  764 

Oscillations,  55;  axis  of,  79;  method  of, 
705 

Oscillating  discharges,  783 

Otto's  gas  engine,  476 

Otto  von  Guericke's  air-pump,  200 

Outcrop,  in 

Overshot  wheels,  150 

Oxyhydrogen  light,  606 

Ozone,  793,  999 


PACINOTTI'S  ring,  917 
Paint,  luminous,  6^6 

Pallet,  Si 

Pane,  fulminating,  769  ;  luminous,  790 

Papin's  digester,  371 

Parabolic  mirrors,  535  ;  curve,  60,  143 

Parachute,  198 

Paradox,  hydrostatic,  103 

Parallel    of    latitude,     82  ;    forces,     36 
centre  of,  27 

Parallel  rays,  501 

Parallelogram  of  forces,  33 

Paramagnetic  bodies,  938 

Partial  current,  961 

Pascal's  law  of  equality  of  pressures,  98 ; 
experiments,  162 

Passage  tint,  677 

Passive  state  of  iron,  851 

Pedal,  279 

Peltier's  cross,  950  ;  effect,  950 

Pendulum,  55  •  Application  to  clocks, 
8 1  ;  ballistic,  8 1  ;  compensation,  320; 
electrical,  724  ;  gridiron,  320 ;  mer- 
curial, 320  ;  length  of  compound,  79  ; 
reversible,  79  j  verification  of  laws  of, 
80 

Penumbra,  503 


Index. 


1025 


PER 

Percussion,  heat  due  to,  479 

Periscopic  glasses,  629 

Permanent  gases,  380 

Persistence  of  impression  on  the  retina, 
625 

Perspective,  aerial,  618 

Perturbations,  magnetic,  692,  693 

Phenakistoscope,  625 

Phenomenon,  5 

Phial  of  four  elements,  106 

Phonautograph,  287 

Phonograph,  Edison's,  291 

Phosphorescence,  635,  636 

Phosphorogenic  rays,  573 

Phosphoroscope,  636 

Photo-electric  microscope,  606 

Photogenic  apparatus,  606 

Photographs  on  paper,  609 ;  on  albu- 
menised  paper  and  glass,  611 

Photography,  608-611 

Photometers,  509,  511 

Photophone,  936 

Physical  phenomena,  5  ;  agents,  6 ; 
properties  of  gases,  152;  shadows.  503  j 

Physics,  object  of,  I 

Physiological  effects  of  the  electric  dis- 
charge, 785  ;  of  the  current,  827  ;  of 
Ruhmkorffs  coil,  923 

Piezometer,  97        *+ 

Pigment  colours,  570 

Pile,  voltaic,  804-818 

Pipes,  organ,  274 

Pisa,  tower  of,  69 

Pistol,  electric,  793 

Piston  of  air-pump,  2OO  ;  rod,  467 

Pitch,  concert,  251;  of  a  note,  246 ; 
a  screw,  45 

Plane,  45  ;  electrical  inclined,  764 ; 
mirrors,  513  ;  wave,  642 

Plante's  secondary  battery,  849 

Plants,  absorption  in,  193 

Plate  electrical  machine,  753 

Plates,  colours  of  thin,  650  ;  vibrations  I 
of,  282 

Plumb  line,  67 

Pluviometer,  983 

Pneumatic  syringe,  154,  479 

Poggendorffs  law,  793 

Point,  boiling,  366,  367 

Points,  action  of,  742;  nodal,  271,  645 

Poisseuille's  apparatus,  147 

Poisson's  coefficient,  88 

Polar  aurora,  1003 

Polarisation,  848 ;  angle  of,  654  ;  cur- 
rent, 848 ;  of  electrodes,  806 ;  by 
double  refraction,  652  ;  by  reflection, 
653  5  ky  single  refraction,  655  ;  ellip- 


PRO 

tical  and  circular,  669,  670,  672  ;  of 
heat,  679 ;  galvanic,  806,  848  ;  light, 
652  ;  of  the  electric  medium,  747  ; 
plane  of,  654  ;  plate,  804 ;  rotatory, 
674 

Polarised  light,  theory  of,  66 1  ;  colours 
produced  by  the  interference  of,  662, 
668  ;  rays,  662 

Polariser,  656 

Polarising  instruments,  656 

Polarity,  806  ;  boreal,  austral,  689 

Pole,  glacial,  997 

Poles,  803 ;  analogous  and  antilogous, 
842  ;  electric,  732  ;  of  the  earth,  698  ; 
magnetic,  698  ;  of  a  magnet,  681 ; 
mutual  action  of,  682  ;  precise  defini- 
tion of,  684  ;  austral  and  boreal,  689 

Polygon  of  forces,  35 

Polyprism,  544 

Ponderable  matter,  6 

Pores,  13 

Porosity,  7,  13  ;  application  of,  15 

Portative  force,  719 

Positive  plate,  80 1  ;  crystals,  643 

Positives  on  glass,  610 

Postal  battery,  889 

Potential  energy,  62  ;  of  electricity,  738  ; 
of  a  Leyden  jar,  782  ;  of  a  sphere,  741 

Pound,  125  ;  avoirdupois,  23,  29  ;  foot, 

59 

Powders,  radiation  from,  443 

Power  of  a  lever,  40 ;  of  a  microscope, 
594;  of  points,  742 

Presbytism,  619,  629 

Press,  hydraulic,  108 

Pressure,  centre  of,  102  ;  on  a  body  in  a 
liquid,  112;  atmospheric,  158  ;  amount 
of,  on  human  body,  163  ;  experiment 
illustrating,  210;  influence  on  melting 
point,  339 ;  heat  produced  by,  479  ; 
electricity  produced  by,  731 

Pressures,  equality  of,  98  ;  vertical  down- 
ward, 99  ;  vertical  upward,  100 ;  in- 
dependent of  form  of  vessel,  101  ;  on 
the  sides  of  vessels,  102 

Prevost's  theory,  415 

Primary  coil,  893 

Primitive  current,  961 

Principal  current,  961 

Principle  of  Archimedes,  113 

Prisms,  543-547 ;  double  refracting,  659  ; 
Nicol's,  660  ;  with  variable  angle,  544 

Problems  on  expansion  of  gases,  332  ; 
on  mixtures  of  gases  and  vapours,  384 ; 
on  hygrometry,  401 

Projectile,  motion  of,  51 

Proof  plane,  735 

3U 


1026 


Index. 


PRO 

Propagation  of  light,  502 

Protoplasm,  827 

Protuberances,  579 

Pulley,  41, 

Pump,  air,  200  ;  condensing,  209  ;  filter, 

206 
Pumps,  different  kinds  of,  215  ;  suction, 

216  ;  suction  and  force,  217 
Punctum  caecum,  612 
Pupil,  612 

Psychrometer,  398,  974 
Pyroelectricity,  732 
Pyroheliometer,  480 
Pyrometers,  311  ;  electric,  949 


U  ADR  ANTAL  deviation,  715 
Quadrant  electrometer,  756 


RADIANT  heat,  411  ;  detection  and  j 
measurement     of,     412 ;     causes   | 
which   modify  the   intensity   of,  414 ; 
Alelloni's  researches  on,  428  ;  relation 
of  gases  and  vapours  to,  438 ;  relation 
to  sound,  4460; 

Radiated  heat,  403,  411 

Radiating  power,   425  ;  identity   of  ab-   j 
sorbing    and    radiating,    426 ;    causes 
which  modify,  &c.,  427  ;  of  gases,  441 

Radiation,  cold  produced  by,  495  ;  from    : 
powders,  443  ;  of  gases,  luminous,  and   | 
obscure,    432  ;   laws   of,    413 ;    solar, 
480 

Radiative  power,  985 

Radiometer,  445 

Railway,  electrical,  917 

Rain,  983;  clouds,  983;  bow,  1002;  fall,  : 
974,  983  ;  gauge,  983  ;  drop,  velocity  : 
of,  48 

Ram,  hydraulic,  150;  powder,  479 

Ramsclen's  electrical  machine,  753 

Rarefaction  in  air-pump,  200  ;  by  Spren- 
gel's  pump,  205 

Ray,     incident,     536 ;    luminous,     501  ; 
ordinary  and  extraordinary,  641 

Rays,    actinic,    or   Ritteric,    433 ;  diver- 
gent   and   convergent,  501  ;  frigorific, 
422;  of  heat,  411,  429  ;  Herschelian, 
430 ;    invisible,    429 ;    obscure,    433  ;   i 
path  of,  in  eye,  615;  phosphorogenic,    | 
573  >  polarised,  662  ;  transmutation  of 
thermal,  434 

Reaction  and  action,  39 

Real  volume*,  14  ;  foci,  552  ;  focus,  525  ; 
image,  528,  556 

Reaumur  scale,  303 


RHE 

Receiver  of  air-pump,  200 

Recomposition  of  white  light,  567 

Reed  instruments,  272 

Reeds,  free  and  beating,  272 

Reflected  light,  intensity  of,  519 

Reflecting  power,  423 ;  goniometer, 
534;  sextant,  521;  stereoscope,  623; 
telescope,  598 

Reflection,  apparent,  of  cold,  422  ;  of 
heat,  418  ;  from  concave  mirrors,  419  ; 
irregular,  518  ;  laws  of,  417  ;  verifi- 
cation of  laws  of,  420 ;  in  a  vacuum, 
421  ;  of  light,  511-541  ;  of  sound, 
236 

Refracting  crystals,  639,  652,  663 ;  stereo- 
scope, 624  ;  telescope,  598 

Refraction,  536-545  ;  double,  639 ;  po- 
larisation by,  652  ;  explanation  of 
single,  638  ;  of  sound,  238 

Refractive  index,  538  ;  determination  of, 
562  ;  of  gases,  550  ;  of  liquids,  549  ; 
of  solids,  548  ;  table  of,  550 ;  indices 
of  media  of  eye,  613 

Refractory  substances,  338 

Refrangibility  of  light,  alteration  of,  582 

Regelation,  990 

Regnault's  experiments,  229  ;  determi- 
nation of  density  of  gases,  336  ;  mano- 
meter, 1 86  ;  metl^ls  of  determining 
the  expansion  of  gases,  333  ;  of  specific 
heat,  454 ;  of  tension  of  aqueous  va- 
pour, 356,  358  ;  hygrometer,  397 

Regnier's  electric  lamp,  838 

Regulator  of  the  electric  light,  835,  836 

Reis's  telephone,  885 

Relay,  889 

Remanent  magnetism,  883 

Repulsions,  magnetic,  705  ;  electrical 
laws  of,  731 

Reservoir,  common,  726 

Residual  charge,  748,  773 

Residue,  electric,  773 

Resilience,  773 

Resinous  electricity,  727,  728 

Resistance  of  a  conductor,  825  ;  of  an 
element,  957 

Resonance,  237  ;  box,  251  ;  globe,  255 

Rest,  1 8 

Resultant  of  forces,  32-34 

Retina,  612  ;  persistence  of  impression 
on,  625 

Return  shock,  1000 

Reversible  pendulum,  79 

Reversion,  method  of,  696 ;  spectroscope, 

577 

Rheometer,  821 
Rheoscope,  821 


Index. 


1027 


RHE 


SOL 


Rheoscopic  frog,  968 

Rheostat,  951 

Rhomb,  Fresnel's,  671 

Rhumbs,  697,  975 

Right  ascension,  600 

Rime,  987 

Ring  inductor,  919 

Rings,  coloured,  666  ;  Gravesand's,  295  ; 

in  biaxial  crystals,  667  ;  Newton's,  650, 

651  ;  Nobili's,  852 
Ritchie's  experiment,  426 
Ritteric  rays,  433 
Robinson's  anemometer,  974 
Rock    salt,    heat    transmitted    through, 

437 

Rods,  vibrations  of.  281 

Roget's  vibrating  spiral,  859 

Rose's  fusible  metal,  340 

Rotary  engine,  471 

Rotating  mirror,  520,  795 

Rotation,  electrodynamic  and  electro- 
magnetic, of  liquids,  869  ;  winds,  978 

Rotation  of  the  earth,  80 ;  of  magnets 
by  currents,  912  ;  of  currents  by  mag- 
nets, 868 ;  of  induced  currents  by 
magnets,  928 

Rotatory  power  of  liquids,  676  ;  polari- 
sation, 673,  674;  coloration  produced 
by,  675 

Rousseau's  densimeter,  130 

Roy  and  Ramsden's  measurement  of 
linear  expansion,  361 

Rubbers,  753 

Rubidium,  578 

Ruhlmann's  barometric  and  thermome- 
tric  observations,  179 

Ruhmkorffs  coil,  921  ;  effects  produced 
by,  923 

Rumford's  photometer,  509 

Rutherford's  thermometers,  310 


QACCHARIMETER,  677 

x^     Saccharometer,  126 

Safety-catch,  829  ;  tube,  379  ;  valve,  108, 

371  ;  whistle,  466 
Sagitta  of  meniscus,  169 
Salimeters,  129 
Salts,  decomposition  of,  843 
Saturation,    degree  of,    392 ;    magnetic, 

716;  of  colours,  570 
Saussure's  hygrometer,  399 
Savart's  toothed  wheel,  241 
Scale  of  hardness,  93 
Scales  in   music,  248  ;  chromatic,   250  ; 

of  a  thermometer,  303  ;  conversion  of, 

into  one  another,  303 


Scattered  heat,  424;  light,  518 

Schehallien  experiment,  67 

Scheiner's  experiment,  619 

Schwendler's  platinum  light  standard, 
838 

Scintillation  of  stars,  541 

Sciopticon,  604 

Sclerotica,  612 

Scott's  phonautograph,  287 

Scraping  sound,  281 

Scratching  sound,  281 

Screw,  II,  45 

Secchi's  meteorograph,  974 

Secondary  axis,  555  ;  batteries,  849  ; 
currents,  806;  coil,  893 

Second  of  time,  21,  25 

Seconds  pendulum,  79 

Secular  magnetic  variations,  692 

Segments,  ventral  and  nodal,  269 

Segner's  water-wheel,  149 

Selenite,  664 

Selenium,  95.1 

Self-induction,  905 

Semicircular  deviation,  715 

Semi-conductors,  725 

Semiprism,  526 

Semitones,  249 

Senarmont's  experiment,  406 

Sensitive  membrane,  229 

Serein,  985 

Series,  thermo-electric,  940 

Serum,  12 

Sextant,  521 

Shadows,  503 

Shaft,  467 

Shock,  electric,  770-785  ;  return,  1000 

Shooting  stars,  480 

Short  sight,  629 

Siemens'  armature,  914;  dynamo-elec- 
trical machine,  918  ;  unit,  9^2  ;  elec- 
trical thermometer,  960 

Sight,  line  of,  595 

Silent  discharge,  793 

Silver,  voltameter,  846 

Simoom,  977 

Sine  compass,  824 

Singing  of  liquids,  363 

Sinuous  currents,  86 1 

Sirocco,  977 

Size,  estimation  of,  618 

Sky,  969 

Sleet,  088 

Slide  valve,  469 

Smee's  battery,  811 

Snow,  988  ;  line,  991 

Soap-bubble,  colours  of,  650 

Solar   microscope,    605  ;    light,    thermal 


1028 


Index. 


SOL 

analysis     of,    430 ;     radiation;     480 ;  j 
spectrum,  564  ;  properties  of  the,  5735 
dark  lines   of,    574,    579  ;   time,  21  ; 
day,  21 

Soleil's  saccharimeter,  677 

Solenoids,  874-878 ;  action  of  currents 
on,  875  ;  of  magnets  and  of  earth  on, 
876,  877  ;  on  solenoids,  878 

Solidification,  343 ;  change  of  volume 
on,  343,  346  ;  retardation  of,  345 

Solidity,  4,  .7 

Solids,  conductivity  of,  404 ;  index  of 
refraction  in,  548 ;  diamagnetism  of, 
938  ;  linear  and  cubical  expansion  of, 

3H>  319 

Solids,  formulse  of  expansion,  318 

Solution,  342 

Sondhauss's  experiments,  238 

Sonometer,  266,  932 

Sonorous  body,  222 

Sound,  221  ;  cause  of,  223  ;  not  propa- 
gated in  vacuo,  222 ;  propagated  in  all 
elastic  bodies,  224  ;  propagation  of,  in 
air,  225  ;  causes  which  influence  inten-  j 
sity  of,  226  ;  apparatus  to  strengthen,  j 
227 ;  interference  of,  261 ;  velocity  of,  in 
air,  230  ;  in  gases,  231-232  ;  in  liquids, 
234 ;  solids,  235  ;  reflection  of,  236 ; 
refraction  of,  237  ;  relation  of  radiant 
heat  to,  4460 ;  transmission  of,  228  ; 
waves,  229 

Sound,  Helmholtz's  analysis  of,  255 

Sound,  Konig's  apparatus,  255;  Kundt's, 
277 

Sounder,  896 

Sounds,  intensity  of,  289 ;  limit  of  per-   j 
ceptible,  244 ;  synthesis  of,  257  ;  per-   j 
captions  of,  260;  produced  by  currents, 
865 

Space,  measure  of,  22 

Spar,  Iceland,  659 

Spark  and  brush  discharge,    787 ;  elec-    j 
trical,  762,  787  ;  duration  and  velocity 
of,  795 

Speaking  trumpet,  239 ;  tubes,  228 

Specific  gravity,  24,  ii£J__j24;  bottle 
hydrometer,  I2O,"~I>I ;  of  solids,  120; 
of  gases,  335  ;  of  liquids,  123  ;  tables 
of,  124,  125 

Specific  heat,  448-460 ;  compound  bo- 
dies, 564  ;  determination  of,  by  fusion 
of  ice,  450 ;  by  method  of  mixtures, 
452  ;  by  Regnault's  apparatus,  454  ; 
of  solids  and  liquids,  456,  457 ;  of  j 
gases,  460 

Specific  inductive  capacity,  748 

Spectacles,  630 


SUN 

Spectra,  648 

Spectral  analysis,  575  ;  colours  and  pig- 
ment, 571 

Spectroscope,  576  ;  direct  vision,  577  ; 
experiments  with,  578  ;  uses  of  the, 
580 

Spectrum,  calorific,  573  ;  chemical,  573 

Spectrum,  430;  colours  of,  566;  pure, 
565  ;  solar,  564,  577 

Spectrum,  dark  lines  of,  574 

Spectrum,  diffraction,  648 

Spectrum,  luminous  properties  of,  573 

Spectrum  of  aurora  borealis,  1003  ;  pro- 
perties of,  573 

Specular  reflection,  518 

Spherical  aberration,  533,  55^  5  mirrors, 
524  ;  focus  of,  525  ;  formulae  for,  530, 

531 
Spheroidal  form   of  liquids,    84  ;    state, 

385 

Spherometer,  n 

Spiral,  882  ;  Roget's  vibrating,  859 
Spirit-level,  no 
Sprengel's  air-pump,  205 
Springs,  1010  ;  intermittent,  214 
Stable  equilibrium,  70 
Stars,  declination  of,  600 ;  spectral  analysis 

of,  582 

Staubbach,  76 
Steam-engines,  465  ;  boiler,  466  ;  double 

action,    or  Watt's,    467 ;    pipe,    207 ; 

various  kinds  of,  472 ;  work  of,  473  ; 

heating  by,  490 
Steeling,  857 
Stereoscopes,  622-624 
Sterometer,  185 
Stethoscope,  240 
Stills,  376 

Stool,  insulating,  762 
Stopcock,  doubly  exhausting,  202  ;  Gay- 

Lussac's,  382 
Storage  batteries,  849 
Storms,  magnetic,  694 
Stoves,  489  ;  Norwegian,  410 
Stratification  of  electric  light,  924 
Stratus,  981 

Stringed  instruments,  279 
Strings,    265 ;    transverse    vibration  of, 

265 

Subdominant  chords,  248 
Suction  pump,    216  ;   and   force   pump, 

217;     load    which    piston     supports, 

218 

Sulphate  of  mercury  battery,  812 
Sun,  510  ;  analysis  of,  579  ;  constitution 

of,  579 
Sun-spots,  701 


Index. 


1029 


SUR 

Surface  level,  67  ;  tension,  137  ; 
coloured,  581 

Suspension,  axis  of,  71  ;  Cardan's,  160 

Suspensory  ligament,  612 

Swan  lamps,  838 

Swimming,  118  ;  -bladder  of  fishes,  117 

Switch,  932 

Symmer's  theory  of  electricity,  728 

Synthesis  of  sounds,  257 

Syphon,  213 ;  barometer,  167 ;  inter- 
mittent, 214;  recorder,  892 

Syren,  242 

Syringe,  pneumatic,  154,  479 


TAMTAM  rnetal,  94 
Tangent  compass,  or  galvanometer, 
823,  847 

Tasimeter,  933 

Tears  of  wine,  136 

Telegraph,  cables,  Cowper's  writing, 
890; -induction  in,  891  ;  electric,  886- 
890 ;  electrochemical,  892 ;  dial, 
888  ;  Morse's,  889 

Telegraphy,  duplex,  893 

Telephone,  885,  930 ;  Edison's,  934  ; 
Reis's,  882  ;  toy,  235 

Telescopes,  595-601  ;  astronomical,  595 ; 
Galilean,  597  ;  Gregorian,  599  ;  Her- 
schelian,  601  ;  Newtonian,  600  ;  re- 
flecting, Rosse's,  601 

Telluric  lines,  573 

Temper,  94 

Temperature,  297,  448  ;  correction  for, 
in  barometer,  170  ;  critical,  370  ;  of 
a  body,  297  ;  determined  by  specific 
heat,  457 

Temperature,  absolute  zero  of,  496  ;  in- 
fluence of,  on  specific  gravity,  123  ; 
mean,  1004  ;  how  modified,  1005  ; 
distribution  of,  1009  ;  of  lakes,  seas, 
and  springs,  1010 

Temperatures,  different  remarkable,  312  ;  j 
influence  on  expansion,  318 

Tempering,  90,  94 

Tenacity,  7,  91 

Tension,  117,  736,  922  ;  maximum  of, 
electrical  machine,  755  ;  maximum  of, 
vapours,  353  ;  of  aqueous  vapour  at 
various  temperatures,  355-361  ;  of 
vapours  of  different  liquids,  359  ;  of 
mixed  liquids  in  two  communicating  j 
vessels,  361  ;  free  surface,  137 

Terquem's  experiment,  735 

Terrestrial  currents,  901  ;  heat,  481  ;  | 
magnetic  couple,  690  ;  magnetism,  721 ;  j 
telescope,  596 


TOW 

Terrestrial  gravitation,  67,  82 

Terrestrial  magnetic  couple,  690 

Tetanus,  827 

Thallium,  578 

Thaumatrope,  625 

Theodolite,  10  '    \ 

Theory,  5  ;  of  induction,  747 

Thermal  analysis,  430 ;  unit,  447,  484  ; 
springs,  1010 

Thermal  effects  of  the  current,  829,  830 

Thermal  rays,  transmutation  of,  434  ; 
unit,  447 

Thermobarometer,  369 

Thermochrose,  436 

Thermo-electric  battery,  412,  944  ; 
couples,  942;  currents,  941,  943,  9475 
pile,  412,  431,  943  ;  series,  940 

Thermo-electricity,  939 

Thermo-element,  940 

Thermometer,  electric,  792 

Thermometers,  298 ;  Becquerel's  elec- 
trical, 948 ;  correction  of  readings,  328  ; 
differential,  308  ;  division  of  tubes  in, 
299  ;  filling,  300  ;  graduation  of,  301  ; 
determination  of  fixed  points  of,  302  ; 
scale  of,  303  ;  displacement  of  zero, 
304  ;  limits  to  use  of,  305  ;  alcohol, 
306  ;  conditions  of  delicacy  of,  307  ; 
Kinnersley's,  792 ;  Leslie's,  308 ; 
Matthiessen's,  308 ;  Breguet's,  309  ; 
maximum  and  minimum,  310  ;  Siemens' 
electrical,  960  ;  weight,  323  ;  air,  331, 

334 

Thermometry,  297-300 

Thermo-multiplier,  Melloni's,  412,  946 

Thermomotive  wheel,  476 

Thennoscope,  308 

Thomson's  electrometers,  780,  781  ;  gal- 
vanometer, 822  ;  apparatus  for  atmo- 
spheric electricity,  993 

Thread  of  a  screw,  45 

Thunder,  998 

Timbre,  246 

Time,  measure  of,  21  ;  mean  solar,  21 

Tint,  570  ;  transition,  677 

Tones,  combinational,  263  ;  differentia], 
263 

Tonic,  248 

Toothed  wheel,  241 

Torricelh's  experiment,  161 ;  theorem, 
142  ;  vacuum,  1 68 

Torsion,  angle  of,  89  ;  balance,  89,  704, 
734  ;  force  of,  89 

Total  reflection,  540 

Tourmaline,  658,  732 ;  pincette,  666 

Tourniquet,  hydraulic,  149 

Tower  of  Pisa,  69 


1030 


Index. 


TOY 


voc 


Toy  telephone,  235 

Traction,  elasticity  of,  88 

Trajectory,  25 

Transformation  of  energy,  64 

Transit,  21 

Transition  tint,  677 

Translucent  bodies,  5°° 

Transmission  of  heat,  403  ;  of  light,  499, 

542  ;  by  the  current,  844 
Transmission  of  sound,  228 
Transmitter  -of  photophone^  936 
Transparency,  7,  500 
Transparent  media,  542-549 
Transpiration  of  gase%  192 
Triad,  harmonic,  247 
Triangle,  281 
Triangle  of  forces,  35 
Trumpet,  speaking,  ear,  239 
Tubes,  Geissler's,  205,  925  ;   luminous, 

789  ;  safety,  379  ;  speaking,  228 
Tuning-fork,  251,  281,  290 
Turbines,  150 
Twilight,  518 
Twinkling  of  stars,  541 
Tympanum,  260 
Tyndall's  researches,  431,  446^,  986,  991 


T  TLTRAGASEOUS  state,  927 
\^J       Unannealed  glass,    colours   pro- 
duced  by,  668 

Undershot  wheels,  150 

Undulation,  length  of,  225,  637 

Undulatory  theory,  499,  637 

Uniaxial  crystals,  640-643  ;  double 
refraction  in,  642  ;  positive  and  nega- 
tive, 643 

Unit  jar,  Harris's,  778  ;  Jacobi's,  952  ; 
Siemens',  952  ;  thermal,  447 

Unit  of  length,  area  and  volume,  22  ; 
heat,  447  ;  of  work,  61 

Unstable  equilibrium,  70 

Urinometer,  129 


\  7ACUUM,    application   of,    to   con-  | 
V       struction  of  air-pump,  200 ;  extent 
of,     produced     by      air-pump,      201  ; 
Crookes's,    446;    fall  of  bodies  in   a,    i 
76  ;formation  of  vapour  in,  352  ;   heat 
radiated  in,  413  ;  reflection  in  a,  421  ; 
Torricellian,  168 

Valency,  change  of,  458 

Valve,  safety,  108,  371  ;  chest,  466 

Vane,  electrical,  764 

Vaporisation,    350  ;  latent  heat  of,   372, 
462 


Vapour,  aqueous,  tension  of,  at  various 
temperatures,  357-361  ;  formation  of, 
in  closed  tube,  370  ;  latent  heat  of,  372 

Vapours,  349  ;  absorption  of  heat  by. 
435  ;  absorptive  powers  of,  440 ; 
density  of,  Gay-Lussac's  method,  386  ; 
Hofmann's,  387  ;  .densities  of,  389; 
determination  of  latent  heat  of,  372, 
462  ;  Dumas's  method,  388  ;  elastic 
force  of,  351  ;  formation  of,  in  vacuo, 
352;  saturated,  353;  unsaturated, 
354  ;  tension  of  different  liquids,  359  ; 
of  mixed  liquids,  360  ;  in  communicat- 
ing vessels,  361 

Variations,  annual,  693 ;  accidental, 
694 ;  barometric,  171;  causes  of, 
1 72  ;  diurnal,  693  ;  relation  of,  to 
weather,  173  ;  in  magnetic  declination, 
691,  695 

Varley  unit,  952 

Velocity,  25  ;  direction  of,  56  ;  of  efflux, 
142  ;  of  electricity,  795  ;  of  light, 
505-507 ;  graphic  representation  of 
changes  of,  56 ;  Kundt's  method,  277  ; 
molecular,  294 ;  of  sound  in  air,  230  ; 
gases,  231,  232  ;  formula  for  calculat- 
ing, 232  ;  of  winds,  975 

Velocities,  composition  of,  52  ;  examples 
of,  25 

Vena  contracta,  145 

Ventral  and  nodal  segment,  269,  274 

Vernier,  10 

Vertical  line,  67 

Vestibule  of  the  ear,  260 

Vibrating  spiral,  Roget's,  859 

Vibration,  222;  arc  of,  55  ;  produced  by 
currents,  884 ;  of  tuning-forks,  290 

Vibrations,  262 ;  formulae,  275  ;  of 
membranes,  283  ;  laws  of,  267  ;  mea- 
surement of  number  of,  241 ;  number 
of,  producing  each  note,  251  ;  of  mu- 
sical pipe,  275  ;  of  rods,  281  ;  of 
plates,  282;  of  strings,  265,  267,  270 

Victoria  Regia,  485 

View,  field  of,  593 

Vinometers,  129 

Virtual  and  real  images,  5J45  focus, 
525  ;  velocity,  46 

Viscosity,  96 ;  of  gases,  446 

Vision,  distance  of  distinct,  619  ;  bino- 
cular, 621 

Visual  angle,  617 

Vis  viva,  59,  448,  477 

Vital  fluid,  797 

Vitreous  body,  612;  electricity,  727; 
fusion,  338;  humour,  612 

Vocal  chords,  259 


Index. 


1031 


VOL 

Volatile  liquids,  349 

Volta's  condensing  electroscope,  779 ; 
electrophorus,  752;  fundamental  ex- 
periment, 798 

Voltaic  arc,  833  ;  couple,  801  ;  currents, 
819  ;  induction,  900  ;  pile  and  battery, 
804,  805,  815,  832 

Voltameter,  silver,  846 ;  Faraday's,  846 

Volume,  22  ;  unit  of,  22,  24  ;  determi- 
nation of,  114;  change  of,  on  solidi- 
fication, 346  ;  of  a  liquid  and  that  of 
its  vapour,  relation  between,  390 

Volumometer,  185 

\on  Ebner's  electrical  machine,  794 

Voss's  electrical  machine,  759 


WALKER'S  battery,  811,  886 
Water  bellows,  207  ;  decompo- 
sition of,  123  ;  hammer,  76  ;  hot,  heat- 
ing by,  492  ;  level,  109 

Water,  maximum  density  of,  330 ;  spouts, 
984 ;  wheels,  150 

Watt's  engine,  467 

Wave,  condensed,  225  ;  expanded,  225  ; 
lengths,  637,  649  ;  plane,  642  ;  of  a 
note,  253 

Weather,  its  influence  on  barometric  va- 
riations, 171,  172;  glasses,  174;  charts, 
979 ;  forecasts,  979 

Wedge,  44 

Wedgwood's  pyrometer,  311 

Weighing,  method  of  double,  75 

Weight,  23,  82  ;  relative,  43 ;  of  bodies 
weighed  in  air,  correction  for  loss 
of,  402;  of  gases,  155;  thermometer, 

324 

Weights  and  measures,  125 
Wells,  artesian,  in 
Wells's  theory  of  dew,  987 
Werdermann's  electric  lamp,  838 
Wet-bulb  hygrometer,  398 
Wheatstone's  bridge,    955  ;  photometer, 

509;   rheostat,   951;    rotating  mirror, 

795  ;  and  Cooke's  telegraph,  887 
Wheel  and  axle,  42 
Wheel  barometer,    174;    thermomotive, 

476 


ZON 

Wheels,  friction,  77;  escapement,  Si; 
water,  150 

Whirl,  electrical,  764 

Whispering  galleries,  237 

Whistle,  safety,  466 

White  light,  decomposition  of,  564 ;  re- 
composition  of,  567 

WThite's  pulley,  41 

Wiedemann  and  Franz's  tables  of  con- 
ductivity, 404 

Wiedemann's  determination  of  electro- 
motive force,  959 

Wild's  magneto-electrical  machine,  915 

Winckler's  cushions,  753 

Wind  chest,  272 ;  instruments,  270,  280 

Windhaussen's  ice  machine,  494 

Winds,  causes  of,  976 ;  direction  and 
velocity  of,  974,  975,  1005  ;  law  of  ro- 
tation of,  978  ;  periodical,  regular,  and 
variable,  977 

Wine,  alcoholic  value  of,  378  ;  tears  of, 
136 

Wire  telegraph,  886 

Wollaston's  battery,  805  ;  camera  lucida, 
6oj  ;  cryophprus,  373  j  doublet,  586, 

Wood,  conductivity  of,  404 

Wood's  fusible  metal,  340 

Work,  34,  59  ;  measure  of,  60  ;  of  an 
engine,  472  ;  rate  of,  473  ;  unit  of,  6 1  ; 
internal  and  external,  of  bodies,  295  ; 
of  a  voltaic  battery,  832  ;  required  for 
the  production  of  electricity,  761 

Writing  telegraphs,  889,  890 

YARD,  British,  22,  125 
Yellow  spot,  612 

Young  and  Fresnel's  experiment,  645 
Young's  modulus,  88 

ZAMBONI'S  pile,  817 
Zero,   absolute,  496  ;  aqueous  va- 
pours below,  355  ;  displacement  of,  304 
Zigzag  lightning,  985 
Zinc,  amalgamated,  816  ;  carbon  battery, 

810 

Zoetrope,  625 
Zone,  isothermal,    1007 


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